diff --git a/.gitignore b/.gitignore index db94c89a1..4dd696ee1 100644 --- a/.gitignore +++ b/.gitignore @@ -1,6 +1,11 @@ # use glob syntax. syntax: glob +# To ignore compiled binaries that have no extensions we need to first ignore everything, then unignore files with extensions and directories +* +!*.* +!*/ + extern/ !extern/Makefile* !extern/f5to*/ @@ -24,10 +29,13 @@ extern/ *.h5 *.f5 *.bdf +!tests/integration_tests/input_files/*.bdf +!examples/**/*.bdf *.su2 *.tar.gz *.png *.plt +*.szplt *_cs.* *.phy *.bin @@ -44,6 +52,12 @@ reports/ *.pxi *.vtk *.cfg +*.pkl +*.png +*.gif +*.mp4 .vscode .DS_Store .pre-commit-config.yaml + +**/__pycache__/ diff --git a/conda/meta.yaml b/conda/meta.yaml index 9e888c5c8..9fd3c33d9 100644 --- a/conda/meta.yaml +++ b/conda/meta.yaml @@ -75,6 +75,7 @@ requirements: - metis >=5.1 - mpi4py - pynastran + - numba test: requires: diff --git a/examples/mach_tutorial_wing/analysis.py b/examples/mach_tutorial_wing/analysis.py new file mode 100644 index 000000000..ceb290dff --- /dev/null +++ b/examples/mach_tutorial_wing/analysis.py @@ -0,0 +1,397 @@ +""" +============================================================================== +Analysis of the MACH tutorial wing with blade stiffened constitutive model +============================================================================== +@Date : 2023/06/27 +@Author : Alasdair Christison Gray +@Description : This file performs a basic structural analysis of the MACH +tutorial wing's wingbox using the blade stiffened shell constitutive model and +a composite material. This case is based on the setup used in the paper: +"Geometrically Nonlinear High-fidelity Aerostructural Optimization Including +Geometric Design Variables" (https://doi.org/10.2514/6.2023-3316) +""" + +# ============================================================================== +# Standard Python modules +# ============================================================================== +import os +from pprint import pprint + +# ============================================================================== +# External Python modules +# ============================================================================== +import numpy as np +from tacs import elements, constitutive, functions, pyTACS, TACS +from mpi4py import MPI + +comm = MPI.COMM_WORLD + +dtype = TACS.dtype + +# Instantiate FEAAssembler +structOptions = { + "printtiming": True, +} + +# ============================================================================== +# Composite properties +# ============================================================================== +# The material properties are taken from "Aerostructural tradeoffs for tow-steered +# composite wings" by Tim Brooks, https://doi.org/10.2514/1.C035699 +# The ply fractions are taken from chapter 7 of the PhD thesis of Johannes Dillinger, +# available at https://repository.tudelft.nl/islandora/object/uuid%3A20484651-fd5d-49f2-9c56-355bc680f2b7 +compositeProperties = { + "E11": 117.9e9, # Young's modulus in 11 direction (Pa) + "E22": 9.7e9, # Young's modulus in 22 direction (Pa) + "G12": 4.8e9, # in-plane 1-2 shear modulus (Pa) + "G13": 4.8e9, # Transverse 1-3 shear modulus (Pa) + "G23": 4.8e9, # Transverse 2-3 shear modulus (Pa) + "nu12": 0.35, # 1-2 poisson's ratio + "rho": 1.55e3, # density kg/m^3 + "T1": 1648e6, # Tensile strength in 1 direction (Pa) + "C1": 1034e6, # Compressive strength in 1 direction (Pa) + "T2": 64e6, # Tensile strength in 2 direction (Pa) + "C2": 228e6, # Compressive strength in 2 direction (Pa) + "S12": 71e6, # Shear strength direction (Pa) +} +skinPlyAngles = np.deg2rad(np.array([0.0, -45.0, 45.0, 90.0])).astype(dtype) +skinPlyFracs = np.array([44.41, 22.2, 22.2, 11.19], dtype=dtype) / 100.0 +sparRibPlyAngles = np.deg2rad(np.array([0.0, -45.0, 45.0, 90.0])).astype(dtype) +sparRibPlyFracs = np.array([10.0, 35.0, 35.0, 20.0], dtype=dtype) / 100.0 + +kcorr = dtype(5.0 / 6.0) # shear correction factor + +# ============================================================================== +# Design variable values, bounds, and scaling factors +# ============================================================================== +# Panel length +panelLengthMax = np.inf +panelLengthMin = 0.0 +panelLengthScale = 1.0 + +# Stiffener pitch +stiffenerPitch = dtype(0.2) # m +stiffenerPitchMax = 0.5 # m +stiffenerPitchMin = 0.05 # m +stiffenerPitchScale = 1.0 + +# Panel thickness +panelThickness = dtype(0.02) # m +panelThicknessMax = 0.1 # m +panelThicknessMin = 0.002 # m +panelThicknessScale = 100.0 + +# ply fraction bounds +plyFractionMax = 1.0 +plyFractionMin = 0.1 +plyFractionScale = 1.0 + +# Stiffener height +stiffenerHeight = dtype(0.05) # m +stiffenerHeightMax = 0.1 # m +stiffenerHeightMin = 0.002 # m +stiffenerHeightScale = 10.0 + +# Stiffener thickness +stiffenerThickness = dtype(0.02) # m +stiffenerThicknessMax = 0.1 # m +stiffenerThicknessMin = 0.002 # m +stiffenerThicknessScale = 100.0 + +# --- Stiffener axis directions --- +TESparDirection = np.array([0.34968083, 0.93686889, 0.0]) +VerticalDirection = np.array([0.0, 0.0, 1.0]) + +# ============================================================================== +# Element callback function +# ============================================================================== + + +def elemCallBack(dvNum, compID, compDescript, elemDescripts, specialDVs, **kwargs): + prop = constitutive.MaterialProperties( + rho=compositeProperties["rho"], + E1=compositeProperties["E11"], + E2=compositeProperties["E22"], + G12=compositeProperties["G12"], + G13=compositeProperties["G13"], + G23=compositeProperties["G23"], + nu12=compositeProperties["nu12"], + T1=compositeProperties["T1"], + C1=compositeProperties["C1"], + T2=compositeProperties["T2"], + C2=compositeProperties["C2"], + S12=compositeProperties["S12"], + ) + ply = constitutive.OrthotropicPly(1.0, prop) + + # Use a 0-deg biased layup for the skin and a +-45-deg biased layup spars and ribs. + # Align the stiffeners in the skins with the trailing edge spar, and the stiffeners + # in the spars and ribs vertically. + # The panel length values I set here are approximate, to get the real values, you'd + # need to run an optimization with panel length design variables and constraints. + if "SKIN" in compDescript: + plyAngles = skinPlyAngles + panelPlyFractions = skinPlyFracs + refAxis = TESparDirection + panelLength = 0.65 + else: + plyAngles = sparRibPlyAngles + panelPlyFractions = sparRibPlyFracs + refAxis = VerticalDirection + if "RIB" in compDescript: + panelLength = 0.38 + elif "SPAR" in compDescript: + panelLength = 0.36 + + # Always use the 0-deg biased layup for the stiffeners + stiffenerPlyFractions = skinPlyFracs + numPlies = len(plyAngles) + + # --- Setup DV numbering and scaling --- + + # The ordering of the DVs used by the BladeStiffenedShell model is: + # - panel length + # - stiffener pitch + # - panel thickness + # - panel ply fractions (not used in this case) + # - stiffener height + # - stiffener thickness + # - stiffener ply fractions (not used in this case) + currDVNum = dvNum + DVScales = [] + + panelLengthNum = currDVNum + DVScales.append(panelLengthScale) + currDVNum += 1 + + stiffenerPitchNum = currDVNum + DVScales.append(stiffenerPitchScale) + currDVNum += 1 + + panelThicknessNum = currDVNum + DVScales.append(panelThicknessScale) + currDVNum += 1 + + panelPlyFracNums = -np.ones(numPlies).astype(np.intc) + + stiffenerHeightNum = currDVNum + DVScales.append(stiffenerHeightScale) + currDVNum += 1 + + stiffenerThicknessNum = currDVNum + DVScales.append(stiffenerThicknessScale) + currDVNum += 1 + + stiffenerPlyFracNums = -np.ones(numPlies).astype(np.intc) + + con = constitutive.BladeStiffenedShellConstitutive( + panelPly=ply, + stiffenerPly=ply, + kcorr=kcorr, + panelLength=panelLength, + panelLengthNum=panelLengthNum, + stiffenerPitch=stiffenerPitch, + stiffenerPitchNum=stiffenerPitchNum, + panelThick=panelThickness, + panelThickNum=panelThicknessNum, + numPanelPlies=numPlies, + panelPlyAngles=plyAngles, + panelPlyFracs=panelPlyFractions, + panelPlyFracNums=panelPlyFracNums, + stiffenerHeight=stiffenerHeight, + stiffenerHeightNum=stiffenerHeightNum, + stiffenerThick=stiffenerThickness, + stiffenerThickNum=stiffenerThicknessNum, + numStiffenerPlies=numPlies, + stiffenerPlyAngles=plyAngles, + stiffenerPlyFracs=stiffenerPlyFractions, + stiffenerPlyFracNums=stiffenerPlyFracNums, + ) + con.setStiffenerPitchBounds(stiffenerPitchMin, stiffenerPitchMax) + con.setPanelThicknessBounds(panelThicknessMin, panelThicknessMax) + con.setStiffenerHeightBounds(stiffenerHeightMin, stiffenerHeightMax) + con.setStiffenerThicknessBounds(stiffenerThicknessMin, stiffenerThicknessMax) + + # --- Create reference axis transform to define the stiffener direction --- + transform = elements.ShellRefAxisTransform(refAxis) + + # --- Create the element object --- + if elemDescripts[0] == "CQUAD4": + elem = elements.Quad4Shell(transform, con) + elif elemDescripts[0] == "CQUAD9": + elem = elements.Quad9Shell(transform, con) + elif elemDescripts[0] == "CQUAD16": + elem = elements.Quad16Shell(transform, con) + + return elem, DVScales + + +# ============================================================================== +# Create pyTACS assembler +# ============================================================================== +structOptions = { + "printtiming": True, +} + +bdfFile = os.path.join(os.path.dirname(__file__), "wingbox-L2-Order2.bdf") +FEAAssembler = pyTACS(bdfFile, options=structOptions, comm=comm) + +# Set up elements and TACS assembler +FEAAssembler.initialize(elemCallBack) + +# ============================================================================== +# Setup static problem +# ============================================================================== +problem = FEAAssembler.createStaticProblem("StructAnalysis") + +# Add TACS Functions +problem.addFunction("mass", functions.StructuralMass) + +# Add failure and mass functions for each skin and spar/rib group +failureGroups = ["l_skin", "u_skin", "spar", "rib"] +if failureGroups is not None: + for group in failureGroups: + compIDs = FEAAssembler.selectCompIDs(include=group.upper()) + problem.addFunction( + f"{group}_ksFailure", + functions.KSFailure, + compIDs=compIDs, + safetyFactor=1.5, + ksWeight=100.0, + ) + problem.addFunction( + f"{group}_mass", + functions.StructuralMass, + compIDs=compIDs, + ) +problem.addFunction("compliance", functions.Compliance) + +# Add gravity load +g = np.zeros(3) +g[-1] = -9.81 +problem.addInertialLoad(2.5 * g) + +# Add simple distributed vertical load over the skins +totalForce = 0.5 * 2.5 * 55e3 * 9.81 +F = np.zeros(6) +F[2] = totalForce +skinCompIDs = FEAAssembler.selectCompIDs("SKIN") +problem.addLoadToComponents(skinCompIDs, F, averageLoad=True) + +# ============================================================================== +# Setup constraints +# ============================================================================== + +thicknessAdjCon = 2.5e-3 # 2.5mm +heightAdjCon = 1e-2 # 1cm +pitchAdjCon = 5e-2 # 5cm +thickDiffMax = ( + 2.5e-3 # 2.5mm, Max allowable thickness difference between skin and stiffener +) +stiffAspectMax = 10.0 # Maximum allowable stiffener aspect ratio (height/thickness) +stiffAspectMin = 2.0 # Minimum allowable stiffener aspect ratio (height/thickness) + +compIDs = {} +for group in ["SPAR", "U_SKIN", "L_SKIN", "RIB"]: + compIDs[group] = FEAAssembler.selectCompIDs(include=group.upper()) + +constraints = [] + +# Add adjacency constraints on panel thickness, stiffener thickness and stiffener height to everything but the ribs +adjCon = FEAAssembler.createAdjacencyConstraint("AdjCon") +for group in ["SPAR", "U_SKIN", "L_SKIN"]: + adjCon.addConstraint( + conName=group + "_panelThicknessAdj", + compIDs=compIDs[group], + lower=-thicknessAdjCon, + upper=thicknessAdjCon, + dvIndex=2, + ) + adjCon.addConstraint( + conName=group + "_stiffenerThicknessAdj", + compIDs=compIDs[group], + lower=-thicknessAdjCon, + upper=thicknessAdjCon, + dvIndex=4, + ) + adjCon.addConstraint( + conName=group + "_stiffenerHeightAdj", + compIDs=compIDs[group], + lower=-heightAdjCon, + upper=heightAdjCon, + dvIndex=3, + ) + adjCon.addConstraint( + conName=group + "_stiffenerPitchAdj", + compIDs=compIDs[group], + lower=-pitchAdjCon, + upper=pitchAdjCon, + dvIndex=1, + ) +constraints.append(adjCon) + +# Add constraints between the DV's on each panel +dvCon = FEAAssembler.createDVConstraint("DVCon") +# Limit the difference in thickness between the panel and stiffener +# -thickDiffMax <= (panelThickness - stiffenerThickness) <= thickDiffMax +dvCon.addConstraint( + conName="thickDiffLimit", + lower=-thickDiffMax, + upper=thickDiffMax, + dvIndices=[2, 4], + dvWeights=[1.0, -1.0], +) +# Limit the aspect ratio of the stiffener +# stiffenerHeight - (stiffAspectMax * stiffenerThickness) <= 0 +dvCon.addConstraint( + conName="stiffenerAspectMax", + upper=0.0, + dvIndices=[3, 4], + dvWeights=[1.0, -stiffAspectMax], +) +# stiffenerHeight - (stiffAspectMin * stiffenerThickness) >= 0 +dvCon.addConstraint( + conName="stiffenerAspectMin", + lower=0.0, + dvIndices=[3, 4], + dvWeights=[1.0, -stiffAspectMin], +) +# Ensure there is space between the stiffeners +# 2*flangeFraction - stiffenerPitch <= 0 +dvCon.addConstraint( + conName="stiffSpacingMin", + upper=0.0, + dvIndices=[3, 2], + dvWeights=[2.0, -1.0], +) +constraints.append(dvCon) + +panelLengthCon = FEAAssembler.createPanelLengthConstraint("PanelLengthCon") +panelLengthCon.addConstraint("PanelLength", dvIndex=0) +constraints.append(panelLengthCon) + +# ============================================================================== +# Solve static problem +# ============================================================================== +# Solve structural problem +problem.solve() + +# Evaluate functions +funcs = {} +problem.evalFunctions(funcs) +for constraint in constraints: + constraint.evalConstraints(funcs) + +if comm.rank == 0: + pprint(funcs) + +# Solve adjoints and evaluate function sensitivities +funcsSens = {} +problem.evalFunctionsSens(funcsSens) +for constraint in constraints: + constraint.evalConstraintsSens(funcsSens) +# if comm.rank == 0: +# pprint(funcsSens) + +# Write out solution +problem.writeSolution(outputDir=os.path.dirname(__file__)) diff --git a/examples/mach_tutorial_wing/benchmark/benchmark_mach_tutorial.py b/examples/mach_tutorial_wing/benchmark/benchmark_mach_tutorial.py new file mode 100644 index 000000000..2a92f3cb6 --- /dev/null +++ b/examples/mach_tutorial_wing/benchmark/benchmark_mach_tutorial.py @@ -0,0 +1,180 @@ +""" +This script is used to regression test the example against historical values. +""" + +import numpy as np +import unittest +import sys +import os + +# Set the path to the example script we're testing +example_path = os.path.join(os.path.dirname(__file__), "..") +sys.path.append(example_path) + +# Reference values for eval functions +FUNC_REF = { + "StructAnalysis_compliance": 155457.77449517886, + "StructAnalysis_l_skin_ksFailure": 0.6688990169113461, + "StructAnalysis_l_skin_mass": 1056.704174594214, + "StructAnalysis_mass": 3196.8719514874, + "StructAnalysis_rib_ksFailure": 0.25352002232016596, + "StructAnalysis_rib_mass": 686.2303380471093, + "StructAnalysis_spar_ksFailure": 0.6336362974489301, + "StructAnalysis_spar_mass": 400.0665693788245, + "StructAnalysis_u_skin_ksFailure": 0.46504728373719834, + "StructAnalysis_u_skin_mass": 1053.8708694672512, + "AdjCon_L_SKIN_panelThicknessAdj": np.zeros(21), + "AdjCon_L_SKIN_stiffenerHeightAdj": np.zeros(21), + "AdjCon_L_SKIN_stiffenerPitchAdj": np.zeros(21), + "AdjCon_L_SKIN_stiffenerThicknessAdj": np.zeros(21), + "AdjCon_SPAR_panelThicknessAdj": np.zeros(42), + "AdjCon_SPAR_stiffenerHeightAdj": np.zeros(42), + "AdjCon_SPAR_stiffenerPitchAdj": np.zeros(42), + "AdjCon_SPAR_stiffenerThicknessAdj": np.zeros(42), + "AdjCon_U_SKIN_panelThicknessAdj": np.zeros(21), + "AdjCon_U_SKIN_stiffenerHeightAdj": np.zeros(21), + "AdjCon_U_SKIN_stiffenerPitchAdj": np.zeros(21), + "AdjCon_U_SKIN_stiffenerThicknessAdj": np.zeros(21), + "DVCon_stiffSpacingMin": 0.08 * np.ones(111), + "DVCon_stiffenerAspectMax": -0.15 * np.ones(111), + "DVCon_stiffenerAspectMin": 0.01 * np.ones(111), + "DVCon_thickDiffLimit": np.zeros(111), + "PanelLengthCon_PanelLength": np.array( + [ + 2.06290983e-01, + 1.64727032e-01, + 1.11972828e-01, + 4.52157850e-02, + 3.01025244e-02, + 1.49892651e-02, + -1.23995700e-04, + -1.52372550e-02, + -3.03505139e-02, + -4.54637746e-02, + -6.05770331e-02, + -7.56902922e-02, + -9.08035515e-02, + -1.05916809e-01, + -1.21030068e-01, + -1.36143326e-01, + -1.51256582e-01, + -1.66369840e-01, + -1.81483095e-01, + -1.96596350e-01, + -2.11709604e-01, + -2.26822855e-01, + -2.41936108e-01, + 2.26290983e-01, + 1.84727032e-01, + 1.31972828e-01, + 6.52157850e-02, + 5.01025244e-02, + 3.49892651e-02, + 1.98760043e-02, + 4.76274500e-03, + -1.03505139e-02, + -2.54637746e-02, + -4.05770331e-02, + -5.56902922e-02, + -7.08035515e-02, + -8.59168091e-02, + -1.01030068e-01, + -1.16143326e-01, + -1.31256582e-01, + -1.46369840e-01, + -1.61483095e-01, + -1.76596350e-01, + -1.91709604e-01, + -2.06822855e-01, + -4.80049559e-02, + -1.04612092e-02, + 2.52563166e-02, + 2.52563166e-02, + 1.15523772e-02, + -2.15156100e-03, + -1.58554993e-02, + -2.95594381e-02, + -4.32633758e-02, + -5.69673146e-02, + -7.06712519e-02, + -8.43751890e-02, + -9.80791272e-02, + -1.11783064e-01, + -1.25487000e-01, + -1.39190937e-01, + -1.52894872e-01, + -1.66598808e-01, + -1.80302742e-01, + -1.94006675e-01, + -2.07710608e-01, + -2.21414538e-01, + -1.16529874e-01, + -1.16796551e-01, + -1.16293732e-01, + -1.16638202e-01, + -1.15940931e-01, + -1.16308447e-01, + 5.22872841e-02, + 5.21318043e-02, + 5.22872765e-02, + 5.21318003e-02, + 5.22872662e-02, + 5.21317938e-02, + 5.22872561e-02, + 5.21317878e-02, + 5.22872452e-02, + 5.21317814e-02, + 5.22872344e-02, + 5.21317755e-02, + 5.22872203e-02, + 5.21317668e-02, + 5.22872061e-02, + 5.21317584e-02, + 5.22871905e-02, + 5.21317492e-02, + 5.22871741e-02, + 5.21317400e-02, + 5.22871538e-02, + 5.21317276e-02, + 5.22871321e-02, + 5.21317148e-02, + 5.22871098e-02, + 5.21317025e-02, + 5.22870747e-02, + 5.21316787e-02, + 5.22870535e-02, + 5.21316706e-02, + 5.22870060e-02, + 5.21316382e-02, + 5.22869736e-02, + 5.21316234e-02, + 5.22869117e-02, + 5.21315825e-02, + 5.22868606e-02, + 5.21315567e-02, + ] + ), +} + + +class ExampleBenchmark(unittest.TestCase): + N_PROCS = 8 # this is how many MPI processes to use for this TestCase. + + def setUp(self): + # Import the example to automatically run the script + import analysis + + self.example = analysis + + def benchmark_funcs(self): + """ + Test the example eval functions against reference values + """ + func_dict = self.example.funcs + + # Test functions values against historical values + for func_name in FUNC_REF: + with self.subTest(function=func_name): + np.testing.assert_allclose( + func_dict[func_name], FUNC_REF[func_name], rtol=1e-6, atol=1e-6 + ) diff --git a/examples/mach_tutorial_wing/wingbox-L2-Order2.bdf b/examples/mach_tutorial_wing/wingbox-L2-Order2.bdf new file mode 100644 index 000000000..5a06935b9 --- /dev/null +++ b/examples/mach_tutorial_wing/wingbox-L2-Order2.bdf @@ -0,0 +1,52608 @@ +$ Input file generated by pyLayout +SOL 103 +CEND +BEGIN BULK +GRID* 1 0 1.497321429e+00 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+$ Shell element data for family RIBS/RIB.00/SEG.00 +CQUAD4 1 1 1 12 13 2 +CQUAD4 2 1 2 13 14 3 +CQUAD4 3 1 3 14 15 4 +CQUAD4 4 1 4 15 16 5 +CQUAD4 5 1 5 16 17 6 +CQUAD4 6 1 6 17 18 7 +CQUAD4 7 1 7 18 19 8 +CQUAD4 8 1 8 19 20 9 +CQUAD4 9 1 9 20 21 10 +CQUAD4 10 1 10 21 22 11 +CQUAD4 11 1 12 23 24 13 +CQUAD4 12 1 13 24 25 14 +CQUAD4 13 1 14 25 26 15 +CQUAD4 14 1 15 26 27 16 +CQUAD4 15 1 16 27 28 17 +CQUAD4 16 1 17 28 29 18 +CQUAD4 17 1 18 29 30 19 +CQUAD4 18 1 19 30 31 20 +CQUAD4 19 1 20 31 32 21 +CQUAD4 20 1 21 32 33 22 +CQUAD4 21 1 23 34 35 24 +CQUAD4 22 1 24 35 36 25 +CQUAD4 23 1 25 36 37 26 +CQUAD4 24 1 26 37 38 27 +CQUAD4 25 1 27 38 39 28 +CQUAD4 26 1 28 39 40 29 +CQUAD4 27 1 29 40 41 30 +CQUAD4 28 1 30 41 42 31 +CQUAD4 29 1 31 42 43 32 +CQUAD4 30 1 32 43 44 33 +CQUAD4 31 1 34 45 46 35 +CQUAD4 32 1 35 46 47 36 +CQUAD4 33 1 36 47 48 37 +CQUAD4 34 1 37 48 49 38 +CQUAD4 35 1 38 49 50 39 +CQUAD4 36 1 39 50 51 40 +CQUAD4 37 1 40 51 52 41 +CQUAD4 38 1 41 52 53 42 +CQUAD4 39 1 42 53 54 43 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137 126 +CQUAD4 115 1 126 137 138 127 +CQUAD4 116 1 127 138 139 128 +CQUAD4 117 1 128 139 140 129 +CQUAD4 118 1 129 140 141 130 +CQUAD4 119 1 130 141 142 131 +CQUAD4 120 1 131 142 143 132 +CQUAD4 121 1 133 144 145 134 +CQUAD4 122 1 134 145 146 135 +CQUAD4 123 1 135 146 147 136 +CQUAD4 124 1 136 147 148 137 +CQUAD4 125 1 137 148 149 138 +CQUAD4 126 1 138 149 150 139 +CQUAD4 127 1 139 150 151 140 +CQUAD4 128 1 140 151 152 141 +CQUAD4 129 1 141 152 153 142 +CQUAD4 130 1 142 153 154 143 +CQUAD4 131 1 144 155 156 145 +CQUAD4 132 1 145 156 157 146 +CQUAD4 133 1 146 157 158 147 +CQUAD4 134 1 147 158 159 148 +CQUAD4 135 1 148 159 160 149 +CQUAD4 136 1 149 160 161 150 +CQUAD4 137 1 150 161 162 151 +CQUAD4 138 1 151 162 163 152 +CQUAD4 139 1 152 163 164 153 +CQUAD4 140 1 153 164 165 154 +CQUAD4 141 1 155 166 167 156 +CQUAD4 142 1 156 167 168 157 +CQUAD4 143 1 157 168 169 158 +CQUAD4 144 1 158 169 170 159 +CQUAD4 145 1 159 170 171 160 +CQUAD4 146 1 160 171 172 161 +CQUAD4 147 1 161 172 173 162 +CQUAD4 148 1 162 173 174 163 +CQUAD4 149 1 163 174 175 164 +CQUAD4 150 1 164 175 176 165 +CQUAD4 151 1 166 177 178 167 +CQUAD4 152 1 167 178 179 168 +CQUAD4 153 1 168 179 180 169 +CQUAD4 154 1 169 180 181 170 +CQUAD4 155 1 170 181 182 171 +CQUAD4 156 1 171 182 183 172 +CQUAD4 157 1 172 183 184 173 +CQUAD4 158 1 173 184 185 174 +CQUAD4 159 1 174 185 186 175 +CQUAD4 160 1 175 186 187 176 +CQUAD4 161 1 177 188 189 178 +CQUAD4 162 1 178 189 190 179 +CQUAD4 163 1 179 190 191 180 +CQUAD4 164 1 180 191 192 181 +CQUAD4 165 1 181 192 193 182 +CQUAD4 166 1 182 193 194 183 +CQUAD4 167 1 183 194 195 184 +CQUAD4 168 1 184 195 196 185 +CQUAD4 169 1 185 196 197 186 +CQUAD4 170 1 186 197 198 187 +CQUAD4 171 1 188 199 200 189 +CQUAD4 172 1 189 200 201 190 +CQUAD4 173 1 190 201 202 191 +CQUAD4 174 1 191 202 203 192 +CQUAD4 175 1 192 203 204 193 +CQUAD4 176 1 193 204 205 194 +CQUAD4 177 1 194 205 206 195 +CQUAD4 178 1 195 206 207 196 +CQUAD4 179 1 196 207 208 197 +CQUAD4 180 1 197 208 209 198 +CQUAD4 181 1 199 210 211 200 +CQUAD4 182 1 200 211 212 201 +CQUAD4 183 1 201 212 213 202 +CQUAD4 184 1 202 213 214 203 +CQUAD4 185 1 203 214 215 204 +CQUAD4 186 1 204 215 216 205 +CQUAD4 187 1 205 216 217 206 +CQUAD4 188 1 206 217 218 207 +CQUAD4 189 1 207 218 219 208 +CQUAD4 190 1 208 219 220 209 +CQUAD4 191 1 210 221 222 211 +CQUAD4 192 1 211 222 223 212 +CQUAD4 193 1 212 223 224 213 +CQUAD4 194 1 213 224 225 214 +CQUAD4 195 1 214 225 226 215 +CQUAD4 196 1 215 226 227 216 +CQUAD4 197 1 216 227 228 217 +CQUAD4 198 1 217 228 229 218 +CQUAD4 199 1 218 229 230 219 +CQUAD4 200 1 219 230 231 220 +$ Shell element data for family RIBS/RIB.01/SEG.00 +CQUAD4 201 2 232 243 244 233 +CQUAD4 202 2 233 244 245 234 +CQUAD4 203 2 234 245 246 235 +CQUAD4 204 2 235 246 247 236 +CQUAD4 205 2 236 247 248 237 +CQUAD4 206 2 237 248 249 238 +CQUAD4 207 2 238 249 250 239 +CQUAD4 208 2 239 250 251 240 +CQUAD4 209 2 240 251 252 241 +CQUAD4 210 2 241 252 253 242 +CQUAD4 211 2 243 254 255 244 +CQUAD4 212 2 244 255 256 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279 2 317 328 329 318 +CQUAD4 280 2 318 329 330 319 +CQUAD4 281 2 320 331 332 321 +CQUAD4 282 2 321 332 333 322 +CQUAD4 283 2 322 333 334 323 +CQUAD4 284 2 323 334 335 324 +CQUAD4 285 2 324 335 336 325 +CQUAD4 286 2 325 336 337 326 +CQUAD4 287 2 326 337 338 327 +CQUAD4 288 2 327 338 339 328 +CQUAD4 289 2 328 339 340 329 +CQUAD4 290 2 329 340 341 330 +CQUAD4 291 2 331 342 343 332 +CQUAD4 292 2 332 343 344 333 +CQUAD4 293 2 333 344 345 334 +CQUAD4 294 2 334 345 346 335 +CQUAD4 295 2 335 346 347 336 +CQUAD4 296 2 336 347 348 337 +CQUAD4 297 2 337 348 349 338 +CQUAD4 298 2 338 349 350 339 +CQUAD4 299 2 339 350 351 340 +CQUAD4 300 2 340 351 352 341 +CQUAD4 301 2 342 353 354 343 +CQUAD4 302 2 343 354 355 344 +CQUAD4 303 2 344 355 356 345 +CQUAD4 304 2 345 356 357 346 +CQUAD4 305 2 346 357 358 347 +CQUAD4 306 2 347 358 359 348 +CQUAD4 307 2 348 359 360 349 +CQUAD4 308 2 349 360 361 350 +CQUAD4 309 2 350 361 362 351 +CQUAD4 310 2 351 362 363 352 +CQUAD4 311 2 353 364 365 354 +CQUAD4 312 2 354 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8183 59 8852 8861 8862 8853 +CQUAD4 8184 59 8853 8862 8863 8854 +CQUAD4 8185 59 8854 8863 8864 8855 +CQUAD4 8186 59 8855 8864 8865 8856 +CQUAD4 8187 59 8856 8865 8866 8857 +CQUAD4 8188 59 8857 8866 8867 8858 +CQUAD4 8189 59 8858 8867 8868 8859 +CQUAD4 8190 59 8859 8868 3464 3463 +CQUAD4 8191 59 3233 3234 8869 8860 +CQUAD4 8192 59 8860 8869 8870 8861 +CQUAD4 8193 59 8861 8870 8871 8862 +CQUAD4 8194 59 8862 8871 8872 8863 +CQUAD4 8195 59 8863 8872 8873 8864 +CQUAD4 8196 59 8864 8873 8874 8865 +CQUAD4 8197 59 8865 8874 8875 8866 +CQUAD4 8198 59 8866 8875 8876 8867 +CQUAD4 8199 59 8867 8876 8877 8868 +CQUAD4 8200 59 8868 8877 3465 3464 +$ Shell element data for family SPARS/SPAR.01/SEG.14 +CQUAD4 8201 60 3455 3456 8887 8878 +CQUAD4 8202 60 8878 8887 8888 8879 +CQUAD4 8203 60 8879 8888 8889 8880 +CQUAD4 8204 60 8880 8889 8890 8881 +CQUAD4 8205 60 8881 8890 8891 8882 +CQUAD4 8206 60 8882 8891 8892 8883 +CQUAD4 8207 60 8883 8892 8893 8884 +CQUAD4 8208 60 8884 8893 8894 8885 +CQUAD4 8209 60 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8237 60 8910 8919 8920 8911 +CQUAD4 8238 60 8911 8920 8921 8912 +CQUAD4 8239 60 8912 8921 8922 8913 +CQUAD4 8240 60 8913 8922 3690 3689 +CQUAD4 8241 60 3459 3460 8923 8914 +CQUAD4 8242 60 8914 8923 8924 8915 +CQUAD4 8243 60 8915 8924 8925 8916 +CQUAD4 8244 60 8916 8925 8926 8917 +CQUAD4 8245 60 8917 8926 8927 8918 +CQUAD4 8246 60 8918 8927 8928 8919 +CQUAD4 8247 60 8919 8928 8929 8920 +CQUAD4 8248 60 8920 8929 8930 8921 +CQUAD4 8249 60 8921 8930 8931 8922 +CQUAD4 8250 60 8922 8931 3691 3690 +CQUAD4 8251 60 3460 3461 8932 8923 +CQUAD4 8252 60 8923 8932 8933 8924 +CQUAD4 8253 60 8924 8933 8934 8925 +CQUAD4 8254 60 8925 8934 8935 8926 +CQUAD4 8255 60 8926 8935 8936 8927 +CQUAD4 8256 60 8927 8936 8937 8928 +CQUAD4 8257 60 8928 8937 8938 8929 +CQUAD4 8258 60 8929 8938 8939 8930 +CQUAD4 8259 60 8930 8939 8940 8931 +CQUAD4 8260 60 8931 8940 3692 3691 +CQUAD4 8261 60 3461 3462 8941 8932 +CQUAD4 8262 60 8932 8941 8942 8933 +CQUAD4 8263 60 8933 8942 8943 8934 +CQUAD4 8264 60 8934 8943 8944 8935 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8969 8960 +CQUAD4 8293 60 8960 8969 8970 8961 +CQUAD4 8294 60 8961 8970 8971 8962 +CQUAD4 8295 60 8962 8971 8972 8963 +CQUAD4 8296 60 8963 8972 8973 8964 +CQUAD4 8297 60 8964 8973 8974 8965 +CQUAD4 8298 60 8965 8974 8975 8966 +CQUAD4 8299 60 8966 8975 8976 8967 +CQUAD4 8300 60 8967 8976 3696 3695 +$ Shell element data for family SPARS/SPAR.01/SEG.15 +CQUAD4 8301 61 3686 3687 8986 8977 +CQUAD4 8302 61 8977 8986 8987 8978 +CQUAD4 8303 61 8978 8987 8988 8979 +CQUAD4 8304 61 8979 8988 8989 8980 +CQUAD4 8305 61 8980 8989 8990 8981 +CQUAD4 8306 61 8981 8990 8991 8982 +CQUAD4 8307 61 8982 8991 8992 8983 +CQUAD4 8308 61 8983 8992 8993 8984 +CQUAD4 8309 61 8984 8993 8994 8985 +CQUAD4 8310 61 8985 8994 3918 3917 +CQUAD4 8311 61 3687 3688 8995 8986 +CQUAD4 8312 61 8986 8995 8996 8987 +CQUAD4 8313 61 8987 8996 8997 8988 +CQUAD4 8314 61 8988 8997 8998 8989 +CQUAD4 8315 61 8989 8998 8999 8990 +CQUAD4 8316 61 8990 8999 9000 8991 +CQUAD4 8317 61 8991 9000 9001 8992 +CQUAD4 8318 61 8992 9001 9002 8993 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+$XSUPER 23 2 1 8.475000000e+00* +$* 1.399900000e+01 7.917731158e-02 +$XSUPER 23 2 2 8.475000000e+00* +$* 1.399900000e+01-4.570422120e-02 +ENDDATA diff --git a/setup.py b/setup.py index 65a2d8785..a3b3ae1e3 100644 --- a/setup.py +++ b/setup.py @@ -123,7 +123,13 @@ def get_mpi_flags(): long_description_content_type="text/markdown", author="Graeme J. Kennedy", author_email="graeme.kennedy@ae.gatech.edu", - install_requires=["numpy", "mpi4py>=3.1.1", "scipy>=1.2.1", "pynastran>=1.3.3"], + install_requires=[ + "numpy", + "mpi4py>=3.1.1", + "scipy>=1.2.1", + "pynastran>=1.3.3", + "numba", + ], extras_require=optional_dependencies, packages=find_packages(include=["tacs*"]), ext_modules=cythonize(exts, include_path=inc_dirs), diff --git a/src/TacsUtilities.cpp b/src/TacsUtilities.cpp index 1c5f1e790..811178593 100644 --- a/src/TacsUtilities.cpp +++ b/src/TacsUtilities.cpp @@ -967,3 +967,69 @@ void TACSMatrixHash::reset(int new_table_size) { table = new_table; table_size = new_table_size; } + +TacsScalar ksAggregation(const TacsScalar f[], const int numVals, + const double ksWeight) { + TacsScalar maxVal = f[0]; + for (int ii = 1; ii < numVals; ii++) { + if (TacsRealPart(f[ii]) > TacsRealPart(maxVal)) { + maxVal = f[ii]; + } + } + return ksAggregation(f, maxVal, numVals, ksWeight); +} + +TacsScalar ksAggregation(const TacsScalar f[], const TacsScalar maxVal, + const int numVals, const double ksWeight) { + TacsScalar aggregatedValue = 0.0; + for (int ii = 0; ii < numVals; ii++) { + aggregatedValue += exp(ksWeight * (f[ii] - maxVal)); + } + return maxVal + log(aggregatedValue) / ksWeight; +} + +TacsScalar ksAggregationSens(const TacsScalar f[], const int numVals, + const double ksWeight, TacsScalar dKSdf[]) { + TacsScalar maxVal = f[0]; + for (int ii = 1; ii < numVals; ii++) { + if (TacsRealPart(f[ii]) > TacsRealPart(maxVal)) { + maxVal = f[ii]; + } + } + TacsScalar sum = 0.0; + memset(dKSdf, 0, numVals * sizeof(TacsScalar)); + for (int ii = 0; ii < numVals; ii++) { + TacsScalar val = exp(ksWeight * (f[ii] - maxVal)); + sum += val; + dKSdf[ii] = val; + } + for (int ii = 0; ii < numVals; ii++) { + dKSdf[ii] /= sum; + } + + return maxVal + log(sum) / ksWeight; +} + +TacsScalar ksAggregationSensProduct(const TacsScalar f[], const int numVals, + const int numVars, const double ksWeight, + TacsScalar **dfdx, TacsScalar dKSdx[]) { + TacsScalar maxVal = f[0]; + for (int ii = 1; ii < numVals; ii++) { + if (TacsRealPart(f[ii]) > TacsRealPart(maxVal)) { + maxVal = f[ii]; + } + } + TacsScalar sum = 0.0; + memset(dKSdx, 0, numVars * sizeof(TacsScalar)); + for (int ii = 0; ii < numVals; ii++) { + TacsScalar val = exp(ksWeight * (f[ii] - maxVal)); + sum += val; + for (int jj = 0; jj < numVars; jj++) { + dKSdx[jj] += val * dfdx[ii][jj]; + } + } + for (int jj = 0; jj < numVars; jj++) { + dKSdx[jj] /= sum; + } + return maxVal + log(sum) / ksWeight; +} diff --git a/src/TacsUtilities.h b/src/TacsUtilities.h index 8474c49d5..d4489225e 100644 --- a/src/TacsUtilities.h +++ b/src/TacsUtilities.h @@ -220,4 +220,60 @@ class TACSMatrixHash : public TACSObject { MemNode *mem_root, *mem; }; +/** + * @brief Compute the KS aggregate of a set of values + * + * @param f The values to aggregate + * @param numVals The number of values to aggregate + * @param ksWeight The KS weight parameter (rho) + * @return TacsScalar The aggregated value + */ +TacsScalar ksAggregation(const TacsScalar f[], const int numVals, + const double ksWeight); + +/** + * @brief Compute the KS aggregate of a set of values + * + * @param f The values to aggregate + * @param maxVal The maximum of the values + * @param numVals The number of values to aggregate + * @param ksWeight The KS weight parameter (rho) + * @return TacsScalar The aggregated value + */ +TacsScalar ksAggregation(const TacsScalar f[], const TacsScalar maxVal, + const int numVals, const double ksWeight); + +/** + * @brief Compute the derivative of the KS aggregate with respect to the input + * values + * + * @param f The values to aggregate + * @param numVals The number of values to aggregate + * @param ksWeight The KS weight parameter (rho) + * @param dKSdf Array to store the derivative in, dKSdf[i] = dKS/df[i] + * @return TacsScalar The aggregated value + */ +TacsScalar ksAggregationSens(const TacsScalar f[], const int numVals, + const double ksWeight, TacsScalar dKSdf[]); + +/** + * @brief Given the sensitivities of f w.r.t x, compute the sensitivity of KS(f) + * w.r.t x + * + * This function is essentially computing the product, dKS/dx = dKS/df * df/dx, + * without explicitly storing the matrix dKS/df + * + * @param f Values to aggregate + * @param numVals Number of values to aggregate + * @param numVars Number of variables sensitivities are w.r.t + * @param ksWeight The KS weight parameter (rho) + * @param dfdx The sensitivities of f w.r.t x, dfdx[i][j] = df[i]/dx[j] + * @param dKSdx The array to store the sensitivities of KS(f) w.r.t x, dKSdx[i]= + * dKS/dx[i] + * @return TacsScalar The aggregated value + */ +TacsScalar ksAggregationSensProduct(const TacsScalar f[], const int numVals, + const int numVars, const double ksWeight, + TacsScalar **dfdx, TacsScalar dKSdx[]); + #endif // TACS_UTILITIES_H diff --git a/src/constitutive/Makefile b/src/constitutive/Makefile index c68b9f998..989c8d836 100644 --- a/src/constitutive/Makefile +++ b/src/constitutive/Makefile @@ -25,6 +25,7 @@ CXX_OBJS = TACSMaterialProperties.o \ TACSIsoTubeBeamConstitutive.o \ TACSIsoRectangleBeamConstitutive.o \ TACSPhaseChangeMaterialConstitutive.o \ + TACSBladeStiffenedShellConstitutive.o \ DIR=${TACS_DIR}/src/constitutive diff --git a/src/constitutive/TACSBladeStiffenedShellConstitutive.cpp b/src/constitutive/TACSBladeStiffenedShellConstitutive.cpp new file mode 100644 index 000000000..39feb0c33 --- /dev/null +++ b/src/constitutive/TACSBladeStiffenedShellConstitutive.cpp @@ -0,0 +1,2912 @@ +/* +============================================================================= +Blade-Stiffened Shell Constitutive Model +============================================================================= +@File : TACSBladeStiffenedShellConstitutive.cpp +@Date : 2023/04/06 +@Author : Alasdair Christison Gray +@Description : Constitutive model for a blade-stiffened shell. Based on the +bladeFSDT model from previous versions of TACS developed by Graeme Kennedy. +*/ + +// ============================================================================= +// Standard Library Includes +// ============================================================================= + +// ============================================================================= +// Extension Includes +// ============================================================================= +#include "TACSBladeStiffenedShellConstitutive.h" + +#include "TACSMaterialProperties.h" +#include "TACSShellConstitutive.h" + +const char* TACSBladeStiffenedShellConstitutive::constName = + "TACSBladeStiffenedShellConstitutive"; + +// ============================================================================== +// Constructor +// ============================================================================== + +TACSBladeStiffenedShellConstitutive::TACSBladeStiffenedShellConstitutive( + TACSOrthotropicPly* _panelPly, TACSOrthotropicPly* _stiffenerPly, + TacsScalar _kcorr, TacsScalar _panelLength, int _panelLengthNum, + TacsScalar _stiffenerPitch, int _stiffenerPitchNum, TacsScalar _panelThick, + int _panelThickNum, int _numPanelPlies, TacsScalar _panelPlyAngles[], + TacsScalar _panelPlyFracs[], int _panelPlyFracNums[], + TacsScalar _stiffenerHeight, int _stiffenerHeightNum, + TacsScalar _stiffenerThick, int _stiffenerThickNum, int _numStiffenerPlies, + TacsScalar _stiffenerPlyAngles[], TacsScalar _stiffenerPlyFracs[], + int _stiffenerPlyFracNums[], TacsScalar _flangeFraction) { + this->panelPly = _panelPly; + this->panelPly->incref(); + + this->stiffenerPly = _stiffenerPly; + this->stiffenerPly->incref(); + + this->kcorr = _kcorr; + + this->numDesignVars = this->numGeneralDV = this->numPanelDV = + this->numStiffenerDV = 0; + + // --- General DVs --- + // --- Panel length values --- + this->panelLength = _panelLength; + this->panelLengthNum = _panelLengthNum; + this->panelLengthLocalNum = -1; + if (_panelLengthNum >= 0) { + this->panelLengthLocalNum = this->numDesignVars; + this->numDesignVars++; + this->numGeneralDV++; + } + this->panelLengthLowerBound = 0.000; + this->panelLengthUpperBound = 1e20; + + // --- Stiffener pitch values --- + this->stiffenerPitch = _stiffenerPitch; + this->stiffenerPitchNum = _stiffenerPitchNum; + this->stiffenerPitchLocalNum = -1; + if (_stiffenerPitchNum >= 0) { + this->stiffenerPitchLocalNum = this->numDesignVars; + this->numDesignVars++; + this->numGeneralDV++; + } + this->stiffenerPitchLowerBound = 1e-3; + this->stiffenerPitchUpperBound = 1e20; + + // --- Panel DVs --- + // --- Panel thickness values --- + this->panelDVStartNum = this->numDesignVars; + this->panelThick = _panelThick; + this->panelThickNum = _panelThickNum; + this->panelThickLocalNum = -1; + if (_panelThickNum >= 0) { + this->panelThickLocalNum = this->numDesignVars; + this->numDesignVars++; + this->numPanelDV++; + } + this->panelThickLowerBound = 1e-4; + this->panelThickUpperBound = 1e20; + + // --- Panel ply values --- + this->numPanelPlies = _numPanelPlies; + this->panelPlyAngles = new TacsScalar[_numPanelPlies]; + this->panelPlyFracs = new TacsScalar[_numPanelPlies]; + this->panelPlyFracNums = new int[_numPanelPlies]; + this->panelPlyFracLocalNums = new int[_numPanelPlies]; + this->panelPlyFracLowerBounds = new TacsScalar[_numPanelPlies]; + this->panelPlyFracUpperBounds = new TacsScalar[_numPanelPlies]; + for (int ii = 0; ii < _numPanelPlies; ii++) { + this->panelPlyAngles[ii] = _panelPlyAngles[ii]; + this->panelPlyFracs[ii] = _panelPlyFracs[ii]; + this->panelPlyFracNums[ii] = _panelPlyFracNums[ii]; + this->panelPlyFracLocalNums[ii] = -1; + if (_panelPlyFracNums[ii] >= 0) { + this->panelPlyFracLocalNums[ii] = this->numDesignVars; + this->numDesignVars++; + this->numPanelDV++; + } + this->panelPlyFracLowerBounds[ii] = 0.1; + this->panelPlyFracUpperBounds[ii] = 0.9; + } + + // --- Stiffener DVs --- + // --- Stiffener height values --- + this->stiffenerDVStartNum = this->numDesignVars; + this->stiffenerHeight = _stiffenerHeight; + this->stiffenerHeightNum = _stiffenerHeightNum; + this->stiffenerHeightLocalNum = -1; + if (_stiffenerHeightNum >= 0) { + this->stiffenerHeightLocalNum = this->numDesignVars; + this->numDesignVars++; + this->numStiffenerDV++; + } + this->stiffenerHeightLowerBound = 1e-3; + this->stiffenerHeightUpperBound = 1e20; + + // --- Stiffener thickness values --- + this->stiffenerThick = _stiffenerThick; + this->stiffenerThickNum = _stiffenerThickNum; + this->stiffenerThickLocalNum = -1; + if (_stiffenerThickNum >= 0) { + this->stiffenerThickLocalNum = this->numDesignVars; + this->numDesignVars++; + this->numStiffenerDV++; + } + this->stiffenerThickLowerBound = 1e-4; + this->stiffenerThickUpperBound = 1e20; + + // --- Stiffener ply values --- + this->numStiffenerPlies = _numStiffenerPlies; + this->stiffenerPlyAngles = new TacsScalar[_numStiffenerPlies]; + this->stiffenerPlyFracs = new TacsScalar[_numStiffenerPlies]; + this->stiffenerPlyFracNums = new int[_numStiffenerPlies]; + this->stiffenerPlyFracLocalNums = new int[_numStiffenerPlies]; + this->stiffenerPlyFracLowerBounds = new TacsScalar[_numStiffenerPlies]; + this->stiffenerPlyFracUpperBounds = new TacsScalar[_numStiffenerPlies]; + for (int ii = 0; ii < _numStiffenerPlies; ii++) { + this->stiffenerPlyAngles[ii] = _stiffenerPlyAngles[ii]; + this->stiffenerPlyFracs[ii] = _stiffenerPlyFracs[ii]; + this->stiffenerPlyFracNums[ii] = _stiffenerPlyFracNums[ii]; + this->stiffenerPlyFracLocalNums[ii] = -1; + if (_stiffenerPlyFracNums[ii] >= 0) { + this->stiffenerPlyFracLocalNums[ii] = this->numDesignVars; + this->numDesignVars++; + this->numStiffenerDV++; + } + this->stiffenerPlyFracLowerBounds[ii] = 0.1; + this->stiffenerPlyFracUpperBounds[ii] = 0.9; + } + + // --- Stiffener flange fraction --- + this->flangeFraction = _flangeFraction; + + // --- panel and stiffener ply stiffness matrices --- + // Since the ply angles are fixed, the Q and Abar matrices for each ply in the + // panel and stiffener will remain constant, so we can pre-compute them here. + this->panelQMats = new TacsScalar[_numPanelPlies * this->NUM_Q_ENTRIES]; + this->panelAbarMats = new TacsScalar[_numPanelPlies * this->NUM_ABAR_ENTRIES]; + + TACSOrthotropicPly* ply = this->panelPly; + TacsScalar* angles = this->panelPlyAngles; + for (int plyNum = 0; plyNum < _numPanelPlies; plyNum++) { + ply->calculateQbar(angles[plyNum], &panelQMats[plyNum * NUM_Q_ENTRIES]); + ply->calculateAbar(angles[plyNum], + &panelAbarMats[plyNum * NUM_ABAR_ENTRIES]); + } + + this->stiffenerQMats = + new TacsScalar[_numStiffenerPlies * this->NUM_Q_ENTRIES]; + this->stiffenerAbarMats = + new TacsScalar[_numStiffenerPlies * this->NUM_ABAR_ENTRIES]; + + ply = this->stiffenerPly; + angles = this->stiffenerPlyAngles; + for (int plyNum = 0; plyNum < _numStiffenerPlies; plyNum++) { + ply->calculateQbar(angles[plyNum], &stiffenerQMats[plyNum * NUM_Q_ENTRIES]); + ply->calculateAbar(angles[plyNum], + &stiffenerAbarMats[plyNum * NUM_ABAR_ENTRIES]); + } + + // --- Work arrays, these are created to avoid needing to allocate memory + // inside compute methods like evalFailure and evalFailureStrainSens --- + + // Arrays for storing failure values, need values for each ply angle at the + // top and bottom of the panel and at the tip of the stiffener + this->panelPlyFailValues = new TacsScalar[2 * _numPanelPlies]; + this->stiffenerPlyFailValues = new TacsScalar[_numStiffenerPlies]; + + // Arrays for storing failure strain sensitivities + this->panelPlyFailStrainSens = new TacsScalar*[2 * _numPanelPlies]; + this->stiffenerPlyFailStrainSens = new TacsScalar*[_numStiffenerPlies]; + for (int ii = 0; ii < 2 * _numPanelPlies; ii++) { + this->panelPlyFailStrainSens[ii] = new TacsScalar[this->NUM_STRESSES]; + } + for (int ii = 0; ii < _numStiffenerPlies; ii++) { + this->stiffenerPlyFailStrainSens[ii] = + new TacsScalar[TACSBeamConstitutive::NUM_STRESSES]; + } + + // Arrays for storing ply failure sensitivities + this->panelPlyFailSens = new TacsScalar[2 * this->numPanelPlies]; + this->stiffenerPlyFailSens = new TacsScalar[this->numPanelPlies]; +} + +// ============================================================================== +// Destructor +// ============================================================================== +TACSBladeStiffenedShellConstitutive::~TACSBladeStiffenedShellConstitutive() { + this->panelPly->decref(); + this->stiffenerPly->decref(); + + delete[] this->panelPlyAngles; + this->panelPlyAngles = nullptr; + + delete[] this->panelPlyFracs; + this->panelPlyFracs = nullptr; + + delete[] this->panelPlyFracNums; + this->panelPlyFracNums = nullptr; + + delete[] this->panelPlyFracLocalNums; + this->panelPlyFracLocalNums = nullptr; + + delete[] this->stiffenerPlyAngles; + this->stiffenerPlyAngles = nullptr; + + delete[] this->stiffenerPlyFracs; + this->stiffenerPlyFracs = nullptr; + + delete[] this->stiffenerPlyFracNums; + this->stiffenerPlyFracNums = nullptr; + + delete[] this->stiffenerPlyFracLocalNums; + this->stiffenerPlyFracLocalNums = nullptr; + + delete[] this->panelPlyFracLowerBounds; + this->panelPlyFracLowerBounds = nullptr; + + delete[] this->panelPlyFracUpperBounds; + this->panelPlyFracUpperBounds = nullptr; + + delete[] this->stiffenerPlyFracLowerBounds; + this->stiffenerPlyFracLowerBounds = nullptr; + + delete[] this->stiffenerPlyFracUpperBounds; + this->stiffenerPlyFracUpperBounds = nullptr; + + delete[] this->panelPlyFailValues; + this->panelPlyFailValues = nullptr; + + delete[] this->stiffenerPlyFailValues; + this->stiffenerPlyFailValues = nullptr; + + for (int ii = 0; ii < 2 * this->numPanelPlies; ii++) { + delete[] this->panelPlyFailStrainSens[ii]; + this->panelPlyFailStrainSens[ii] = nullptr; + } + delete[] this->panelPlyFailStrainSens; + this->panelPlyFailStrainSens = nullptr; + + for (int ii = 0; ii < this->numStiffenerPlies; ii++) { + delete[] this->stiffenerPlyFailStrainSens[ii]; + this->stiffenerPlyFailStrainSens[ii] = nullptr; + } + delete[] this->stiffenerPlyFailStrainSens; + this->stiffenerPlyFailStrainSens = nullptr; + + delete[] this->panelPlyFailSens; + this->panelPlyFailSens = nullptr; + + delete[] this->stiffenerPlyFailSens; + this->stiffenerPlyFailSens = nullptr; + + delete[] this->panelQMats; + this->panelQMats = nullptr; + delete[] this->panelAbarMats; + this->panelAbarMats = nullptr; + + delete[] this->stiffenerQMats; + this->stiffenerQMats = nullptr; + delete[] this->stiffenerAbarMats; + this->stiffenerAbarMats = nullptr; +} + +// ============================================================================== +// Set non-default values +// ============================================================================== + +void TACSBladeStiffenedShellConstitutive::setStiffenerPitchBounds( + TacsScalar lowerBound, TacsScalar upperBound) { + this->stiffenerPitchLowerBound = lowerBound; + this->stiffenerPitchUpperBound = upperBound; +} + +void TACSBladeStiffenedShellConstitutive::setStiffenerHeightBounds( + TacsScalar lowerBound, TacsScalar upperBound) { + this->stiffenerHeightLowerBound = lowerBound; + this->stiffenerHeightUpperBound = upperBound; +} + +void TACSBladeStiffenedShellConstitutive::setStiffenerThicknessBounds( + TacsScalar lowerBound, TacsScalar upperBound) { + this->stiffenerThickLowerBound = lowerBound; + this->stiffenerThickUpperBound = upperBound; +} + +void TACSBladeStiffenedShellConstitutive::setPanelThicknessBounds( + TacsScalar lowerBound, TacsScalar upperBound) { + this->panelThickLowerBound = lowerBound; + this->panelThickUpperBound = upperBound; +} + +void TACSBladeStiffenedShellConstitutive::setStiffenerPlyFractionBounds( + TacsScalar lowerBounds[], TacsScalar upperBounds[]) { + for (int ii = 0; ii < this->numStiffenerPlies; ii++) { + this->stiffenerPlyFracLowerBounds[ii] = lowerBounds[ii]; + this->stiffenerPlyFracUpperBounds[ii] = upperBounds[ii]; + } +} + +void TACSBladeStiffenedShellConstitutive::setPanelPlyFractionBounds( + TacsScalar lowerBounds[], TacsScalar upperBounds[]) { + for (int ii = 0; ii < this->numPanelPlies; ii++) { + this->panelPlyFracLowerBounds[ii] = lowerBounds[ii]; + this->panelPlyFracUpperBounds[ii] = upperBounds[ii]; + } +} + +void TACSBladeStiffenedShellConstitutive::setStiffenerPlyFractions( + TacsScalar plyFractions[]) { + for (int ii = 0; ii < this->numStiffenerPlies; ii++) { + this->stiffenerPlyFracs[ii] = plyFractions[ii]; + } +} + +void TACSBladeStiffenedShellConstitutive::setPanelPlyFractions( + TacsScalar plyFractions[]) { + for (int ii = 0; ii < this->numPanelPlies; ii++) { + this->panelPlyFracs[ii] = plyFractions[ii]; + } +} + +// ============================================================================== +// Setting/getting design variable information +// ============================================================================== +// Retrieve the global design variable numbers +int TACSBladeStiffenedShellConstitutive::getDesignVarNums(int elemIndex, + int dvLen, + int dvNums[]) { + if (dvNums && dvLen >= this->numDesignVars) { + if (this->panelLengthNum >= 0) { + dvNums[this->panelLengthLocalNum] = panelLengthNum; + } + if (this->stiffenerPitchNum >= 0) { + dvNums[this->stiffenerPitchLocalNum] = stiffenerPitchNum; + } + if (this->panelThickNum >= 0) { + dvNums[this->panelThickLocalNum] = panelThickNum; + } + for (int ii = 0; ii < this->numPanelPlies; ii++) { + if (this->panelPlyFracNums[ii] >= 0) { + dvNums[this->panelPlyFracLocalNums[ii]] = panelPlyFracNums[ii]; + } + } + if (this->stiffenerHeightNum >= 0) { + dvNums[this->stiffenerHeightLocalNum] = stiffenerHeightNum; + } + if (this->stiffenerThickNum >= 0) { + dvNums[this->stiffenerThickLocalNum] = stiffenerThickNum; + } + for (int ii = 0; ii < this->numStiffenerPlies; ii++) { + if (this->stiffenerPlyFracNums[ii] >= 0) { + dvNums[this->stiffenerPlyFracLocalNums[ii]] = stiffenerPlyFracNums[ii]; + } + } + } + return numDesignVars; +} + +// Set the element design variable from the design vector +int TACSBladeStiffenedShellConstitutive::setDesignVars(int elemIndex, int dvLen, + const TacsScalar dvs[]) { + if (dvLen >= this->numDesignVars) { + if (this->panelLengthNum >= 0) { + this->panelLength = dvs[this->panelLengthLocalNum]; + } + if (this->stiffenerPitchNum >= 0) { + this->stiffenerPitch = dvs[this->stiffenerPitchLocalNum]; + } + if (this->panelThickNum >= 0) { + this->panelThick = dvs[this->panelThickLocalNum]; + } + for (int ii = 0; ii < this->numPanelPlies; ii++) { + if (this->panelPlyFracNums[ii] >= 0) { + this->panelPlyFracs[ii] = dvs[this->panelPlyFracLocalNums[ii]]; + } + } + if (this->stiffenerHeightNum >= 0) { + this->stiffenerHeight = dvs[this->stiffenerHeightLocalNum]; + } + if (this->stiffenerThickNum >= 0) { + this->stiffenerThick = dvs[this->stiffenerThickLocalNum]; + } + for (int ii = 0; ii < this->numStiffenerPlies; ii++) { + if (this->stiffenerPlyFracNums[ii] >= 0) { + this->stiffenerPlyFracs[ii] = dvs[this->stiffenerPlyFracLocalNums[ii]]; + } + } + } + return this->numDesignVars; +} + +// Get the element design variables values +int TACSBladeStiffenedShellConstitutive::getDesignVars(int elemIndex, int dvLen, + TacsScalar dvs[]) { + if (dvLen >= this->numDesignVars) { + if (this->panelLengthNum >= 0) { + dvs[this->panelLengthLocalNum] = this->panelLength; + } + if (this->stiffenerPitchNum >= 0) { + dvs[this->stiffenerPitchLocalNum] = this->stiffenerPitch; + } + if (this->panelThickNum >= 0) { + dvs[this->panelThickLocalNum] = this->panelThick; + } + for (int ii = 0; ii < this->numPanelPlies; ii++) { + if (this->panelPlyFracNums[ii] >= 0) { + dvs[this->panelPlyFracLocalNums[ii]] = this->panelPlyFracs[ii]; + } + } + if (this->stiffenerHeightNum >= 0) { + dvs[this->stiffenerHeightLocalNum] = this->stiffenerHeight; + } + if (this->stiffenerThickNum >= 0) { + dvs[this->stiffenerThickLocalNum] = this->stiffenerThick; + } + for (int ii = 0; ii < this->numStiffenerPlies; ii++) { + if (this->stiffenerPlyFracNums[ii] >= 0) { + dvs[this->stiffenerPlyFracLocalNums[ii]] = this->stiffenerPlyFracs[ii]; + } + } + } + return this->numDesignVars; +} + +// Get the lower and upper bounds for the design variable values +int TACSBladeStiffenedShellConstitutive::getDesignVarRange(int elemIndex, + int dvLen, + TacsScalar lb[], + TacsScalar ub[]) { + if (dvLen >= this->numDesignVars) { + if (this->panelLengthNum >= 0) { + lb[this->panelLengthLocalNum] = this->panelLengthLowerBound; + ub[this->panelLengthLocalNum] = this->panelLengthUpperBound; + } + if (this->stiffenerPitchNum >= 0) { + lb[this->stiffenerPitchLocalNum] = this->stiffenerPitchLowerBound; + ub[this->stiffenerPitchLocalNum] = this->stiffenerPitchUpperBound; + } + if (this->panelThickNum >= 0) { + lb[this->panelThickLocalNum] = this->panelThickLowerBound; + ub[this->panelThickLocalNum] = this->panelThickUpperBound; + } + for (int ii = 0; ii < this->numPanelPlies; ii++) { + if (this->panelPlyFracNums[ii] >= 0) { + lb[this->panelPlyFracLocalNums[ii]] = this->panelPlyFracLowerBounds[ii]; + ub[this->panelPlyFracLocalNums[ii]] = this->panelPlyFracUpperBounds[ii]; + } + } + if (this->stiffenerHeightNum >= 0) { + lb[this->stiffenerHeightLocalNum] = this->stiffenerHeightLowerBound; + ub[this->stiffenerHeightLocalNum] = this->stiffenerHeightUpperBound; + } + if (this->stiffenerThickNum >= 0) { + lb[this->stiffenerThickLocalNum] = this->stiffenerThickLowerBound; + ub[this->stiffenerThickLocalNum] = this->stiffenerThickUpperBound; + } + for (int ii = 0; ii < this->numStiffenerPlies; ii++) { + if (this->stiffenerPlyFracNums[ii] >= 0) { + lb[this->stiffenerPlyFracLocalNums[ii]] = + this->stiffenerPlyFracLowerBounds[ii]; + ub[this->stiffenerPlyFracLocalNums[ii]] = + this->stiffenerPlyFracUpperBounds[ii]; + } + } + } + return this->numDesignVars; +} + +// ============================================================================== +// Evaluate mass properties +// ============================================================================== +// Evaluate the mass per unit area +TacsScalar TACSBladeStiffenedShellConstitutive::evalDensity( + int elemIndex, const double pt[], const TacsScalar X[]) { + // Density due to the panel = thickness * rho + TacsScalar density = this->panelPly->getDensity() * this->panelThick; + // Density due to the stiffeners = rho * A / pitch + density += this->stiffenerPly->getDensity() * this->computeStiffenerArea() / + this->stiffenerPitch; + return density; +} + +// Add the derivative of the density w.r.t. the design variables +void TACSBladeStiffenedShellConstitutive::addDensityDVSens( + int elemIndex, TacsScalar scale, const double pt[], const TacsScalar X[], + int dvLen, TacsScalar dfdx[]) { + TacsScalar panelDensity = this->panelPly->getDensity(); + TacsScalar stiffenerDensity = this->stiffenerPly->getDensity(); + TacsScalar stiffenerArea = this->computeStiffenerArea(); + TacsScalar dAdt, dAdh; + this->computeStiffenerAreaSens(dAdt, dAdh); + + if (this->stiffenerPitchLocalNum >= 0) { + TacsScalar sp = this->stiffenerPitch; + dfdx[this->stiffenerPitchLocalNum] += + -scale * stiffenerDensity * stiffenerArea / (sp * sp); + } + if (this->stiffenerHeightLocalNum >= 0) { + dfdx[this->stiffenerHeightLocalNum] += + scale * stiffenerDensity * dAdh / this->stiffenerPitch; + } + if (this->stiffenerThickLocalNum >= 0) { + dfdx[this->stiffenerThickLocalNum] += + scale * stiffenerDensity * dAdt / this->stiffenerPitch; + } + if (this->panelThickLocalNum >= 0) { + dfdx[this->panelThickLocalNum] += scale * panelDensity; + } +} + +// Evaluate the mass moments +void TACSBladeStiffenedShellConstitutive::evalMassMoments( + int elemIndex, const double pt[], const TacsScalar X[], + TacsScalar moments[]) { + TacsScalar sPitchInv = 1.0 / this->stiffenerPitch; + TacsScalar sHeight = this->stiffenerHeight; + TacsScalar sThick = this->stiffenerThick; + TacsScalar pThick = this->panelThick; + TacsScalar kf = this->flangeFraction; + TacsScalar panelDensity = this->panelPly->getDensity(); + TacsScalar stiffenerDensity = this->stiffenerPly->getDensity(); + TacsScalar stiffenerArea = this->computeStiffenerArea(); + TacsScalar stiffenerOffset = + this->computeStiffenerCentroidHeight() - 0.5 * pThick; + TacsScalar stiffenerMOI = this->computeStiffenerMOI(); + + moments[0] = + panelDensity * pThick + stiffenerDensity * stiffenerArea * sPitchInv; + + // First moment of area is non-zero because the stiffener makes the section + // asymmteric + moments[1] = -stiffenerDensity * sHeight * sThick * + (kf * pThick + kf * sThick + pThick + sHeight + 2.0 * sThick) * + 0.5 * sPitchInv; + + // Panel contribution to second moment of area + moments[2] = 0.5 * panelDensity * pThick * pThick * pThick / 12.0; + + // Add stiffener MOI about it's own centroid + contribution from parallel axis + // theorm + moments[2] += (stiffenerMOI + 0.5 * stiffenerDensity * stiffenerArea * + stiffenerOffset * stiffenerOffset) * + sPitchInv; +} + +/** + Add the derivative of the pointwise mass times the given scalar + + @param elemIndex The local element index + @param pt The parametric location + @param X The point location + @param scale Scale factor for the moments + @param dvLen the length of the sensitivity array + @param dfdx The sensitivity array +*/ +void TACSBladeStiffenedShellConstitutive::addMassMomentsDVSens( + int elemIndex, const double pt[], const TacsScalar X[], + const TacsScalar scale[], int dvLen, TacsScalar dfdx[]) { + TacsScalar sPitchInv = 1.0 / this->stiffenerPitch; + TacsScalar sHeight = this->stiffenerHeight; + TacsScalar sThick = this->stiffenerThick; + TacsScalar pThick = this->panelThick; + TacsScalar kf = this->flangeFraction; + TacsScalar panelDensity = this->panelPly->getDensity(); + TacsScalar stiffenerDensity = this->stiffenerPly->getDensity(); + TacsScalar stiffenerArea = this->computeStiffenerArea(); + TacsScalar stiffenerOffset = + this->computeStiffenerCentroidHeight() - 0.5 * pThick; + TacsScalar stiffenerMOI = this->computeStiffenerMOI(); + + TacsScalar dzdt, dzdh; + this->computeStiffenerCentroidHeightSens(dzdt, dzdh); + + TacsScalar dAdt, dAdh; + this->computeStiffenerAreaSens(dAdt, dAdh); + + TacsScalar dMOIdt, dMOIdh; + this->computeStiffenerMOISens(dMOIdt, dMOIdh); + + // --- Stiffener pitch sensitivity --- + if (this->stiffenerPitchLocalNum >= 0) { + int ii = this->stiffenerPitchLocalNum; + TacsScalar sPitchInv2 = sPitchInv * sPitchInv; + + // Density contribution + dfdx[ii] -= scale[0] * stiffenerDensity * stiffenerArea * sPitchInv2; + + // First moment of area contribution + dfdx[ii] += scale[1] * stiffenerDensity * sHeight * sThick * + (kf * pThick + kf * sThick + pThick + sHeight + 2.0 * sThick) * + 0.5 * sPitchInv2; + + // Second moment of area contribution + dfdx[ii] -= scale[2] * + (stiffenerMOI + 0.5 * stiffenerDensity * stiffenerArea * + stiffenerOffset * stiffenerOffset) * + sPitchInv2; + } + + // --- Stiffener height sensitivity --- + if (this->stiffenerHeightLocalNum >= 0) { + int ii = this->stiffenerHeightLocalNum; + // --- Density contribution --- + dfdx[ii] += scale[0] * stiffenerDensity * dAdh * sPitchInv; + // --- First moment of area contribution --- + dfdx[ii] += + scale[1] * sPitchInv * + (sThick * stiffenerDensity * + (-kf * pThick - kf * sThick - pThick - 2.0 * sHeight - 2.0 * sThick) * + 0.5); + + // --- Second moment of area contribution --- + // d/dh(MOI + 0.5*rho*A*z^2) = d/dh(MOI) + 0.5*rho*(dAdh*z^2 + 2*A*z*dzdh) + dfdx[ii] += + scale[2] * sPitchInv * + (dMOIdh + 0.5 * stiffenerDensity * stiffenerOffset * + (stiffenerOffset * dAdh + 2.0 * stiffenerArea * dzdh)); + } + + // --- Stiffener thickness sensitivity --- + if (this->stiffenerThickLocalNum >= 0) { + int ii = this->stiffenerThickLocalNum; + + // --- Density contribution --- + dfdx[ii] += scale[0] * stiffenerDensity * dAdt * sPitchInv; + + // --- First moment of area contribution --- + dfdx[ii] += + scale[1] * sPitchInv * + (sHeight * stiffenerDensity * + (-kf * pThick - 2.0 * kf * sThick - pThick - sHeight - 4.0 * sThick) / + 2.0); + + // --- Second moment of area contribution --- + // d/dt(MOI + 0.5*rho*A*z^2) = d/dt(MOI) + 0.5*rho*(dAdt*z^2 + 2*A*z*dzdt) + dfdx[ii] += + scale[2] * sPitchInv * + (dMOIdt + 0.5 * stiffenerDensity * stiffenerOffset * + (stiffenerOffset * dAdt + 2.0 * stiffenerArea * dzdt)); + } + + // --- Panel thickness sensitivity --- + if (this->panelThickLocalNum >= 0) { + int ii = this->panelThickLocalNum; + // Density contribution + dfdx[ii] += scale[0] * panelDensity; + // First moment of area contribution + dfdx[ii] -= scale[1] * (stiffenerDensity * sHeight * sThick * (kf + 1.0) * + 0.5 * sPitchInv); + // Second moment of area contributions + dfdx[ii] += scale[2] * panelDensity * 0.125 * pThick * pThick; + dfdx[ii] -= scale[2] * sPitchInv * 0.5 * stiffenerDensity * 2.0 * + stiffenerArea * stiffenerOffset * 0.5; + } +} + +// ============================================================================== +// Evaluate thermal properties +// ============================================================================== + +// Evaluate the specific heat +TacsScalar TACSBladeStiffenedShellConstitutive::evalSpecificHeat( + int elemIndex, const double pt[], const TacsScalar X[]) { + return 0.0; +} + +// ============================================================================== +// Compute stress/strain/stiffness +// ============================================================================== + +// Evaluate the stress +void TACSBladeStiffenedShellConstitutive::evalStress(int elemIndex, + const double pt[], + const TacsScalar X[], + const TacsScalar e[], + TacsScalar s[]) { + // NOTE: The commented out code below is a theoretically nicer way to compute + // the stress, but it makes it difficult to include the stiffener's + // constribution to the drilling stress. So I've just settled for computing + // the full stiffness matrix and multiplying by the strain. + // ======================================================== + // // Compute the panel stresses + // memset(s, 0, this->NUM_STRESSES * sizeof(TacsScalar)); + // this->computePanelStress(e, s); + + // // Compute the stiffener beam stresses then transform them back to shell + // // stresses + // TacsScalar stiffenerStrain[TACSBeamConstitutive::NUM_STRESSES], + // stiffenerStress[TACSBeamConstitutive::NUM_STRESSES]; + // this->transformStrain(e, stiffenerStrain); + + // this->computeStiffenerStress(stiffenerStrain, stiffenerStress); + // this->addStiffenerStress(stiffenerStress, s); + + // Just compute the stiffness matrix and multiply by the strain + TacsScalar C[NUM_TANGENT_STIFFNESS_ENTRIES]; + this->computeStiffness(C); + TacsScalar* A = &C[0]; + TacsScalar* B = &C[6]; + TacsScalar* D = &C[12]; + TacsScalar* As = &C[18]; + TacsScalar drill = C[21]; + this->computeStress(A, B, D, As, drill, e, s); +} + +// Add the derivative of the product of stress with a vector psi to dfdx +void TACSBladeStiffenedShellConstitutive::addStressDVSens( + int elemIndex, TacsScalar scale, const double pt[], const TacsScalar X[], + const TacsScalar strain[], const TacsScalar psi[], int dvLen, + TacsScalar dfdx[]) { + TacsScalar pInv = 1.0 / this->stiffenerPitch; + TacsScalar stiffScale = pInv * scale; + + TacsScalar A, dAdt, dAdh, Izz, dIzzdt, dIzzdh, J, dJdt, dJdh, z, dzdt, dzdh, + E, G; + A = this->computeStiffenerArea(); + this->computeStiffenerAreaSens(dAdt, dAdh); + Izz = this->computeStiffenerIzz(); + this->computeStiffenerIzzSens(dIzzdt, dIzzdh); + J = this->computeStiffenerJxx(); + this->computeStiffenerJxxSens(dJdt, dJdh); + this->computeEffectiveModulii(this->numStiffenerPlies, this->stiffenerQMats, + this->stiffenerPlyFracs, &E, &G); + z = this->computeStiffenerCentroidHeight() - 0.5 * this->panelThick; + this->computeStiffenerCentroidHeightSens(dzdt, dzdh); + + // Sensitivity of the panel stress values to it's DVs (this has been proven + // correct) + this->addPanelStressDVSens(scale, strain, psi, &dfdx[this->panelDVStartNum]); + + // Transform the psi vector the same way we do for stains + TacsScalar stiffenerPsi[TACSBeamConstitutive::NUM_STRESSES]; + this->transformStrain(psi, stiffenerPsi); + + TacsScalar stiffenerStrain[TACSBeamConstitutive::NUM_STRESSES], + stiffenerStress[TACSBeamConstitutive::NUM_STRESSES]; + this->transformStrain(strain, stiffenerStrain); + this->computeStiffenerStress(stiffenerStrain, stiffenerStress); + + // Add scale * 1/pitch * stiffenerStress^T * d/dx(Te) * stiffenerPsi + this->addStrainTransformProductDVsens(stiffenerStress, psi, stiffScale, dfdx); + + // Add scale * 1/pitch * Cstiffener * stiffenerPsi * d/dx(Te) * strain + TacsScalar psiStress[TACSBeamConstitutive::NUM_STRESSES]; + this->computeStiffenerStress(stiffenerPsi, psiStress); + this->addStrainTransformProductDVsens(psiStress, strain, stiffScale, dfdx); + + // Add scale*1/pitch * stiffenerPsi^T * d/dx(stiffenerStress) + this->addStiffenerStressDVSens(stiffScale, stiffenerStrain, stiffenerPsi, + &dfdx[this->stiffenerDVStartNum]); + + // Add the direct dependence on the stiffener pitch (this has been proven + // correct) + if (this->stiffenerPitchLocalNum >= 0) { + int index = this->stiffenerPitchLocalNum; + TacsScalar panelStress[this->NUM_STRESSES]; + TacsScalar stress[this->NUM_STRESSES]; + + this->computePanelStress(strain, panelStress); + this->evalStress(elemIndex, pt, X, strain, stress); + + for (int jj = 0; jj < this->NUM_STRESSES; jj++) { + dfdx[index] -= stiffScale * (stress[jj] - panelStress[jj]) * psi[jj]; + } + } + + // Add terms related to the stiffener's contribution to the drilling stress + // (the code below here has been proven correct) + + if (this->stiffenerThickNum >= 0) { + dfdx[this->stiffenerThickLocalNum] += + scale * 0.5 * pInv * DRILLING_REGULARIZATION * this->kcorr * G * dAdt * + psi[8] * strain[8]; + } + if (this->stiffenerHeightNum >= 0) { + dfdx[this->stiffenerHeightLocalNum] += + scale * 0.5 * pInv * DRILLING_REGULARIZATION * this->kcorr * G * dAdh * + psi[8] * strain[8]; + } + + for (int ii = 0; ii < this->numStiffenerPlies; ii++) { + if (this->stiffenerPlyFracNums[ii] >= 0) { + TacsScalar* Q = &(this->stiffenerQMats[ii * NUM_Q_ENTRIES]); + TacsScalar dGdf = Q[5]; + dfdx[this->stiffenerPlyFracLocalNums[ii]] += + psi[8] * scale * 0.5 * pInv * DRILLING_REGULARIZATION * this->kcorr * + A * dGdf * strain[8]; + } + } +} + +// Evaluate the tangent stiffness +void TACSBladeStiffenedShellConstitutive::evalTangentStiffness( + int elemIndex, const double pt[], const TacsScalar X[], TacsScalar C[]) { + this->computeStiffness(C); +} + +// ============================================================================== +// Compute failure criteria +// ============================================================================== +// Calculate the point-wise failure criteria +TacsScalar TACSBladeStiffenedShellConstitutive::evalFailure( + int elemIndex, const double pt[], const TacsScalar X[], + const TacsScalar e[]) { + TacsScalar fails[this->NUM_FAILURES]; + TacsScalar aggFail = this->computeFailureValues(e, fails); + return aggFail; +} + +// Compute the failure values for each failure mode of the stiffened panel +TacsScalar TACSBladeStiffenedShellConstitutive::computeFailureValues( + const TacsScalar e[], TacsScalar fails[]) { + // --- Panel material failure --- + fails[0] = this->computePanelFailure(e); + + // --- Stiffener material failure --- + TacsScalar stiffenerStrain[TACSBeamConstitutive::NUM_STRESSES]; + this->transformStrain(e, stiffenerStrain); + fails[1] = this->computeStiffenerFailure(stiffenerStrain); + + // --- Local panel buckling --- + // Compute panel stiffness matrix and loads + TacsScalar panelStiffness[NUM_TANGENT_STIFFNESS_ENTRIES], + stress[NUM_STRESSES]; + this->computePanelStiffness(panelStiffness); + const TacsScalar *A, *D; + this->extractTangentStiffness(panelStiffness, &A, NULL, &D, NULL, NULL); + this->computePanelStress(e, stress); + + // Compute the critical local loads + TacsScalar N1Crit, N12Crit; + TacsScalar D11 = D[0], D12 = D[1], D22 = D[3], D66 = D[5], + L = this->stiffenerPitch; + N1Crit = this->computeCriticalLocalAxialLoad(D11, D22, D12, D66, L); + N12Crit = this->computeCriticalShearLoad(D11, D22, D12 + 2.0 * D66, L); + + // Compute the buckling criteria + fails[2] = this->bucklingEnvelope(-stress[0], N1Crit, stress[2], N12Crit); + + // --- Global buckling --- + TacsScalar D1, D2, D3; + this->computeCriticalGlobalBucklingStiffness(&D1, &D2, &D3); + L = this->panelLength; + + N1Crit = computeCriticalGlobalAxialLoad(D1, L); + N12Crit = this->computeCriticalShearLoad(D1, D2, D3, L); + + this->evalStress(0, NULL, NULL, e, stress); + fails[3] = this->bucklingEnvelope(-stress[0], N1Crit, stress[2], N12Crit); + + return ksAggregation(fails, this->NUM_FAILURES, this->ksWeight); +} + +// Evaluate the derivative of the failure criteria w.r.t. the strain +TacsScalar TACSBladeStiffenedShellConstitutive::evalFailureStrainSens( + int elemIndex, const double pt[], const TacsScalar X[], + const TacsScalar e[], TacsScalar sens[]) { + memset(sens, 0, this->NUM_STRESSES * sizeof(TacsScalar)); + + TacsScalar fails[this->NUM_FAILURES], dKSdf[this->NUM_FAILURES]; + // First compute the sensitivity of the panel failure value + TacsScalar panelFailSens[this->NUM_STRESSES]; + fails[0] = this->evalPanelFailureStrainSens(e, panelFailSens); + + // And now for the stiffener failure value, first in terms of the beam + // strains, and then transformed back to shell strains + TacsScalar stiffenerStrain[TACSBeamConstitutive::NUM_STRESSES], + stiffenerStrainSens[TACSBeamConstitutive::NUM_STRESSES], + stiffenerFailSens[this->NUM_STRESSES]; + this->transformStrain(e, stiffenerStrain); + fails[1] = this->evalStiffenerFailureStrainSens(stiffenerStrain, + stiffenerStrainSens); + this->transformStrainSens(stiffenerStrainSens, stiffenerFailSens); + + // --- Local panel buckling --- + // Compute panel stiffness matrix and loads + TacsScalar panelStiffness[NUM_TANGENT_STIFFNESS_ENTRIES], + panelStress[NUM_STRESSES]; + this->computePanelStiffness(panelStiffness); + const TacsScalar *APanel, *DPanel; + this->extractTangentStiffness(panelStiffness, &APanel, NULL, &DPanel, NULL, + NULL); + this->computePanelStress(e, panelStress); + + // Compute the critical local loads (no need to compute their sensitivities + // because they're not dependent on the strain)) + TacsScalar N1CritLocal, N12CritLocal; + TacsScalar D11 = DPanel[0], D12 = DPanel[1], D22 = DPanel[3], D66 = DPanel[5], + L = this->stiffenerPitch; + N1CritLocal = this->computeCriticalLocalAxialLoad(D11, D22, D12, D66, L); + N12CritLocal = this->computeCriticalShearLoad(D11, D22, D12 + 2.0 * D66, L); + + // Compute the buckling criteria and it's sensitivities + TacsScalar N1LocalSens, N12LocalSens, N1CritLocalSens, N12CritLocalSens; + fails[2] = this->bucklingEnvelopeSens( + -panelStress[0], N1CritLocal, panelStress[2], N12CritLocal, &N1LocalSens, + &N1CritLocalSens, &N12LocalSens, &N12CritLocalSens); + + // --- Global buckling --- + TacsScalar stiffness[NUM_TANGENT_STIFFNESS_ENTRIES], stress[NUM_STRESSES]; + this->computeStiffness(stiffness); + const TacsScalar *A, *B, *D, *As; + TacsScalar drill; + this->extractTangentStiffness(stiffness, &A, &B, &D, &As, &drill); + this->computeStress(A, B, D, As, drill, e, stress); + TacsScalar N1GlobalSens, N1CritGlobalSens, N12GlobalSens, N12CritGlobalSens; + TacsScalar D1, D2, D3; + this->computeCriticalGlobalBucklingStiffness(&D1, &D2, &D3); + L = this->panelLength; + TacsScalar N1CritGlobal = computeCriticalGlobalAxialLoad(D1, L); + TacsScalar N12CritGlobal = this->computeCriticalShearLoad(D1, D2, D3, L); + + fails[3] = this->bucklingEnvelopeSens( + -stress[0], N1CritGlobal, stress[2], N12CritGlobal, &N1GlobalSens, + &N1CritGlobalSens, &N12GlobalSens, &N12CritGlobalSens); + + // Compute the sensitivity of the aggregate failure value to the individual + // failure mode values + TacsScalar fail = + ksAggregationSens(fails, this->NUM_FAILURES, this->ksWeight, dKSdf); + + // Compute the total sensitivity due to the panel and stiffener material + // failure + memset(sens, 0, this->NUM_STRESSES * sizeof(TacsScalar)); + for (int ii = 0; ii < this->NUM_STRESSES; ii++) { + sens[ii] = dKSdf[0] * panelFailSens[ii] + dKSdf[1] * stiffenerFailSens[ii]; + } + + // Now add the sensitivity of the buckling criteria + + // local buckling + N1LocalSens *= dKSdf[2]; + N12LocalSens *= dKSdf[2]; + sens[0] += N1LocalSens * -APanel[0] + N12LocalSens * APanel[2]; + sens[1] += N1LocalSens * -APanel[1] + N12LocalSens * APanel[4]; + sens[2] += N1LocalSens * -APanel[2] + N12LocalSens * APanel[5]; + + // Global buckling + N1GlobalSens *= dKSdf[3]; + N12GlobalSens *= dKSdf[3]; + sens[0] += N1GlobalSens * -A[0] + N12GlobalSens * A[2]; + sens[1] += N1GlobalSens * -A[1] + N12GlobalSens * A[4]; + sens[2] += N1GlobalSens * -A[2] + N12GlobalSens * A[5]; + sens[3] += N1GlobalSens * -B[0] + N12GlobalSens * B[2]; + sens[4] += N1GlobalSens * -B[1] + N12GlobalSens * B[4]; + sens[5] += N1GlobalSens * -B[2] + N12GlobalSens * B[5]; + + return fail; +} + +// Add the derivative of the failure criteria w.r.t. the design variables +void TACSBladeStiffenedShellConstitutive::addFailureDVSens( + int elemIndex, TacsScalar scale, const double pt[], const TacsScalar X[], + const TacsScalar strain[], int dvLen, TacsScalar dfdx[]) { + // TODO: The implementation of this function is not great, it uses a mix of + // forward and backward differentiation and ends up recomputing a lot of + // stuff. It should be rewritten to use only forward or only backward + // differentiation in future. + const int numDV = this->numDesignVars; + + // Compute the failure values and then compute the + // sensitivity of the aggregate failure value w.r.t. them + TacsScalar fails[this->NUM_FAILURES], dKSdf[this->NUM_FAILURES]; + TacsScalar fail = this->computeFailureValues(strain, fails); + ksAggregationSens(fails, this->NUM_FAILURES, this->ksWeight, dKSdf); + + // Sensitivity of the panel failure value to it's DVs + this->addPanelFailureDVSens(strain, scale * dKSdf[0], + &dfdx[this->panelDVStartNum]); + + // Add the direct sensitivity of the stiffener failure value w.r.t DVs + // Sensitivity of the panel failure value to it's DVs + TacsScalar stiffenerStrain[TACSBeamConstitutive::NUM_STRESSES]; + this->transformStrain(strain, stiffenerStrain); + this->addStiffenerFailureDVSens(stiffenerStrain, scale * dKSdf[1], + &dfdx[this->stiffenerDVStartNum]); + + // Add the sensitivity of the stiffener failure value w.r.t. the DVs + // due to the dependence of the stiffener strains on the DVs + TacsScalar stiffenerFailStrainSens[TACSBeamConstitutive::NUM_STRESSES]; + this->evalStiffenerFailureStrainSens(stiffenerStrain, + stiffenerFailStrainSens); + this->addStrainTransformProductDVsens(stiffenerFailStrainSens, strain, + scale * dKSdf[1], dfdx); + + // --- Local panel buckling --- + // Compute panel stiffness matrix and loads + TacsScalar panelStiffness[NUM_TANGENT_STIFFNESS_ENTRIES], + panelStress[NUM_STRESSES]; + this->computePanelStiffness(panelStiffness); + const TacsScalar *A, *D; + this->extractTangentStiffness(panelStiffness, &A, NULL, &D, NULL, NULL); + this->computePanelStress(strain, panelStress); + + // Compute the critical local loads and their sensitivities + TacsScalar N1Crit, N12Crit; + TacsScalar D11 = D[0], D12 = D[1], D22 = D[3], D66 = D[5], + L = this->stiffenerPitch; + + // Create arrays for the sensitivities of the critical loads: + // [dN/dD11, dNdD22, dNdD12, dNdD66, dNdL] + TacsScalar N1CritSens[5], N12CritSens[5]; + N1Crit = this->computeCriticalLocalAxialLoadSens( + D11, D22, D12, D66, L, &N1CritSens[0], &N1CritSens[1], &N1CritSens[2], + &N1CritSens[3], &N1CritSens[4]); + N12Crit = this->computeCriticalShearLoadSens( + D11, D22, D12 + 2.0 * D66, L, &N12CritSens[0], &N12CritSens[1], + &N12CritSens[2], &N12CritSens[4]); + + // N12CritSens[2] is currently dN12Crit/d(D12 + 2D66) + N12CritSens[3] = 2.0 * N12CritSens[2]; + + // Compute the buckling criteria and it's sensitivities to the applied and + // critical loads + TacsScalar dfdN1Local, dfdN12Local, dfdN1CritLocal, dfdN12CritLocal; + fails[2] = this->bucklingEnvelopeSens(-panelStress[0], N1Crit, panelStress[2], + N12Crit, &dfdN1Local, &dfdN1CritLocal, + &dfdN12Local, &dfdN12CritLocal); + dfdN1Local *= dKSdf[2]; + dfdN12Local *= dKSdf[2]; + dfdN1CritLocal *= dKSdf[2]; + dfdN12CritLocal *= dKSdf[2]; + + // Convert sensitivity w.r.t applied loads into sensitivity w.r.t DVs + TacsScalar dfdPanelStress[NUM_STRESSES]; + memset(dfdPanelStress, 0, NUM_STRESSES * sizeof(TacsScalar)); + dfdPanelStress[0] = -dfdN1Local; + dfdPanelStress[2] = dfdN12Local; + this->addPanelStressDVSens(scale, strain, dfdPanelStress, + &dfdx[this->panelDVStartNum]); + + // Convert the sensitivities of the critical loads w.r.t the D matrix entries + // to sensitivities of the buckling failure criteria w.r.t the D matrix + // entries + TacsScalar localBucklingDMatSens[4]; + for (int ii = 0; ii < 4; ii++) { + localBucklingDMatSens[ii] = + N1CritSens[ii] * dfdN1CritLocal + N12CritSens[ii] * dfdN12CritLocal; + } + + // --- Global buckling sensitivity --- + TacsScalar stress[NUM_STRESSES]; + this->evalStress(0, NULL, NULL, strain, stress); + TacsScalar dfdN1Global, dfdN12Global, dfdN1CritGlobal, dfdN12CritGlobal; + TacsScalar D1, D2, D3; + this->computeCriticalGlobalBucklingStiffness(&D1, &D2, &D3); + L = this->panelLength; + N1Crit = computeCriticalGlobalAxialLoad(D1, L); + N12Crit = this->computeCriticalShearLoad(D1, D2, D3, L); + + this->bucklingEnvelopeSens(-stress[0], N1Crit, stress[2], N12Crit, + &dfdN1Global, &dfdN1CritGlobal, &dfdN12Global, + &dfdN12CritGlobal); + dfdN1Global *= dKSdf[3]; + dfdN12Global *= dKSdf[3]; + dfdN1CritGlobal *= dKSdf[3]; + dfdN12CritGlobal *= dKSdf[3]; + + // Add the sensitivity of the buckling failure criteria due to the dependence + // of the applied loads on the DVs + TacsScalar dfdStress[NUM_STRESSES]; + memset(dfdStress, 0, NUM_STRESSES * sizeof(TacsScalar)); + dfdStress[0] = -dfdN1Global; + dfdStress[2] = dfdN12Global; + this->addStressDVSens(elemIndex, scale, pt, X, strain, dfdStress, numDV, + dfdx); + + // Propogate the sensitivity of the buckling failure criteria w.r.t the + // critical loads back to the DVs + TacsScalar dfdD1, dfdD2, dfdD3, dfdPanelLength; + this->computeCriticalShearLoadSens(D1, D2, D3, L, &dfdD1, &dfdD2, &dfdD3, + &dfdPanelLength); + dfdD1 *= dfdN12CritGlobal; + dfdD2 *= dfdN12CritGlobal; + dfdD3 *= dfdN12CritGlobal; + dfdPanelLength *= dfdN12CritGlobal; + // N1CritGlobal = M_PI * M_PI * D1 / (L * L); + dfdD1 += dfdN1CritGlobal * (M_PI * M_PI / (L * L)); + dfdPanelLength += dfdN1CritGlobal * (-2.0 * M_PI * M_PI * D1 / (L * L * L)); + + if (this->panelLengthNum >= 0) { + dfdx[this->panelLengthLocalNum] += scale * dfdPanelLength; + } + + TacsScalar globalBucklingspSens, globalBucklingtpSens, globalBucklinghsSens, + globalBucklingtsSens, globalBucklingQstiffSens[NUM_Q_ENTRIES], + globalBucklingQpanelSens[NUM_Q_ENTRIES]; + this->computeCriticalGlobalBucklingStiffnessSens( + dfdD1, dfdD2, dfdD3, &globalBucklingspSens, &globalBucklingtpSens, + &globalBucklinghsSens, &globalBucklingtsSens, globalBucklingQpanelSens, + globalBucklingQstiffSens); + + // --- Panel thickness sensitivity --- + TacsScalar t = this->panelThick; + if (this->panelThickNum >= 0) { + int dvNum = this->panelThickLocalNum; + // --- Local buckling contribution --- + TacsScalar dMatdt = 0.25 * t * t; // d/dt(t^3/12) = t^2/4 + for (int ii = 0; ii < this->numPanelPlies; ii++) { + TacsScalar* Q = &(this->panelQMats[ii * NUM_Q_ENTRIES]); + dfdx[dvNum] += + scale * dMatdt * this->panelPlyFracs[ii] * + (localBucklingDMatSens[0] * Q[0] + localBucklingDMatSens[1] * Q[3] + + localBucklingDMatSens[2] * Q[1] + localBucklingDMatSens[3] * Q[5]); + } + // --- Global buckling contribution --- + dfdx[dvNum] += scale * globalBucklingtpSens; + } + + // --- Panel Ply fraction sensitivities --- + for (int ii = 0; ii < this->numPanelPlies; ii++) { + if (this->panelPlyFracNums[ii] >= 0) { + int dvNum = this->panelPlyFracLocalNums[ii]; + // --- Local buckling contribution --- + TacsScalar DFactor = t * t * t / 12.0; + TacsScalar* Q = &(this->panelQMats[ii * NUM_Q_ENTRIES]); + // Do df/dx += df/dD11 * dD11/dx + df/dD22 * dD22/dx + df/dD12 * dD12/dx + + // df/dD66 * dD66/dx + dfdx[dvNum] += + scale * DFactor * + (localBucklingDMatSens[0] * Q[0] + localBucklingDMatSens[1] * Q[3] + + localBucklingDMatSens[2] * Q[1] + localBucklingDMatSens[3] * Q[5]); + + // --- Global buckling contribution --- + dfdx[dvNum] += scale * (globalBucklingQpanelSens[0] * Q[0] + + globalBucklingQpanelSens[1] * Q[1] + + globalBucklingQpanelSens[2] * Q[2] + + globalBucklingQpanelSens[3] * Q[3] + + globalBucklingQpanelSens[4] * Q[4] + + globalBucklingQpanelSens[5] * Q[5]); + } + } + + // --- Stiffener height contribution --- + if (this->stiffenerHeightNum >= 0) { + int dvNum = this->stiffenerHeightLocalNum; + // --- Global buckling contribution --- + dfdx[dvNum] += scale * globalBucklinghsSens; + } + + // --- Stiffener thickness contribution --- + if (this->stiffenerThickNum >= 0) { + int dvNum = this->stiffenerThickLocalNum; + // --- Global buckling contribution --- + dfdx[dvNum] += scale * globalBucklingtsSens; + } + + // --- Stiffener ply fraction contributions --- + for (int ii = 0; ii < this->numStiffenerPlies; ii++) { + if (this->stiffenerPlyFracNums[ii] >= 0) { + int dvNum = this->stiffenerPlyFracLocalNums[ii]; + TacsScalar* Q = &(this->stiffenerQMats[ii * NUM_Q_ENTRIES]); + + // --- Global buckling contribution --- + dfdx[dvNum] += scale * (globalBucklingQstiffSens[0] * Q[0] + + globalBucklingQstiffSens[1] * Q[1] + + globalBucklingQstiffSens[2] * Q[2] + + globalBucklingQstiffSens[3] * Q[3] + + globalBucklingQstiffSens[4] * Q[4] + + globalBucklingQstiffSens[5] * Q[5]); + } + } + + // --- Stiffener pitch sensitivity --- + if (this->stiffenerPitchNum >= 0) { + dfdx[this->stiffenerPitchLocalNum] += + scale * (N12CritSens[4] * dfdN12CritLocal + + N1CritSens[4] * dfdN1CritLocal + globalBucklingspSens); + } +} + +// ============================================================================== +// Compute output quantities +// ============================================================================== +// Retrieve the design variable for plotting purposes +TacsScalar TACSBladeStiffenedShellConstitutive::evalDesignFieldValue( + int elemIndex, const double pt[], const TacsScalar X[], int index) { + switch (index) { + case 0: + return this->computeEffectiveThickness(); + case 1: + return this->computeEffectiveBendingThickness(); + case 2: + return this->panelLength; + case 3: + return this->stiffenerPitch; + case 4: + return this->panelThick; + case 5: + return this->stiffenerHeight; + case 6: + return this->stiffenerThick; + } + return 0.0; +} + +TacsScalar +TACSBladeStiffenedShellConstitutive::computeEffectiveBendingThickness() { + TacsScalar IStiff = this->computeStiffenerIzz(); + TacsScalar zStiff = this->computeStiffenerCentroidHeight(); + TacsScalar t = this->panelThick; + TacsScalar AStiff = this->computeStiffenerArea(); + TacsScalar Ieff = t * t * t / 12.0 + + (IStiff + AStiff * zStiff * zStiff) / this->stiffenerPitch; + return cbrt(12.0 * TacsRealPart(Ieff)); +} + +// ============================================================================== +// Helper functions for computing the stiffness matrices +// ============================================================================== + +// Compute the stiffness matrix +void TACSBladeStiffenedShellConstitutive::computeStiffness(TacsScalar C[]) { + TacsScalar* A = &C[0]; + TacsScalar* B = &C[6]; + TacsScalar* D = &C[12]; + TacsScalar* As = &C[18]; + TacsScalar* drill = &C[21]; + + // --- Zero out the C matrix --- + memset(C, 0, this->NUM_TANGENT_STIFFNESS_ENTRIES * sizeof(TacsScalar)); + + // Add the panel's stiffness contributions + this->computePanelStiffness(C); + + // Compute the stiffener's beam stiffness matrix ,then transform it to a shell + // stiffness matrix and add it + TacsScalar Cstiff[TACSBeamConstitutive::NUM_TANGENT_STIFFNESS_ENTRIES]; + this->computeStiffenerStiffness(Cstiff); + this->addStiffenerStiffness(Cstiff, C); +} + +void TACSBladeStiffenedShellConstitutive::computeSmearedStiffness( + const int numPlies, const TacsScalar* const QMats, + const TacsScalar* const AbarMats, const TacsScalar plyFractions[], + TacsScalar Q[], TacsScalar ABar[]) { + // Zero out the Q and ABar matrices + memset(Q, 0, this->NUM_Q_ENTRIES * sizeof(TacsScalar)); + memset(ABar, 0, this->NUM_ABAR_ENTRIES * sizeof(TacsScalar)); + + // Q = sum_i (f_i * Q_i) + for (int plyNum = 0; plyNum < numPlies; plyNum++) { + for (int entry = 0; entry < this->NUM_Q_ENTRIES; entry++) { + Q[entry] += plyFractions[plyNum] * QMats[NUM_Q_ENTRIES * plyNum + entry]; + } + for (int entry = 0; entry < this->NUM_ABAR_ENTRIES; entry++) { + ABar[entry] += + plyFractions[plyNum] * AbarMats[NUM_ABAR_ENTRIES * plyNum + entry]; + } + } +} + +void TACSBladeStiffenedShellConstitutive::computeSmearedStiffness( + const int numPlies, const TacsScalar* const QMats, + const TacsScalar plyFractions[], TacsScalar Q[]) { + // Zero out the Q and ABar matrices + memset(Q, 0, this->NUM_Q_ENTRIES * sizeof(TacsScalar)); + + // Q = sum_i (f_i * Q_i) + for (int plyNum = 0; plyNum < numPlies; plyNum++) { + for (int entry = 0; entry < this->NUM_Q_ENTRIES; entry++) { + Q[entry] += plyFractions[plyNum] * QMats[NUM_Q_ENTRIES * plyNum + entry]; + } + } +} + +// ============================================================================== +// Helper functions for transforming strains/stresses/stiffnesses between the +// panel and stiffener +// ============================================================================== + +// Given the shell mid-plane strains, compute the equivalent beam strains at the +// stiffener centroid +void TACSBladeStiffenedShellConstitutive::transformStrain( + const TacsScalar panelStrain[], TacsScalar stiffenerStrain[]) { + // Compute the offset of the stiffener centroid from the shell mid-plane + TacsScalar z = + this->computeStiffenerCentroidHeight() - 0.5 * this->panelThick; + + // Axial strain (contains contribution from panel bending) + stiffenerStrain[0] = panelStrain[0] + z * panelStrain[3]; + // Torsional strain (rotation around the 1 axis) + stiffenerStrain[1] = -0.5 * panelStrain[5]; + // Vertical bending strain (rotation around 2 axis) + stiffenerStrain[2] = panelStrain[3]; + // Horizontal bending strain (rotation around 3 axis) + stiffenerStrain[3] = 0.0; + // Vertical shear strain + stiffenerStrain[4] = panelStrain[7]; + // Horizontal shear strain (contains contribution from panel twisting) + stiffenerStrain[5] = 0.5 * (panelStrain[2] + z * panelStrain[5]); +} + +void TACSBladeStiffenedShellConstitutive::transformStrainSens( + const TacsScalar stiffenerStrainSens[], TacsScalar panelStrainSens[]) { + memset(panelStrainSens, 0, + TACSBeamConstitutive::NUM_STRESSES * sizeof(TacsScalar)); + TacsScalar z = + this->computeStiffenerCentroidHeight() - 0.5 * this->panelThick; + + panelStrainSens[0] = stiffenerStrainSens[0]; + panelStrainSens[1] = 0.0; + panelStrainSens[2] = 0.5 * stiffenerStrainSens[5]; + panelStrainSens[3] = stiffenerStrainSens[2] + z * stiffenerStrainSens[0]; + panelStrainSens[4] = 0.0; + panelStrainSens[5] = + 0.5 * (z * stiffenerStrainSens[5] - stiffenerStrainSens[1]); + panelStrainSens[6] = 0.0; + panelStrainSens[7] = stiffenerStrainSens[4]; + panelStrainSens[8] = 0.0; +} + +// Add the contribution of the stiffener stress to the panel stress +void TACSBladeStiffenedShellConstitutive::addStiffenerStress( + const TacsScalar stiffenerStress[], TacsScalar panelStress[]) { + TacsScalar pInv = 1.0 / this->stiffenerPitch; + // Compute the offset of the stiffener centroid from the shell mid-plane + TacsScalar z = + this->computeStiffenerCentroidHeight() - 0.5 * this->panelThick; + + panelStress[0] += pInv * stiffenerStress[0]; + panelStress[2] += pInv * 0.5 * stiffenerStress[5]; + panelStress[3] += pInv * stiffenerStress[2] + z * stiffenerStress[0]; + panelStress[5] += pInv * 0.5 * (z * stiffenerStress[5] - stiffenerStress[1]); + panelStress[7] += pInv * stiffenerStress[4]; +} + +// Add the contribution of the stiffener stiffness to the panel stiffness +void TACSBladeStiffenedShellConstitutive::addStiffenerStiffness( + const TacsScalar stiffenerStiffness[], TacsScalar panelStiffness[]) { + TacsScalar pInv = 1.0 / this->stiffenerPitch; + // Compute the offset of the stiffener centroid from the shell mid-plane + TacsScalar z = + this->computeStiffenerCentroidHeight() - 0.5 * this->panelThick; + + // Some shorthand for the entries of the stiffness matrix + TacsScalar* A = &(panelStiffness[0]); + TacsScalar* B = &(panelStiffness[6]); + TacsScalar* D = &(panelStiffness[12]); + TacsScalar* As = &(panelStiffness[18]); + TacsScalar* drill = &(panelStiffness[21]); + + // A: + A[0] += pInv * (stiffenerStiffness[0]); + A[2] += pInv * (stiffenerStiffness[5] / 2.0); + A[5] += pInv * (stiffenerStiffness[20] / 4.0); + + // B: + B[0] += pInv * (z * stiffenerStiffness[0] + stiffenerStiffness[2]); + B[2] += + pInv * (z * stiffenerStiffness[5] / 2.0 - stiffenerStiffness[1] / 2.0); + B[5] += + pInv * (z * stiffenerStiffness[20] / 4.0 - stiffenerStiffness[10] / 4.0); + + // D: + D[0] += pInv * (z * (z * stiffenerStiffness[0] + stiffenerStiffness[2]) + + z * stiffenerStiffness[2] + stiffenerStiffness[11]); + D[2] += + pInv * (z * (z * stiffenerStiffness[5] + stiffenerStiffness[14]) / 2.0 - + z * stiffenerStiffness[1] / 2.0 - stiffenerStiffness[7] / 2.0); + D[5] += + pInv * (z * (z * stiffenerStiffness[20] - stiffenerStiffness[10]) / 4.0 - + z * stiffenerStiffness[10] / 4.0 + stiffenerStiffness[6] / 4.0); + + // As: + As[2] += pInv * (stiffenerStiffness[18]); + + drill[0] += pInv * 0.5 * (stiffenerStiffness[18]) * DRILLING_REGULARIZATION; +} + +void TACSBladeStiffenedShellConstitutive::addStrainTransformProductDVsens( + const TacsScalar lhs[], const TacsScalar rhs[], const TacsScalar scale, + TacsScalar dfdx[]) { + // First compute the sensitivity of the stiffener centroid height w.r.t the + // design variables (panel thickness, stiffener height and stiffener + // thickness) zc = -panelThick/2 + computeStiffenerCentroidHeight() + TacsScalar dzdtp, dzdhs, dzdts; + dzdtp = -0.5; + this->computeStiffenerCentroidHeightSens(dzdts, dzdhs); + + // The sensitivities of the transformation matrix w.r.t the offset are: + // dTe[0,3]/dz = 1 + // dTe[5,5]/dz = 1/2 + + // Therefore: + // df/dfx[i] = dTe[0,3]/dz * lhs[0] *rhs[3] * dz/dx[i] + dTe[5,5]/dz * lhs[5] + // * rhs[5] * dz/dx[i] + + if (this->panelThickNum >= 0) { + dfdx[this->panelThickLocalNum] += + scale * (lhs[0] * rhs[3] + lhs[5] * 0.5 * rhs[5]) * dzdtp; + } + if (this->stiffenerHeightNum >= 0) { + dfdx[this->stiffenerHeightLocalNum] += + scale * (lhs[0] * rhs[3] + lhs[5] * 0.5 * rhs[5]) * dzdhs; + } + if (this->stiffenerThickNum >= 0) { + dfdx[this->stiffenerThickLocalNum] += + scale * (lhs[0] * rhs[3] + lhs[5] * 0.5 * rhs[5]) * dzdts; + } +} + +// ============================================================================== +// Helper functions for computing the panel stress/stiffness/failure +// ============================================================================== +// In future, these methods should be replaced by calls to another shell +// constitutive model + +// Compute the panel stress given the panel strains +void TACSBladeStiffenedShellConstitutive::computePanelStress( + const TacsScalar strain[], TacsScalar stress[]) { + TacsScalar C[this->NUM_TANGENT_STIFFNESS_ENTRIES]; + this->computePanelStiffness(C); + + TacsScalar* A = &C[0]; + TacsScalar* B = &C[6]; + TacsScalar* D = &C[12]; + TacsScalar* As = &C[18]; + TacsScalar drill = C[21]; + + this->computeStress(A, B, D, As, drill, strain, stress); +} + +// Add the derivative of the product of panel stresses with a vector psi to dfdx +void TACSBladeStiffenedShellConstitutive::addPanelStressDVSens( + const TacsScalar scale, const TacsScalar strain[], const TacsScalar psi[], + TacsScalar dfdx[]) { + // The stress calculation is: + // s = C * e + // [ s[0:3] ] = [ A 0 0 0 ][ e[0:3] ] + // [ s[3:6] ] = [ 0 D 0 0 ][ e[3:6] ] + // [ s[6:8] ] = [ 0 0 As 0 ][ e[6:8] ] + // [ s[8] ] = [ 0 0 0 drill ][ e[8] ] + + // Where: A = t * sum_i (plyFrac[i] * Q(theta[i])) + // D = t^3/12 * sum_i (plyFrac[i] * Q(theta[i])) + // As = t * sum_i (plyFrac[i] * Abar(theta[i])) * kcorr + // drill = DRILLING_REGULARIZATION * t/2 * (As[0,0] + As[1,1])) + + // Therefore, the derivative w.r.t the panel thickness is: + // d/dt (psi^T * s) = psi^T * (C * e) = + // psi[0:3]^T * [sum_i (plyFrac[i] * Q(theta[i]))] * e[0:3] + + // psi[3:6]^T * [sum_i (plyFrac[i] * Q(theta[i]))] * e[3:6] + + // psi[6:8]^T * [sum_i (plyFrac[i] * Abar(theta[i]))] * e[6:8] + + // psi[8] * DRILLING_REGULARIZATION * t/2 * (As[0,0] + As[1,1])) * e[8] + + // And the derivative w.r.t the ply fractions is: + // d/dplyFrac[i] (psi^T * s) = psi^T * (C * e) = + // t * psi[0:3]^T * Q(theta[i]) * e[0:3] + + // t^3/12 * psi[3:6]^T * Q(theta[i]) * e[3:6] + + // t * psi[6:8]^T * Abar(theta[i]) * e[6:8] *kcorr + + // t * psi[8] * DRILLING_REGULARIZATION * 1/2 * (As[0,0] + As[1,1])) * + // e[8]*kcorr + + // --- Panel thickness sensitivity --- + if (this->panelThickNum >= 0) { + int index = this->panelThickLocalNum - this->panelDVStartNum; + TacsScalar t24 = this->panelThick * this->panelThick / 4.0; + TacsScalar tInv = 1.0 / this->panelThick; + TacsScalar AMatProd, DMatProd, AsMatProd, drillProd; + + TacsScalar QPanel[this->NUM_Q_ENTRIES]; + TacsScalar AbarPanel[this->NUM_ABAR_ENTRIES]; + this->computeSmearedStiffness(this->numPanelPlies, this->panelQMats, + this->panelAbarMats, this->panelPlyFracs, + QPanel, AbarPanel); + + AMatProd = psi[0] * (QPanel[0] * strain[0] + QPanel[1] * strain[1] + + QPanel[2] * strain[2]) + + psi[1] * (QPanel[1] * strain[0] + QPanel[3] * strain[1] + + QPanel[4] * strain[2]) + + psi[2] * (QPanel[2] * strain[0] + QPanel[4] * strain[1] + + QPanel[5] * strain[2]); + + DMatProd = psi[3] * (QPanel[0] * strain[3] + QPanel[1] * strain[4] + + QPanel[2] * strain[5]) + + psi[4] * (QPanel[1] * strain[3] + QPanel[3] * strain[4] + + QPanel[4] * strain[5]) + + psi[5] * (QPanel[2] * strain[3] + QPanel[4] * strain[4] + + QPanel[5] * strain[5]); + + AsMatProd = + this->kcorr * + (psi[6] * (AbarPanel[0] * strain[6] + AbarPanel[1] * strain[7]) + + psi[7] * (AbarPanel[1] * strain[6] + AbarPanel[2] * strain[7])); + + drillProd = this->kcorr * psi[8] * DRILLING_REGULARIZATION * + (0.5 * (AbarPanel[0] + AbarPanel[2])) * strain[8]; + dfdx[index] += scale * (AMatProd + t24 * DMatProd + AsMatProd + drillProd); + } + + // --- Ply fraction sensitivity --- + TacsScalar t = this->panelThick; + TacsScalar t3 = t * t * t / 12.0; + for (int ii = 0; ii < this->numPanelPlies; ii++) { + if (this->panelPlyFracNums[ii] >= 0) { + int index = this->panelPlyFracLocalNums[ii] - this->panelDVStartNum; + TacsScalar* Q = &(this->panelQMats[NUM_Q_ENTRIES * ii]); + TacsScalar* Abar = &(this->panelAbarMats[NUM_ABAR_ENTRIES * ii]); + + dfdx[index] += + scale * t * + (psi[0] * (Q[0] * strain[0] + Q[1] * strain[1] + Q[2] * strain[2]) + + psi[1] * (Q[1] * strain[0] + Q[3] * strain[1] + Q[4] * strain[2]) + + psi[2] * (Q[2] * strain[0] + Q[4] * strain[1] + Q[5] * strain[2])); + + dfdx[index] += + scale * t3 * + (psi[3] * (Q[0] * strain[3] + Q[1] * strain[4] + Q[2] * strain[5]) + + psi[4] * (Q[1] * strain[3] + Q[3] * strain[4] + Q[4] * strain[5]) + + psi[5] * (Q[2] * strain[3] + Q[4] * strain[4] + Q[5] * strain[5])); + + dfdx[index] += scale * t * this->kcorr * + (psi[6] * (Abar[0] * strain[6] + Abar[1] * strain[7]) + + psi[7] * (Abar[1] * strain[6] + Abar[2] * strain[7])); + + dfdx[index] += this->kcorr * scale * t * psi[8] * + DRILLING_REGULARIZATION * (0.5 * (Abar[0] + Abar[2])) * + strain[8]; + } + } +} + +void TACSBladeStiffenedShellConstitutive::computePanelStiffness( + TacsScalar C[]) { + TacsScalar* A = &C[0]; + TacsScalar* B = &C[6]; + TacsScalar* D = &C[12]; + TacsScalar* As = &C[18]; + + // --- Zero out the C matrix --- + memset(C, 0, this->NUM_TANGENT_STIFFNESS_ENTRIES * sizeof(TacsScalar)); + + // Compute the smeared laminate properties + TacsScalar QPanel[this->NUM_Q_ENTRIES], ABarPanel[this->NUM_ABAR_ENTRIES]; + + this->computeSmearedStiffness(this->numPanelPlies, this->panelQMats, + this->panelAbarMats, this->panelPlyFracs, + QPanel, ABarPanel); + + // Add the panel's contributions to the A and D matrices + TacsScalar t = this->panelThick; + TacsScalar DFactor = t * t * t / 12.0; + + for (int ii = 0; ii < NUM_Q_ENTRIES; ii++) { + A[ii] += t * QPanel[ii]; + D[ii] += DFactor * QPanel[ii]; + } + + // Add the pane;'s contribution to the transverse shear matrix + for (int ii = 0; ii < NUM_ABAR_ENTRIES; ii++) { + As[ii] += t * ABarPanel[ii] * this->kcorr; + } + + // Add the drill stiffness + C[21] = DRILLING_REGULARIZATION * 0.5 * (As[0] + As[2]); +} + +// Compute the failure criteria in the panel +TacsScalar TACSBladeStiffenedShellConstitutive::computePanelFailure( + const TacsScalar strain[]) { + TacsScalar t = this->panelThick; + TacsScalar plyStrain[3]; + TacsScalar* fail = this->panelPlyFailValues; + int numPly = this->numPanelPlies; + + // Compute the strain state at the top of the panel + plyStrain[0] = strain[0] + 0.5 * t * strain[3]; + plyStrain[1] = strain[1] + 0.5 * t * strain[4]; + plyStrain[2] = strain[2] + 0.5 * t * strain[5]; + + // Compute the failure criteria for each ply angle at this strain state + for (int ii = 0; ii < numPly; ii++) { + fail[ii] = this->panelPly->failure(this->panelPlyAngles[ii], plyStrain); + } + + // Now repeat for the bottom of the panel + plyStrain[0] = strain[0] - 0.5 * t * strain[3]; + plyStrain[1] = strain[1] - 0.5 * t * strain[4]; + plyStrain[2] = strain[2] - 0.5 * t * strain[5]; + + for (int ii = 0; ii < numPly; ii++) { + fail[numPly + ii] = + this->panelPly->failure(this->panelPlyAngles[ii], plyStrain); + } + + // Return the aggregated failure value + return ksAggregation(fail, 2 * numPly, this->ksWeight); +} + +// Compute the derivative of the failure criteria in the panel w.r.t the DVs +TacsScalar TACSBladeStiffenedShellConstitutive::evalPanelFailureStrainSens( + const TacsScalar strain[], TacsScalar sens[]) { + TACSOrthotropicPly* ply = this->panelPly; + const int numPlies = this->numPanelPlies; + const int numStrain = TACSShellConstitutive::NUM_STRESSES; + TacsScalar** dFaildStrain = this->panelPlyFailStrainSens; + TacsScalar* fails = this->panelPlyFailValues; + const TacsScalar* angles = this->panelPlyAngles; + const TacsScalar t = this->panelThick; + + memset(sens, 0, numStrain * sizeof(TacsScalar)); + + // Compute the strain state at the top of the panel + TacsScalar plyStrain[3]; + plyStrain[0] = strain[0] + 0.5 * t * strain[3]; + plyStrain[1] = strain[1] + 0.5 * t * strain[4]; + plyStrain[2] = strain[2] + 0.5 * t * strain[5]; + + // Compute the failure criteria at this strain state for each ply angle and + // the sensitivity of the failure criteria w.r.t the strains + for (int ii = 0; ii < numPlies; ii++) { + TacsScalar plyFailStrainSens[3]; + fails[ii] = + ply->failureStrainSens(angles[ii], plyStrain, plyFailStrainSens); + // Convert the sensitivity w.r.t the tip strain to the sensitivity w.r.t + // beam strains + memset(dFaildStrain[ii], 0, numStrain * sizeof(TacsScalar)); + dFaildStrain[ii][0] = plyFailStrainSens[0]; + dFaildStrain[ii][1] = plyFailStrainSens[1]; + dFaildStrain[ii][2] = plyFailStrainSens[2]; + dFaildStrain[ii][3] = 0.5 * t * plyFailStrainSens[0]; + dFaildStrain[ii][4] = 0.5 * t * plyFailStrainSens[1]; + dFaildStrain[ii][5] = 0.5 * t * plyFailStrainSens[2]; + } + + // Now repeat for the bottom of the panel + plyStrain[0] = strain[0] - 0.5 * t * strain[3]; + plyStrain[1] = strain[1] - 0.5 * t * strain[4]; + plyStrain[2] = strain[2] - 0.5 * t * strain[5]; + + for (int ii = 0; ii < numPlies; ii++) { + TacsScalar plyFailStrainSens[3]; + fails[numPlies + ii] = + ply->failureStrainSens(angles[ii], plyStrain, plyFailStrainSens); + + memset(dFaildStrain[numPlies + ii], 0, numStrain * sizeof(TacsScalar)); + dFaildStrain[numPlies + ii][0] = plyFailStrainSens[0]; + dFaildStrain[numPlies + ii][1] = plyFailStrainSens[1]; + dFaildStrain[numPlies + ii][2] = plyFailStrainSens[2]; + dFaildStrain[numPlies + ii][3] = -0.5 * t * plyFailStrainSens[0]; + dFaildStrain[numPlies + ii][4] = -0.5 * t * plyFailStrainSens[1]; + dFaildStrain[numPlies + ii][5] = -0.5 * t * plyFailStrainSens[2]; + } + + TacsScalar fail = ksAggregationSensProduct( + fails, 2 * numPlies, numStrain, this->ksWeight, dFaildStrain, sens); + + return fail; +} + +// Add the derivative of the panel's failure w.r.t it's DVs +void TACSBladeStiffenedShellConstitutive::addPanelFailureDVSens( + const TacsScalar strain[], const TacsScalar scale, TacsScalar dfdx[]) { + // In order to add values directly to the dfdx array, we need to first compute + // the failure values for each ply, then compute the sensitivity of the + // aggregated failure value with respect to each ply's value. Then we can + // compute the sensitivity of each ply failure value with respect to the panel + // thickness and add the weighted sensitivity to the dfdx array. + + if (this->panelThickNum >= 0) { + TACSOrthotropicPly* ply = this->panelPly; + const int numPlies = this->numPanelPlies; + const int numStrain = TACSBeamConstitutive::NUM_STRESSES; + TacsScalar* dKSdFail = this->panelPlyFailSens; + TacsScalar* fails = this->panelPlyFailValues; + const TacsScalar* angles = this->panelPlyAngles; + const TacsScalar t = this->panelThick; + + // Compute the strain state at the top of the panel + TacsScalar plyStrain[3]; + plyStrain[0] = strain[0] + 0.5 * t * strain[3]; + plyStrain[1] = strain[1] + 0.5 * t * strain[4]; + plyStrain[2] = strain[2] + 0.5 * t * strain[5]; + + // Compute the failure criteria at this strain state for each ply angle + for (int ii = 0; ii < numPlies; ii++) { + fails[ii] = ply->failure(angles[ii], plyStrain); + } + + // Now repeat for the bottom of the panel + plyStrain[0] = strain[0] - 0.5 * t * strain[3]; + plyStrain[1] = strain[1] - 0.5 * t * strain[4]; + plyStrain[2] = strain[2] - 0.5 * t * strain[5]; + + for (int ii = 0; ii < numPlies; ii++) { + fails[numPlies + ii] = ply->failure(angles[ii], plyStrain); + } + + // Compute the sensitivity of the aggregated failure w.r.t each ply failure + ksAggregationSens(fails, 2 * numPlies, this->ksWeight, dKSdFail); + + // Compute the the sensitivity of the failure criteria w.r.t the strains + plyStrain[0] = strain[0] + 0.5 * t * strain[3]; + plyStrain[1] = strain[1] + 0.5 * t * strain[4]; + plyStrain[2] = strain[2] + 0.5 * t * strain[5]; + for (int ii = 0; ii < numPlies; ii++) { + TacsScalar plyFailStrainSens[3]; + ply->failureStrainSens(angles[ii], plyStrain, plyFailStrainSens); + // Convert the sensitivity w.r.t the strain to the sensitivity w.r.t + // panel thickness + dfdx[0] += + scale * dKSdFail[ii] * 0.5 * + (strain[3] * plyFailStrainSens[0] + strain[4] * plyFailStrainSens[1] + + strain[5] * plyFailStrainSens[2]); + } + + // Now repeat for the bottom of the panel + plyStrain[0] = strain[0] - 0.5 * t * strain[3]; + plyStrain[1] = strain[1] - 0.5 * t * strain[4]; + plyStrain[2] = strain[2] - 0.5 * t * strain[5]; + + for (int ii = 0; ii < numPlies; ii++) { + TacsScalar plyFailStrainSens[3]; + ply->failureStrainSens(angles[ii], plyStrain, plyFailStrainSens); + + dfdx[0] -= + scale * dKSdFail[numPlies + ii] * 0.5 * + (strain[3] * plyFailStrainSens[0] + strain[4] * plyFailStrainSens[1] + + strain[5] * plyFailStrainSens[2]); + } + } +} + +// ============================================================================== +// Helper functions for computing the stiffner's strain/stress/stiffness +// ============================================================================== +// In future, these methods should be replaced by calls to a beam +// constitutive model + +// Compute the beam stresses in the stiffener +void TACSBladeStiffenedShellConstitutive::computeStiffenerStress( + const TacsScalar stiffenerStrain[], TacsScalar stiffenerStress[]) { + int n = TACSBeamConstitutive::NUM_TANGENT_STIFFNESS_ENTRIES; + TacsScalar C[n]; + memset(C, 0, n * sizeof(TacsScalar)); + this->computeStiffenerStiffness(C); + TACSBeamConstitutive::computeStress(C, stiffenerStrain, stiffenerStress); +} + +void TACSBladeStiffenedShellConstitutive::addStiffenerStressDVSens( + const TacsScalar scale, const TacsScalar strain[], const TacsScalar psi[], + TacsScalar dfdx[]) { + TacsScalar psiStrain[TACSBeamConstitutive::NUM_STRESSES]; + for (int ii = 0; ii < TACSBeamConstitutive::NUM_STRESSES; ii++) { + psiStrain[ii] = psi[ii] * strain[ii]; + } + + // Compute the cross-section properties and their derivatives + TacsScalar A = this->computeStiffenerArea(); + TacsScalar Izz = this->computeStiffenerIzz(); + TacsScalar J = this->computeStiffenerJxx(); + TacsScalar dAdt, dAdh, dIzzdt, dIzzdh, dJdt, dJdh; + this->computeStiffenerAreaSens(dAdt, dAdh); + this->computeStiffenerIzzSens(dIzzdt, dIzzdh); + this->computeStiffenerJxxSens(dJdt, dJdh); + + // Compute the beam laminate properties + TacsScalar E, G, K; + this->computeEffectiveModulii(this->numStiffenerPlies, this->stiffenerQMats, + this->stiffenerPlyFracs, &E, &G); + K = this->kcorr; + + // --- Stiffener height sensitivities --- + if (this->stiffenerHeightNum >= 0) { + int index = this->stiffenerHeightLocalNum - this->stiffenerDVStartNum; + dfdx[index] += + scale * + ((E * psiStrain[0] + K * G * (psiStrain[4] + psiStrain[5])) * dAdh + + (E * psiStrain[2]) * dIzzdh + (G * psiStrain[1]) * dJdh); + } + + // --- Stiffener thickness sensitivities --- + if (this->stiffenerThickNum >= 0) { + int index = this->stiffenerThickLocalNum - this->stiffenerDVStartNum; + dfdx[index] += + scale * + ((E * psiStrain[0] + K * G * (psiStrain[4] + psiStrain[5])) * dAdt + + (E * psiStrain[2]) * dIzzdt + (G * psiStrain[1]) * dJdt); + } + + // --- Ply fraction sensitivities --- + for (int ii = 0; ii < this->numStiffenerPlies; ii++) { + if (this->stiffenerPlyFracNums[ii] >= 0) { + int index = + this->stiffenerPlyFracLocalNums[ii] - this->stiffenerDVStartNum; + + TacsScalar* Q = &(this->stiffenerQMats[ii * NUM_Q_ENTRIES]); + TacsScalar* Abar = &(this->stiffenerQMats[ii * NUM_ABAR_ENTRIES]); + + TacsScalar dEdx = Q[0] - (Q[1] * Q[1]) / Q[3]; + TacsScalar dGdx = Q[5]; + dfdx[index] += scale * (dEdx * (psiStrain[0] * A + psiStrain[2] * Izz) + + dGdx * (psiStrain[1] * J + psiStrain[4] * A * K + + psiStrain[5] * A * K)); + } + } +} + +// Compute the stiffener's beam stiffness matrix +void TACSBladeStiffenedShellConstitutive::computeStiffenerStiffness( + TacsScalar C[]) { + // --- Zero out the C matrix --- + memset( + C, 0, + TACSBeamConstitutive::NUM_TANGENT_STIFFNESS_ENTRIES * sizeof(TacsScalar)); + + TacsScalar A = this->computeStiffenerArea(); + TacsScalar Izz = this->computeStiffenerIzz(); + TacsScalar J = this->computeStiffenerJxx(); + + TacsScalar E, G; + this->computeEffectiveModulii(this->numStiffenerPlies, this->stiffenerQMats, + this->stiffenerPlyFracs, &E, &G); + + // Populate the matrix + C[0] = E * A; // C[0, 0] + C[6] = G * J; // C[1, 1] + C[11] = E * Izz; // C[2, 2] + C[18] = this->kcorr * G * A; // C[4, 4] + C[20] = this->kcorr * G * A; // C[5, 5] +} + +void TACSBladeStiffenedShellConstitutive::computeEffectiveModulii( + const int numPlies, const TacsScalar QMats[], const TacsScalar plyFracs[], + TacsScalar* E, TacsScalar* G) { + *E = 0.; + *G = 0.; + for (int plyNum = 0; plyNum < numPlies; plyNum++) { + const TacsScalar* Q = &(QMats[plyNum * NUM_Q_ENTRIES]); + *E += plyFracs[plyNum] * (Q[0] - Q[1] * Q[1] / Q[3]); + *G += plyFracs[plyNum] * Q[5]; + } + + // In theory the code below should produce exactly the same results as the + // code above, but for some reason (probably related to floating point + // arithmetic), it produces results that don't quite match complex step + // derivatives w.r.t the ply fractions + /* + TacsScalar Q[this->NUM_Q_ENTRIES], ABar[this->NUM_ABAR_ENTRIES]; + + this->computeSmearedStiffness(this->numStiffenerPlies, this->stiffenerQMats, + this->stiffenerAbarMats, + this->stiffenerPlyFracs, Q, ABar); + + // Compute the effective elastic and shear moduli + TacsScalar Q11 = Q[0]; + TacsScalar Q12 = Q[1]; + TacsScalar Q22 = Q[3]; + TacsScalar Q66 = Q[5]; + E = Q11 - Q12 * Q12 / Q22; + G = Q66; + */ +} + +// Compute the failure criteria for the stiffener +TacsScalar TACSBladeStiffenedShellConstitutive::computeStiffenerFailure( + const TacsScalar stiffenerStrain[]) { + TACSOrthotropicPly* ply = this->stiffenerPly; + + // Compute the strain state at the tip of the stiffener + TacsScalar zTipOffset = -(this->stiffenerHeight + this->stiffenerThick) - + this->computeStiffenerCentroidHeight(); + TacsScalar tipStrain[3]; + memset(tipStrain, 0, 3 * sizeof(TacsScalar)); + tipStrain[0] = stiffenerStrain[0] + zTipOffset * stiffenerStrain[2]; + + // Compute the failure criteria at this strain state for each ply angle + for (int ii = 0; ii < this->numStiffenerPlies; ii++) { + this->stiffenerPlyFailValues[ii] = + ply->failure(this->stiffenerPlyAngles[ii], tipStrain); + } + + // Returned the aggregated value over all plies + return ksAggregation(this->stiffenerPlyFailValues, this->numStiffenerPlies, + this->ksWeight); +} + +TacsScalar TACSBladeStiffenedShellConstitutive::evalStiffenerFailureStrainSens( + const TacsScalar strain[], TacsScalar sens[]) { + TACSOrthotropicPly* ply = this->stiffenerPly; + const int numPlies = this->numStiffenerPlies; + const int numStrain = TACSBeamConstitutive::NUM_STRESSES; + TacsScalar** dFaildStrain = this->stiffenerPlyFailStrainSens; + TacsScalar* fails = this->stiffenerPlyFailValues; + const TacsScalar* angles = this->stiffenerPlyAngles; + + memset(sens, 0, numStrain * sizeof(TacsScalar)); + + // Compute the strain state at the tip of the stiffener + TacsScalar zTipOffset = -(this->stiffenerHeight + this->stiffenerThick) - + this->computeStiffenerCentroidHeight(); + TacsScalar tipStrain[3]; + memset(tipStrain, 0, 3 * sizeof(TacsScalar)); + tipStrain[0] = strain[0] + zTipOffset * strain[2]; + + // Compute the failure criteria at this strain state for each ply angle and + // the sensitivity of the failure criteria w.r.t the strains + for (int ii = 0; ii < numPlies; ii++) { + TacsScalar plyFailStrainSens[3]; + fails[ii] = + ply->failureStrainSens(angles[ii], tipStrain, plyFailStrainSens); + // Convert the sensitivity w.r.t the tip strain to the sensitivity w.r.t + // beam strains + memset(dFaildStrain[ii], 0, numStrain * sizeof(TacsScalar)); + dFaildStrain[ii][0] = plyFailStrainSens[0]; + dFaildStrain[ii][2] = zTipOffset * plyFailStrainSens[0]; + } + + TacsScalar fail = ksAggregationSensProduct( + fails, numPlies, numStrain, this->ksWeight, dFaildStrain, sens); + + return fail; +} + +void TACSBladeStiffenedShellConstitutive::addStiffenerFailureDVSens( + const TacsScalar strain[], const TacsScalar scale, TacsScalar dfdx[]) { + TACSOrthotropicPly* ply = this->stiffenerPly; + TacsScalar* fails = this->stiffenerPlyFailValues; + const TacsScalar* angles = this->stiffenerPlyAngles; + TacsScalar* dKSdFail = this->panelPlyFailSens; + const int hNum = this->stiffenerHeightLocalNum - this->stiffenerDVStartNum; + const int tNum = this->stiffenerThickLocalNum - this->stiffenerDVStartNum; + + TacsScalar zTipOffset = -(this->stiffenerHeight + this->stiffenerThick) - + this->computeStiffenerCentroidHeight(); + TacsScalar dTipStraindh, dTipStraindt; + this->computeStiffenerCentroidHeightSens(dTipStraindt, dTipStraindh); + dTipStraindh = -dTipStraindh - 1.0; + dTipStraindt = -dTipStraindt - 1.0; + + // Compute the strain state at the tip of the stiffener + TacsScalar tipStrain[3]; + memset(tipStrain, 0, 3 * sizeof(TacsScalar)); + tipStrain[0] = strain[0] + zTipOffset * strain[2]; + dTipStraindh *= strain[2]; + dTipStraindt *= strain[2]; + + // Compute the failure criteria at this strain state for each ply angle + for (int ii = 0; ii < this->numStiffenerPlies; ii++) { + fails[ii] = ply->failure(angles[ii], tipStrain); + } + + // Compute the sensitivity of the KS aggregation w.r.t the failure values + ksAggregationSens(fails, this->numStiffenerPlies, this->ksWeight, dKSdFail); + + // Now go back through each ply, compute the strain sensitivity of it's + // failure, then convert it to a DV sensitivity and add it to the dfdx array + for (int ii = 0; ii < this->numStiffenerPlies; ii++) { + TacsScalar plyFailStrainSens[3]; + ply->failureStrainSens(angles[ii], tipStrain, plyFailStrainSens); + if (hNum >= 0) { + dfdx[hNum] += scale * dKSdFail[ii] * dTipStraindh * plyFailStrainSens[0]; + } + if (tNum >= 0) { + dfdx[tNum] += scale * dKSdFail[ii] * dTipStraindt * plyFailStrainSens[0]; + } + } +} + +// ============================================================================== +// Helper functions for computing stiffener cross-section properties +// ============================================================================== +TacsScalar TACSBladeStiffenedShellConstitutive::computeStiffenerArea() { + return (1.0 + this->flangeFraction) * this->stiffenerHeight * + this->stiffenerThick; +} + +void TACSBladeStiffenedShellConstitutive::computeStiffenerAreaSens( + TacsScalar& dAdt, TacsScalar& dAdh) { + dAdh = (1.0 + this->flangeFraction) * this->stiffenerThick; + dAdt = (1.0 + this->flangeFraction) * this->stiffenerHeight; +} + +TacsScalar +TACSBladeStiffenedShellConstitutive::computeStiffenerCentroidHeight() { + return -((1.0 + 0.5 * this->flangeFraction) * this->stiffenerThick + + 0.5 * this->stiffenerHeight) / + (1.0 + this->flangeFraction); +} + +void TACSBladeStiffenedShellConstitutive::computeStiffenerCentroidHeightSens( + TacsScalar& dzdt, TacsScalar& dzdh) { + TacsScalar kf = this->flangeFraction; + dzdh = -0.5 / (1.0 + kf); + dzdt = -(1.0 + 0.5 * kf) / (1.0 + kf); +} + +TacsScalar TACSBladeStiffenedShellConstitutive::computeStiffenerIzz() { + TacsScalar sh = this->stiffenerHeight; + TacsScalar st = this->stiffenerThick; + TacsScalar kf = this->flangeFraction; + TacsScalar sh2 = sh * sh; + TacsScalar st2 = st * st; + TacsScalar kf2 = kf * kf; + return sh * st * + (kf2 * st2 + 4.0 * kf * sh2 + 6.0 * kf * sh * st + 4.0 * kf * st2 + + sh2) / + (12.0 * (kf + 1.0)); +} + +void TACSBladeStiffenedShellConstitutive::computeStiffenerIzzSens( + TacsScalar& dIdt, TacsScalar& dIdh) { + TacsScalar sh = this->stiffenerHeight; + TacsScalar st = this->stiffenerThick; + TacsScalar kf = this->flangeFraction; + TacsScalar sh2 = sh * sh; + TacsScalar st2 = st * st; + TacsScalar kf2 = kf * kf; + + dIdt = sh * + (3.0 * kf2 * st2 + 4.0 * kf * sh2 + 12.0 * kf * sh * st + + 12.0 * kf * st2 + sh2) / + (12.0 * (kf + 1.0)); + + dIdh = st * + (kf2 * st2 + 12.0 * kf * sh2 + 12.0 * kf * sh * st + 4.0 * kf * st2 + + 3.0 * sh2) / + (12.0 * (kf + 1.0)); +} + +TacsScalar TACSBladeStiffenedShellConstitutive::computeStiffenerJxx() { + TacsScalar sh = this->stiffenerHeight; + TacsScalar st = this->stiffenerThick; + TacsScalar kf = this->flangeFraction; + return sh * (st * st * st) * (kf + 1.0) / 3.0; +} + +void TACSBladeStiffenedShellConstitutive::computeStiffenerJxxSens( + TacsScalar& dJdt, TacsScalar& dJdh) { + TacsScalar sh = this->stiffenerHeight; + TacsScalar st = this->stiffenerThick; + TacsScalar kf = this->flangeFraction; + + dJdt = sh * (st * st) * (kf + 1.0); + dJdh = (st * st * st) * (kf + 1.0) / 3.0; +} + +TacsScalar TACSBladeStiffenedShellConstitutive::computeStiffenerMOI() { + TacsScalar rho = this->stiffenerPly->getDensity(); + TacsScalar sh = this->stiffenerHeight; + TacsScalar st = this->stiffenerThick; + TacsScalar kf = this->flangeFraction; + TacsScalar A1 = sh * st; // Area of the stiffener web + TacsScalar A2 = kf * A1; // Area of the stiffener flange + TacsScalar z1 = -(st + 0.5 * sh); // Centroid of the stiffener web + TacsScalar z2 = -(0.5 * st); // Centroid of the stiffener flange + TacsScalar zc = + this->computeStiffenerCentroidHeight(); // Centroid of the whole + // stiffener section + + // Offsets of each area from the centroid of the whole stiffener section + TacsScalar dz1 = z1 - zc; + TacsScalar dz2 = z2 - zc; + + TacsScalar MOI1 = rho * A1 * sh * sh / + 12.0; // MOI of the stiffener web about it's own centroid + TacsScalar MOI2 = rho * A2 * st * st / 12.0; // MOI of the stiffener flange + // about it's own centroid + + // Parallel axis theorem to get the MOI of the whole stiffener about its + // centroid + TacsScalar MOI = MOI1 + MOI2 + rho * (A1 * dz1 * dz1 + A2 * dz2 * dz2); + return MOI; +} + +void TACSBladeStiffenedShellConstitutive::computeStiffenerMOISens( + TacsScalar& dMOIdt, TacsScalar& dMOIdh) { + TacsScalar rho = this->stiffenerPly->getDensity(); + TacsScalar sh = this->stiffenerHeight; + TacsScalar st = this->stiffenerThick; + TacsScalar kf = this->flangeFraction; + TacsScalar sh2 = sh * sh; + TacsScalar st2 = st * st; + TacsScalar kf2 = kf * kf; + + dMOIdt = 0.25 * sh * rho * + (1.0 * kf2 * st2 + 4.0 / 3.0 * kf * sh2 + 4.0 * kf * sh * st + + 4.0 * kf * st2 + sh2 / 3.0) / + (kf + 1.0); + + dMOIdh = 0.25 * st * rho * + (kf2 / 3.0 * st2 + 4.0 * kf * sh2 + 4.0 * kf * sh * st + + 4.0 / 3.0 * kf * st2 + 1.0 * sh2) / + (kf + 1.0); +} + +// ============================================================================== +// Buckling functions +// ============================================================================== + +void TACSBladeStiffenedShellConstitutive:: + computeCriticalGlobalBucklingStiffness(TacsScalar* D1, TacsScalar* D2, + TacsScalar* D3) { + // Compute the Q matrices for the panel and stiffener + TacsScalar QPanel[this->NUM_Q_ENTRIES], QStiffener[this->NUM_Q_ENTRIES]; + this->computeSmearedStiffness(this->numPanelPlies, this->panelQMats, + this->panelPlyFracs, QPanel); + this->computeSmearedStiffness(this->numStiffenerPlies, this->stiffenerQMats, + this->stiffenerPlyFracs, QStiffener); + + TacsScalar E1p, E1s, Ap, As, Ip, Is, Jp, Js, zs, tp, ps, tp3; + tp = this->panelThick; + tp3 = tp * tp * tp; + ps = this->stiffenerPitch; + Ap = tp * ps; + As = this->computeStiffenerArea(); + Ip = ps * tp3 / 12.0; + Is = this->computeStiffenerIzz(); + zs = this->computeStiffenerCentroidHeight(); + Js = this->computeStiffenerJxx(); + Jp = ps * tp3 / 12.0; + + // Compute the effective modulii of the panel and stiffener + E1p = QPanel[0] - QPanel[1] * QPanel[1] / QPanel[3]; + E1s = QStiffener[0] - QStiffener[1] * QStiffener[1] / QStiffener[3]; + + // --- 1-Direction bending stiffness --- + // Compute the modulus weighted centroid of the panel and stiffener + TacsScalar zn = E1s * As * (-0.5 * tp + zs) / (E1s * As + E1p * Ap); + + *D1 = (E1p * (Ip + Ap * zn * zn) + E1s * (Is + As * (zn - zs) * (zn - zs))) / + ps; + + // --- 2-direction bending stiffness --- + // TacsScalar D2Panel = (tp3 * QPanel[3]) / 12.0; + // TacsScalar D2Stiff = ((tp + 0.5 * ts) * (tp + 0.5 * ts) * (tp + 0.5 * ts) * + // (QPanel[3] + QStiffener[3])) / + // 6.0; + // *D2 = ps / ((ps - hs * kf) / D2Panel + (hs * kf) / D2Stiff); + // NOTE: I am ignoring the contribution of the stiffener flange to the + // 2-direction bending stiffness so that the stiffness used for the buckling + // calculation is consistent with the stiffness matrix. Not sure whether this + // is a good idea or not. + *D2 = tp3 / 12.0 * QPanel[3]; + + // --- Twisting stiffness --- + // Compute the shear modulus weighted centroid of the panel and stiffener + TacsScalar zg = 0.25 * QStiffener[5] * As * (-0.5 * tp + zs) / + (QStiffener[5] * As + QPanel[5] * Ap); + *D3 = (QPanel[5] * (Jp + Ap * zg * zg) + + 0.25 * QStiffener[5] * (Js + As * (zg - zs) * (zg - zs))) / + ps; + + TacsScalar C[NUM_TANGENT_STIFFNESS_ENTRIES]; +} + +void TACSBladeStiffenedShellConstitutive:: + computeCriticalGlobalBucklingStiffnessSens( + const TacsScalar dfdD1, const TacsScalar dfdD2, const TacsScalar dfdD3, + TacsScalar* psSens, TacsScalar* tpSens, TacsScalar* hsSens, + TacsScalar* tsSens, TacsScalar QpanelSens[], TacsScalar QstiffSens[]) { + // Zero the sensitivities + *tpSens = 0.0; + *psSens = 0.0; + *hsSens = 0.0; + *tsSens = 0.0; + memset(QstiffSens, 0, NUM_Q_ENTRIES * sizeof(TacsScalar)); + memset(QpanelSens, 0, NUM_Q_ENTRIES * sizeof(TacsScalar)); + + // Compute the Q matrices for the panel and stiffener + TacsScalar QPanel[this->NUM_Q_ENTRIES], QStiffener[this->NUM_Q_ENTRIES]; + this->computeSmearedStiffness(this->numPanelPlies, this->panelQMats, + this->panelPlyFracs, QPanel); + this->computeSmearedStiffness(this->numStiffenerPlies, this->stiffenerQMats, + this->stiffenerPlyFracs, QStiffener); + + TacsScalar E1p, E1s, Ap, As, Ip, Is, Jp, Js, zs, tp, ps, tp3; + tp = this->panelThick; + tp3 = tp * tp * tp; + ps = this->stiffenerPitch; + Ap = tp * ps; + As = this->computeStiffenerArea(); + Ip = ps * tp3 / 12.0; + Is = this->computeStiffenerIzz(); + zs = this->computeStiffenerCentroidHeight(); + Js = this->computeStiffenerJxx(); + Jp = ps * tp3 / 12.0; + + // Compute the effective modulii of the panel and stiffener + E1p = QPanel[0] - QPanel[1] * QPanel[1] / QPanel[3]; + E1s = QStiffener[0] - QStiffener[1] * QStiffener[1] / QStiffener[3]; + + // --- 1-Direction bending stiffness --- + + // Compute the modulus weighted centroid of the panel and stiffener + TacsScalar zn = E1s * As * (-0.5 * tp + zs) / (E1s * As + E1p * Ap); + TacsScalar zn2 = zn * zn; + TacsScalar zns2 = (zn - zs) * (zn - zs); + TacsScalar pInv = 1.0 / ps; + + // D1 = (E1p * (Ip + Ap * zn * zn) + E1s * (Is + As * (zn - zs) * (zn - zs))) + // / ps; + + TacsScalar E1pSens = dfdD1 * ((Ap * zn2 + Ip) / ps); + TacsScalar IpSens = dfdD1 * (E1p / ps); + TacsScalar ApSens = dfdD1 * (E1p * zn2 / ps); + TacsScalar ZnSens = + dfdD1 * (2.0 * (Ap * E1p * zn + As * E1s * (zn - zs)) / ps); + TacsScalar E1sSens = dfdD1 * ((As * zns2 + Is) / ps); + TacsScalar IsSens = dfdD1 * (E1s / ps); + TacsScalar AsSens = dfdD1 * (E1s * zns2 / ps); + TacsScalar ZsSens = dfdD1 * (2.0 * As * E1s * (-zn + zs) / ps); + *psSens += + dfdD1 * ((-E1p * (Ap * zn2 + Ip) - E1s * (As * zns2 + Is)) * pInv * pInv); + + // --- 2-direction bending stiffness --- + // D2 = tp3 / 12.0 * QPanel[3]; + *tpSens = dfdD2 * tp * tp / 4.0 * QPanel[3]; + QpanelSens[3] = dfdD2 * tp3 / 12.0; + + // --- Twisting stiffness --- + // D3 = (Gp * (Jp + Ap * zg**2) + 1 / 4 * Gs * (Js + As * (zg - zs) ** 2)) / + // ps Compute the shear modulus weighted centroid of the panel and stiffener + TacsScalar Gp = QPanel[5]; + TacsScalar Gs = QStiffener[5]; + TacsScalar zg = 0.25 * Gs * As * (-0.5 * tp + zs) / (Gs * As + Gp * Ap); + TacsScalar zg2 = zg * zg; + TacsScalar zgs2 = (zg - zs) * (zg - zs); + + TacsScalar GpSens = dfdD3 * ((Ap * zg2 + Jp) / ps); + TacsScalar JpSens = dfdD3 * (Gp / ps); + TacsScalar zgSens = + dfdD3 * ((2.0 * Ap * Gp * zg + 0.5 * As * Gs * (zg - zs)) / ps); + TacsScalar GsSens = dfdD3 * (0.25 * (As * zgs2 + Js) / ps); + TacsScalar JsSens = dfdD3 * (0.25 * Gs / ps); + ApSens += dfdD3 * (Gp * zg2 / ps); + AsSens += dfdD3 * (0.25 * Gs * zgs2 / ps); + ZsSens += dfdD3 * (0.5 * As * Gs * (-zg + zs) / ps); + *psSens += dfdD3 * ((-Gp * (Ap * zg2 + Jp) - 0.25 * Gs * (As * zgs2 + Js)) * + pInv * pInv); + + // Now we need to propogate the sensitivities w.r.t intermediate variables + // back to the inputs we want : + // zn = E1s * As * (-0.5 * tp + zs) / (E1s * As + E1p * Ap); + TacsScalar AE2 = (Ap * E1p + As * E1s) * (Ap * E1p + As * E1s); + E1sSens += ZnSens * (-Ap * As * E1p * (0.5 * tp - zs) / AE2); + AsSens += ZnSens * (-Ap * E1p * E1s * (0.5 * tp - zs) / AE2); + *tpSens += ZnSens * (-0.5 * As * E1s / (Ap * E1p + As * E1s)); + ZsSens += ZnSens * (As * E1s / (Ap * E1p + As * E1s)); + E1pSens += ZnSens * (Ap * As * E1s * (0.5 * tp - zs) / AE2); + ApSens += ZnSens * (As * E1p * E1s * (0.5 * tp - zs) / AE2); + + // zg = 0.25 * QStiffener[5] * As * (-0.5 * tp + zs) / (QStiffener[5] * As + + // QPanel[5] * Ap); + TacsScalar AG2 = (Ap * Gp + As * Gs) * (Ap * Gp + As * Gs); + GsSens += zgSens * (-0.25 * Ap * As * Gp * (0.5 * tp - zs) / AG2); + AsSens += zgSens * (-0.25 * Ap * Gp * Gs * (0.5 * tp - zs) / AG2); + *tpSens += zgSens * (-0.125 * As * Gs / (Ap * Gp + As * Gs)); + ZsSens += zgSens * (0.25 * As * Gs / (Ap * Gp + As * Gs)); + GpSens += zgSens * (0.25 * Ap * As * Gs * (0.5 * tp - zs) / AG2); + ApSens += zgSens * (0.25 * As * Gp * Gs * (0.5 * tp - zs) / AG2); + + // E1pSens + // E1p = QPanel[0] - QPanel[1] * QPanel[1] / QPanel[3]; + QpanelSens[0] += E1pSens; + QpanelSens[1] += E1pSens * (-2.0 * QPanel[1] / QPanel[3]); + QpanelSens[3] += + E1pSens * ((QPanel[1] * QPanel[1]) / (QPanel[3] * QPanel[3])); + + // E1sSens + // E1s = QStiff[0] - QStiff[1] * QStiff[1] / QStiff[3]; + QstiffSens[0] += E1sSens; + QstiffSens[1] += E1sSens * (-2.0 * QStiffener[1] / QStiffener[3]); + QstiffSens[3] += E1sSens * ((QStiffener[1] * QStiffener[1]) / + (QStiffener[3] * QStiffener[3])); + + // GpSens + // Gp = QPanel[5] + QpanelSens[5] += GpSens; + + // GsSens + // Gs = QStiffener[5] + QstiffSens[5] += GsSens; + + // IpSens + // Ip = ps * tp3 / 12.0; + *tpSens += IpSens * ps * (tp * tp / 4.0); + *psSens += IpSens * (tp3 / 12.0); + + // JpSens + // Jp = ps * tp3 / 12.0 + *psSens += JpSens * tp3 / 12.0; + *tpSens += JpSens * ps * tp * tp / 4.0; + + // ApSens + // Ap = tp * ps + *psSens += ApSens * tp; + *tpSens += ApSens * ps; + + // AsSens + TacsScalar dAdt, dAdh; + this->computeStiffenerAreaSens(dAdt, dAdh); + *tsSens += AsSens * dAdt; + *hsSens += AsSens * dAdh; + + // Js + TacsScalar dJdt, dJdh; + this->computeStiffenerJxxSens(dJdt, dJdh); + *tsSens += JsSens * dJdt; + *hsSens += JsSens * dJdh; + + // IsSens + TacsScalar dIdt, dIdh; + this->computeStiffenerIzzSens(dIdt, dIdh); + *tsSens += IsSens * dIdt; + *hsSens += IsSens * dIdh; + + // ZsSens + TacsScalar dZdt, dZdh, dzdtp; + this->computeStiffenerCentroidHeightSens(dZdt, dZdh); + *tsSens += ZsSens * dZdt; + *hsSens += ZsSens * dZdh; +} + +void TACSBladeStiffenedShellConstitutive::testGlobalBucklingStiffnessSens() { + const TacsScalar eps = 1e-6; + // Get the number of DVs + int num_dvs = this->getDesignVars(0, 0, NULL); + TacsScalar* DV0 = new TacsScalar[num_dvs]; + TacsScalar* DVPert = new TacsScalar[num_dvs]; + this->getDesignVars(0, num_dvs, DV0); + for (int i = 0; i < num_dvs; i++) { + DVPert[i] = DV0[i]; + } + + TacsScalar D1, D2, D3, tpSens[3], psSens[3], tsSens[3], hsSens[3], + QpSens[NUM_Q_ENTRIES], QsSens[NUM_Q_ENTRIES]; + this->computeCriticalGlobalBucklingStiffness(&D1, &D2, &D3); + this->computeCriticalGlobalBucklingStiffnessSens(1.0, 0.0, 0.0, &psSens[0], + &tpSens[0], &hsSens[0], + &tsSens[0], QpSens, QsSens); + this->computeCriticalGlobalBucklingStiffnessSens(0.0, 1.0, 0.0, &psSens[1], + &tpSens[1], &hsSens[1], + &tsSens[1], QpSens, QsSens); + this->computeCriticalGlobalBucklingStiffnessSens(0.0, 0.0, 1.0, &psSens[2], + &tpSens[2], &hsSens[2], + &tsSens[2], QpSens, QsSens); + + TacsScalar tpSensRelError[3], psSensRelError[3], tsSensRelError[3], + hsSensRelError[3]; + + // ============================================================================== + // stiffener pitch sensititivity + // ============================================================================== + printf("\nStiffener pitch sensitivity: \n"); + printf(" Analytic: D1sens = % 011.7e, D2sens = % 011.7e, D3sens = % 011.7e\n", + TacsRealPart(psSens[0]), TacsRealPart(psSens[1]), + TacsRealPart(psSens[2])); + TacsScalar D1Pert, D2Pert, D3Pert; +#ifdef TACS_USE_COMPLEX + DVPert[this->stiffenerPitchLocalNum] += TacsScalar(0.0, 1e-200); +#else + DVPert[this->stiffenerPitchLocalNum] += eps; +#endif + this->setDesignVars(0, num_dvs, DVPert); + this->computeCriticalGlobalBucklingStiffness(&D1Pert, &D2Pert, &D3Pert); + +#ifdef TACS_USE_COMPLEX + TacsScalar psSensFD = TacsImagPart(D1Pert) * 1e200; +#else + TacsScalar psSensFD = (D1Pert - D1) / eps; +#endif + if (psSens[0] == TacsScalar(0.)) { + psSensRelError[0] = 0.; + } else { + psSensRelError[0] = (psSensFD - psSens[0]) / psSens[0]; + } + printf(" FD: D1sens = % 011.7e, ", TacsRealPart(psSensFD)); + +#ifdef TACS_USE_COMPLEX + psSensFD = TacsImagPart(D2Pert) * 1e200; +#else + psSensFD = (D2Pert - D2) / eps; +#endif + if (psSens[1] == TacsScalar(0.)) { + psSensRelError[1] = 0.; + } else { + psSensRelError[1] = (psSensFD - psSens[1]) / psSens[1]; + } + printf("D2sens = % 011.7e, ", TacsRealPart(psSensFD)); + +#ifdef TACS_USE_COMPLEX + psSensFD = TacsImagPart(D3Pert) * 1e200; +#else + psSensFD = (D3Pert - D3) / eps; +#endif + if (psSens[2] == TacsScalar(0.)) { + psSensRelError[2] = 0.; + } else { + psSensRelError[2] = (psSensFD - psSens[2]) / psSens[2]; + } + printf("D3sens = % 011.7e\n", TacsRealPart(psSensFD)); + printf("Rel Error: D1sens = % 011.7e, D2sens = % 011.7e, D3sens = % 011.7e\n", + TacsRealPart(psSensRelError[0]), TacsRealPart(psSensRelError[1]), + TacsRealPart(psSensRelError[2])); + + DVPert[this->stiffenerPitchLocalNum] = DV0[this->stiffenerPitchLocalNum]; + this->setDesignVars(0, num_dvs, DVPert); + + // ============================================================================== + // Panel thickness sensitivity + // ============================================================================== + printf("\nPanel thickness sensitivity: \n"); + printf(" Analytic: D1sens = % 011.7e, D2sens = % 011.7e, D3sens = % 011.7e\n", + TacsRealPart(tpSens[0]), TacsRealPart(tpSens[1]), + TacsRealPart(tpSens[2])); +#ifdef TACS_USE_COMPLEX + DVPert[this->panelThickLocalNum] += TacsScalar(0.0, 1e-200); +#else + DVPert[this->panelThickLocalNum] += eps; +#endif + this->setDesignVars(0, num_dvs, DVPert); + this->computeCriticalGlobalBucklingStiffness(&D1Pert, &D2Pert, &D3Pert); + +#ifdef TACS_USE_COMPLEX + TacsScalar tpSensFD = TacsImagPart(D1Pert) * 1e200; +#else + TacsScalar tpSensFD = (D1Pert - D1) / eps; +#endif + if (tpSens[0] == TacsScalar(0.)) { + tpSensRelError[0] = 0.; + } else { + tpSensRelError[0] = (tpSensFD - tpSens[0]) / tpSens[0]; + } + printf(" FD: D1sens = % 011.7e, ", TacsRealPart(tpSensFD)); + +#ifdef TACS_USE_COMPLEX + tpSensFD = TacsImagPart(D2Pert) * 1e200; +#else + tpSensFD = (D2Pert - D2) / eps; +#endif + if (tpSens[1] == TacsScalar(0.)) { + tpSensRelError[1] = 0.; + } else { + tpSensRelError[1] = (tpSensFD - tpSens[1]) / tpSens[1]; + } + printf("D2sens = % 011.7e, ", TacsRealPart(tpSensFD)); + +#ifdef TACS_USE_COMPLEX + tpSensFD = TacsImagPart(D3Pert) * 1e200; +#else + tpSensFD = (D3Pert - D3) / eps; +#endif + if (tpSens[2] == TacsScalar(0.)) { + tpSensRelError[2] = 0.; + } else { + tpSensRelError[2] = (tpSensFD - tpSens[2]) / tpSens[2]; + } + printf("D3sens = % 011.7e\n", TacsRealPart(tpSensFD)); + printf("Rel Error: D1sens = % 011.7e, D2sens = % 011.7e, D3sens = % 011.7e\n", + TacsRealPart(tpSensRelError[0]), TacsRealPart(tpSensRelError[1]), + TacsRealPart(tpSensRelError[2])); + + DVPert[this->panelThickLocalNum] = DV0[this->panelThickLocalNum]; + this->setDesignVars(0, num_dvs, DVPert); + + // ============================================================================== + // Stiffener Height sensitivity + // ============================================================================== + printf("\nStiffener Height sensitivity: \n"); + printf(" Analytic: D1sens = % 011.7e, D2sens = % 011.7e, D3sens = % 011.7e\n", + TacsRealPart(hsSens[0]), TacsRealPart(hsSens[1]), + TacsRealPart(hsSens[2])); +#ifdef TACS_USE_COMPLEX + DVPert[this->stiffenerHeightLocalNum] += TacsScalar(0.0, 1e-200); +#else + DVPert[this->stiffenerHeightLocalNum] += eps; +#endif + this->setDesignVars(0, num_dvs, DVPert); + this->computeCriticalGlobalBucklingStiffness(&D1Pert, &D2Pert, &D3Pert); + +#ifdef TACS_USE_COMPLEX + TacsScalar hsSensFD = TacsImagPart(D1Pert) * 1e200; +#else + TacsScalar hsSensFD = (D1Pert - D1) / eps; +#endif + if (hsSens[0] == TacsScalar(0.)) { + hsSensRelError[0] = 0.; + } else { + hsSensRelError[0] = (hsSensFD - hsSens[0]) / hsSens[0]; + } + printf(" FD: D1sens = % 011.7e, ", TacsRealPart(hsSensFD)); + +#ifdef TACS_USE_COMPLEX + hsSensFD = TacsImagPart(D2Pert) * 1e200; +#else + hsSensFD = (D2Pert - D2) / eps; +#endif + if (hsSens[1] == TacsScalar(0.)) { + hsSensRelError[1] = 0.; + } else { + hsSensRelError[1] = (hsSensFD - hsSens[1]) / hsSens[1]; + } + printf("D2sens = % 011.7e, ", TacsRealPart(hsSensFD)); + +#ifdef TACS_USE_COMPLEX + hsSensFD = TacsImagPart(D3Pert) * 1e200; +#else + hsSensFD = (D3Pert - D3) / eps; +#endif + if (hsSens[2] == TacsScalar(0.)) { + hsSensRelError[2] = 0.; + } else { + hsSensRelError[2] = (hsSensFD - hsSens[2]) / hsSens[2]; + } + printf("D3sens = % 011.7e\n", TacsRealPart(hsSensFD)); + printf("Rel Error: D1sens = % 011.7e, D2sens = % 011.7e, D3sens = % 011.7e\n", + TacsRealPart(hsSensRelError[0]), TacsRealPart(hsSensRelError[1]), + TacsRealPart(hsSensRelError[2])); + + DVPert[this->stiffenerHeightLocalNum] = DV0[this->stiffenerHeightLocalNum]; + this->setDesignVars(0, num_dvs, DVPert); + + // ============================================================================== + // Stiffener thickness sensitivity + // ============================================================================== + printf("\nStiffener thickness sensitivity: \n"); + printf(" Analytic: D1sens = % 011.7e, D2sens = % 011.7e, D3sens = % 011.7e\n", + TacsRealPart(tsSens[0]), TacsRealPart(tsSens[1]), + TacsRealPart(tsSens[2])); +#ifdef TACS_USE_COMPLEX + DVPert[this->stiffenerThickLocalNum] += TacsScalar(0.0, 1e-200); +#else + DVPert[this->stiffenerThickLocalNum] += eps; +#endif + this->setDesignVars(0, num_dvs, DVPert); + this->computeCriticalGlobalBucklingStiffness(&D1Pert, &D2Pert, &D3Pert); + +#ifdef TACS_USE_COMPLEX + TacsScalar tsSensFD = TacsImagPart(D1Pert) * 1e200; +#else + TacsScalar tsSensFD = (D1Pert - D1) / eps; +#endif + if (tsSens[0] == TacsScalar(0.)) { + tsSensRelError[0] = 0.; + } else { + tsSensRelError[0] = (tsSensFD - tsSens[0]) / tsSens[0]; + } + printf(" FD: D1sens = % 011.7e, ", TacsRealPart(tsSensFD)); + +#ifdef TACS_USE_COMPLEX + tsSensFD = TacsImagPart(D2Pert) * 1e200; +#else + tsSensFD = (D2Pert - D2) / eps; +#endif + if (tsSens[1] == TacsScalar(0.)) { + tsSensRelError[1] = 0.; + } else { + tsSensRelError[1] = (tsSensFD - tsSens[1]) / tsSens[1]; + } + printf("D2sens = % 011.7e, ", TacsRealPart(tsSensFD)); + +#ifdef TACS_USE_COMPLEX + tsSensFD = TacsImagPart(D3Pert) * 1e200; +#else + tsSensFD = (D3Pert - D3) / eps; +#endif + if (tsSens[2] == TacsScalar(0.)) { + tsSensRelError[2] = 0.; + } else { + tsSensRelError[2] = (tsSensFD - tsSens[2]) / tsSens[2]; + } + printf("D3sens = % 011.7e\n", TacsRealPart(tsSensFD)); + printf("Rel Error: D1sens = % 011.7e, D2sens = % 011.7e, D3sens = % 011.7e\n", + TacsRealPart(tsSensRelError[0]), TacsRealPart(tsSensRelError[1]), + TacsRealPart(tsSensRelError[2])); + + DVPert[this->stiffenerThickLocalNum] = DV0[this->stiffenerThickLocalNum]; + this->setDesignVars(0, num_dvs, DVPert); + + delete[] DV0; + delete[] DVPert; +} + +TacsScalar +TACSBladeStiffenedShellConstitutive::computeCriticalLocalAxialLoadSens( + const TacsScalar D11, const TacsScalar D22, const TacsScalar D12, + const TacsScalar D66, const TacsScalar L, TacsScalar* D11Sens, + TacsScalar* D22Sens, TacsScalar* D12Sens, TacsScalar* D66Sens, + TacsScalar* LSens) { + double pi2 = M_PI * M_PI; + TacsScalar L2 = L * L; + TacsScalar root = sqrt(D11 * D22); + + *D11Sens = pi2 * root / (D11 * L2); + *D12Sens = 2.0 * pi2 / L2; + *D22Sens = pi2 * root / (D22 * L2); + *D66Sens = 4.0 * pi2 / L2; + *LSens = 4.0 * pi2 * (-D12 - 2.0 * D66 - root) / (L2 * L); + + return 2.0 * pi2 / L2 * (root + D12 + 2.0 * D66); +} + +TacsScalar TACSBladeStiffenedShellConstitutive::computeCriticalShearLoad( + TacsScalar D1, TacsScalar D2, TacsScalar D3, TacsScalar L) { + double ks = 50.0; + TacsScalar xi = sqrt(D1 * D2) / D3; + + TacsScalar N12_crit_1 = + (4.0 / (L * L)) * sqrt(D3 * D1 * xi) * (8.125 + 5.045 / xi); + TacsScalar N12_crit_2 = + (4.0 / (L * L)) * sqrt(D1 * D3) * (11.7 + 0.532 * xi + 0.938 * xi * xi); + + TacsScalar N12_min = 0.0; + if (TacsRealPart(N12_crit_1) < TacsRealPart(N12_crit_2)) { + N12_min = N12_crit_1; + } else { + N12_min = N12_crit_2; + } + + TacsScalar N12_diff = fabs(N12_crit_1 - N12_crit_2); + TacsScalar N12_crit = N12_min - log(1.0 + exp(-ks * N12_diff)) / ks; + + return N12_crit; +} + +TacsScalar TACSBladeStiffenedShellConstitutive::computeCriticalShearLoadSens( + const TacsScalar D1, const TacsScalar D2, const TacsScalar D3, + const TacsScalar L, TacsScalar* D1Sens, TacsScalar* D2Sens, + TacsScalar* D3Sens, TacsScalar* LSens) { + TacsScalar L2 = L * L; + TacsScalar L3 = L2 * L; + TacsScalar D32 = D3 * D3; + TacsScalar root = sqrt(D1 * D2); + TacsScalar xi = root / D3; + + TacsScalar N12CritVals[2]; + N12CritVals[0] = -(4.0 / L2) * sqrt(D3 * D1 * xi) * (8.125 + 5.045 / xi); + N12CritVals[1] = + -(4.0 / L2) * sqrt(D1 * D3) * (11.7 + 0.532 * xi + 0.938 * xi * xi); + + TacsScalar N12Crit, N12CritSens[2]; + N12Crit = ksAggregationSens(N12CritVals, 2, 50., N12CritSens); + N12Crit *= -1.0; + + TacsScalar dN12Crit1_dD1 = + sqrt(D1 * root) * (5.045 * D3 + 24.375 * root) / (D1 * L2 * root); + TacsScalar dN12Crit2_dD1 = + sqrt(D1 * D3) * (5.628 * D1 * D2 + 23.4 * D32 + 2.128 * D3 * root) / + (D1 * D32 * L2); + + *D1Sens = dN12Crit1_dD1 * N12CritSens[0] + dN12Crit2_dD1 * N12CritSens[1]; + + TacsScalar dN12Crit1_dD2 = + sqrt(D1 * root) * (-5.045 * D3 + 8.125 * root) / (D2 * L2 * root); + TacsScalar dN12Crit2_dD2 = + sqrt(D1 * D3) * (3.752 * D1 * D2 + 1.064 * D3 * root) / (D2 * D32 * L2); + + *D2Sens = dN12Crit1_dD2 * N12CritSens[0] + dN12Crit2_dD2 * N12CritSens[1]; + + TacsScalar dN12Crit1_dD3 = 20.18 * sqrt(D1 * root) / (L2 * root); + TacsScalar dN12Crit2_dD3 = + sqrt(D1 * D3) * (-5.628 * D1 * D2 + 23.4 * D32 - 1.064 * D3 * root) / + (D32 * D3 * L2); + + *D3Sens = dN12Crit1_dD3 * N12CritSens[0] + dN12Crit2_dD3 * N12CritSens[1]; + + TacsScalar dN12Crit1_dL = + sqrt(D1 * root) * (-40.36 * D3 - 65.0 * root) / (L3 * root); + + TacsScalar dN12Crit2_dL = + sqrt(D1 * D3) * (-7.504 * D1 * D2 - 93.6 * D32 - 4.256 * D3 * root) / + (D32 * L3); + + *LSens = dN12Crit1_dL * N12CritSens[0] + dN12Crit2_dL * N12CritSens[1]; + + return N12Crit; +} + +// Test that the derivatives computed by computeCriticalShearLoadSens are +// correct by testing them against finite-difference values +bool TACSBladeStiffenedShellConstitutive::testCriticalShearLoadSens( + const TacsScalar D1, const TacsScalar D2, const TacsScalar D3, + const TacsScalar L) { + TacsScalar D1Sens, D2Sens, D3Sens, LSens; + TacsScalar N12Crit = computeCriticalShearLoadSens(D1, D2, D3, L, &D1Sens, + &D2Sens, &D3Sens, &LSens); + + TacsScalar eps = 1e-6; + const double tol = 1e-5; + TacsScalar D1SensFD, D2SensFD, D3SensFD, LSensFD; + TacsScalar D1SensRelError, D2SensRelError, D3SensRelError, LSensRelError; + TacsScalar N12CritFD = computeCriticalShearLoad(D1 + eps, D2, D3, L); + D1SensFD = (N12CritFD - N12Crit) / eps; + D1SensRelError = (D1Sens - D1SensFD) / (D1SensFD); + + N12CritFD = computeCriticalShearLoad(D1, D2 + eps, D3, L); + D2SensFD = (N12CritFD - N12Crit) / eps; + D2SensRelError = (D2Sens - D2SensFD) / (D2SensFD); + + N12CritFD = computeCriticalShearLoad(D1, D2, D3 + eps, L); + D3SensFD = (N12CritFD - N12Crit) / eps; + D3SensRelError = (D3Sens - D3SensFD) / (D3SensFD); + + N12CritFD = computeCriticalShearLoad(D1, D2, D3, L + eps); + LSensFD = (N12CritFD - N12Crit) / eps; + LSensRelError = (LSens - LSensFD) / (LSensFD); + + printf("testCriticalShearLoadSens results:\n"); + printf("----------------------------------\n"); + printf("D1 = % 011.7e\n", D1); + printf("D2 = % 011.7e\n", D2); + printf("D3 = % 011.7e\n", D3); + printf("L = % 011.7e\n", L); + printf("N12Crit = % 011.7e\n", N12Crit); + printf( + "D1Sens = % 011.7e | D1SensFD = % 011.7e | D1SensRelError = % 011.7e\n", + D1Sens, D1SensFD, D1SensRelError); + printf( + "D2Sens = % 011.7e | D2SensFD = % 011.7e | D2SensRelError = % 011.7e\n", + D2Sens, D2SensFD, D2SensRelError); + printf( + "D3Sens = % 011.7e | D3SensFD = % 011.7e | D3SensRelError = % 011.7e\n", + D3Sens, D3SensFD, D3SensRelError); + printf( + " LSens = % 011.7e | LSensFD = % 011.7e | LSensRelError = % 011.7e\n", + LSens, LSensFD, LSensRelError); + printf( + "------------------------------------------------------------------------" + "\n"); + + return fabs(TacsRealPart(D1SensRelError)) < tol && + fabs(TacsRealPart(D2SensRelError)) < tol && + fabs(TacsRealPart(D3SensRelError)) < tol && + fabs(TacsRealPart(LSensRelError)) < tol; +} + +TacsScalar TACSBladeStiffenedShellConstitutive::bucklingEnvelope( + const TacsScalar N1, const TacsScalar N1Crit, const TacsScalar N12, + const TacsScalar N12Crit) { + TacsScalar N1Term = N1 / N1Crit; + TacsScalar N12Term = N12 / N12Crit; + TacsScalar root = sqrt(N1Term * N1Term + 4.0 * N12Term * N12Term); + return 0.5 * (N1Term + root); +} + +// Compute the sensitivity of the buckling failure criterion w.r.t the loads and +// critical loads +TacsScalar TACSBladeStiffenedShellConstitutive::bucklingEnvelopeSens( + const TacsScalar N1, const TacsScalar N1Crit, const TacsScalar N12, + const TacsScalar N12Crit, TacsScalar* dfdN1, TacsScalar* dfdN1Crit, + TacsScalar* dfdN12, TacsScalar* dfdN12Crit) { + TacsScalar N1Term = N1 / N1Crit; + TacsScalar N12Term = N12 / N12Crit; + TacsScalar root = sqrt(N1Term * N1Term + 4.0 * N12Term * N12Term); + if (dfdN1 != NULL) { + // *dfdN1 = 1.0 / N1Crit; + *dfdN1 = N1 / (2.0 * N1Crit * N1Crit * root) + 1.0 / (2.0 * N1Crit); + } + if (dfdN12 != NULL) { + *dfdN12 = 2.0 * N12 / (N12Crit * N12Crit * root); + } + if (dfdN1Crit != NULL) { + *dfdN1Crit = -N1 * N1 / (2.0 * N1Crit * N1Crit * N1Crit * root) - + N1 / (2.0 * N1Crit * N1Crit); + } + if (dfdN12Crit != NULL) { + *dfdN12Crit = -2.0 * N12 * N12 / (N12Crit * N12Crit * N12Crit * root); + } + return bucklingEnvelope(N1, N1Crit, N12, N12Crit); +} + +bool TACSBladeStiffenedShellConstitutive::testBucklingEnvelopeSens( + const TacsScalar N1, const TacsScalar N1Crit, const TacsScalar N12, + const TacsScalar N12Crit) { + const double tol = 1e-5; + TacsScalar dfdN1, dfdN1Crit, dfdN12, dfdN12Crit; + TacsScalar f = bucklingEnvelopeSens(N1, N1Crit, N12, N12Crit, &dfdN1, + &dfdN1Crit, &dfdN12, &dfdN12Crit); + + TacsScalar eps = 1e-6; + TacsScalar N1p = N1 + eps; + TacsScalar N1Critp = N1Crit + eps; + TacsScalar N12p = N12 + eps; + TacsScalar N12Critp = N12Crit + eps; + + TacsScalar fp = bucklingEnvelope(N1p, N1Crit, N12, N12Crit); + TacsScalar dfdN1FD = (fp - f) / eps; + TacsScalar dfdN1RelError = (dfdN1 - dfdN1FD) / dfdN1FD; + + fp = bucklingEnvelope(N1, N1Critp, N12, N12Crit); + TacsScalar dfdN1CritFD = (fp - f) / eps; + TacsScalar dfdN1CritRelError = (dfdN1Crit - dfdN1CritFD) / dfdN1CritFD; + + fp = bucklingEnvelope(N1, N1Crit, N12p, N12Crit); + TacsScalar dfdN12FD = (fp - f) / eps; + TacsScalar dfdN12RelError = (dfdN12 - dfdN12FD) / dfdN12FD; + + fp = bucklingEnvelope(N1, N1Crit, N12, N12Critp); + TacsScalar dfdN12CritFD = (fp - f) / eps; + TacsScalar dfdN12CritRelError = (dfdN12Crit - dfdN12CritFD) / dfdN12CritFD; + + printf("testBucklingEnvelopeSens results:"); + printf( + "N1 = % 011.7e, N1Crit = % 011.7e, N12 = % 011.7e, N12Crit = % 011.7e\n", + N1, N1Crit, N12, N12Crit); + printf("f: % 011.7e\n", f); + printf("dfdN1: % 011.7e, dfdN1p: % 011.7e, rel error: % 011.7e\n", dfdN1, + dfdN1FD, dfdN1RelError); + printf("dfdN1Crit: % 011.7e, dfdN1Critp: % 011.7e, rel error: % 011.7e\n", + dfdN1Crit, dfdN1CritFD, dfdN1CritRelError); + printf("dfdN12: % 011.7e, dfdN12p: % 011.7e, rel error: % 011.7e\n", dfdN12, + dfdN12FD, dfdN1CritRelError); + printf("dfdN12Crit: % 011.7e, dfdN12Critp: % 011.7e, rel error: % 011.7e\n", + dfdN12Crit, dfdN12CritFD, dfdN12CritRelError); + + return (fabs(TacsRealPart(dfdN1RelError)) < tol && + fabs(TacsRealPart(dfdN1CritRelError)) < tol && + fabs(TacsRealPart(dfdN12RelError)) < tol && + fabs(TacsRealPart(dfdN12CritRelError)) < tol); +} + +// ============================================================================== +// Utility functions +// ============================================================================== + +void printStiffnessMatrix(const TacsScalar* const C) { + const TacsScalar* A = &C[0]; + const TacsScalar* B = &C[6]; + const TacsScalar* D = &C[12]; + const TacsScalar* As = &C[18]; + TacsScalar drill = C[21]; + + printf("[\n"); + printf( + "[% 03.5e, % 03.5e, % 03.5e | % 03.5e, % 03.5e, % 03.5e | % 03.5e, % " + "03.5e | % 03.5e]\n", + A[0], A[1], A[2], B[0], B[1], B[2], 0., 0., 0.); + printf( + "[% 03.5e, % 03.5e, % 03.5e | % 03.5e, % 03.5e, % 03.5e | % 03.5e, % " + "03.5e | % 03.5e]\n", + A[1], A[3], A[4], B[1], B[3], B[4], 0., 0., 0.); + printf( + "[% 03.5e, % 03.5e, % 03.5e | % 03.5e, % 03.5e, % 03.5e | % 03.5e, % " + "03.5e | % 03.5e]\n", + A[2], A[4], A[5], B[2], B[4], B[5], 0., 0., 0.); + + printf( + "--------------------------------------------------------------------" + "----" + "--------------------------------------------------------\n"); + + printf( + "[% 03.5e, % 03.5e, % 03.5e | % 03.5e, % 03.5e, % 03.5e | % 03.5e, % " + "03.5e | % 03.5e]\n", + B[0], B[1], B[2], D[0], D[1], D[2], 0., 0., 0.); + printf( + "[% 03.5e, % 03.5e, % 03.5e | % 03.5e, % 03.5e, % 03.5e | % 03.5e, % " + "03.5e | % 03.5e]\n", + B[1], B[3], B[4], D[1], D[3], D[4], 0., 0., 0.); + printf( + "[% 03.5e, % 03.5e, % 03.5e | % 03.5e, % 03.5e, % 03.5e | % 03.5e, % " + "03.5e | % 03.5e]\n", + B[2], B[4], B[5], D[2], D[4], D[5], 0., 0., 0.); + + printf( + "--------------------------------------------------------------------" + "----" + "--------------------------------------------------------\n"); + + printf( + "[% 03.5e, % 03.5e, % 03.5e | % 03.5e, % 03.5e, % 03.5e | % 03.5e, % " + "03.5e | % 03.5e]\n", + 0., 0., 0., 0., 0., 0., As[0], As[1], 0.); + printf( + "[% 03.5e, % 03.5e, % 03.5e | % 03.5e, % 03.5e, % 03.5e | % 03.5e, % " + "03.5e | % 03.5e]\n", + 0., 0., 0., 0., 0., 0., As[1], As[2], 0.); + + printf( + "--------------------------------------------------------------------" + "----" + "--------------------------------------------------------\n"); + + printf( + "[% 03.5e, % 03.5e, % 03.5e | % 03.5e, % 03.5e, % 03.5e | % 03.5e, % " + "03.5e | % 03.5e]\n", + 0., 0., 0., 0., 0., 0., 0., 0., drill); + printf("]\n"); +} diff --git a/src/constitutive/TACSBladeStiffenedShellConstitutive.h b/src/constitutive/TACSBladeStiffenedShellConstitutive.h new file mode 100644 index 000000000..c75d2b597 --- /dev/null +++ b/src/constitutive/TACSBladeStiffenedShellConstitutive.h @@ -0,0 +1,1064 @@ +/* +============================================================================= +Blade-Stiffened Shell Constitutive Model +============================================================================= +@File : TACSBladeStiffenedShellConstitutive.h +@Date : 2023/04/05 +@Author : Alasdair Christison Gray +@Description : Constitutive model for a blade-stiffened shell. Based on the +bladeFSDT model from previous versions of TACS developed by Graeme Kennedy. +*/ + +#pragma once + +// ============================================================================= +// Standard Library Includes +// ============================================================================= + +// ============================================================================= +// Extension Includes +// ============================================================================= +#include "TACSBeamConstitutive.h" +#include "TACSMaterialProperties.h" +#include "TACSShellConstitutive.h" +#include "TacsUtilities.h" + +void printStiffnessMatrix(const TacsScalar* const C); + +// ============================================================================= +// Class Declaration +// ============================================================================= + +/** + * @brief Constitutive model for a blade-stiffened shell + * + * This constitutive class models a shell stiffened with T-shaped stiffeners. + * The stiffeners are not explicitly modelled. Instead, their stiffness is + * "smeared" across the shell. + * + * | | ^ + * | | | + * | | | + * | | height + * | <-------pitch------> | | + * Stiffener | | v + * thickness ---> ----------------- ----------------- + * --------------------------------------------------- <--- Panel thickness + * + * ----------> 2-direction + * | + * | + * | + * | + * v + * 3-direction (shell normal) + * + * The stiffener is modelled as a T-shaped beam as shown above, and is modelled + * as pointing in the opposite of the shell normal. The thickness of the + * stiffener web and flange are the same. The ratio of the stiffener flange + * width to the stiffener height is controlled by the flangeFraction parameter, + * which defaults to 1.0 (i.e. the flange width is equal to the stiffener + * height). This value can be set when creating the constitutive object and is + * then fixed. + * + * The panel and stiffener are modelled as laminates, both of which are + * parameterised by an arbitrary number of ply angles and fractions. The + * laminate properties are then computed using a smeared stiffness approach, + * which assumes that the various ply angles are distributed evenly throughout + * the thickness of the panel. This is a valid assumption for thick laminates. + * + * The design variables (in order) for this constitutive model are: + * - Panel length + * - Stiffener pitch + * - Panel thickness + * - Panel ply fractions + * - Stiffener height + * - Stiffener thickness + * - Stiffener ply fractions + * + * The failure criterion returned by this model combines numerous possible + * failure modes into a single value. A material failure criterion (which one + * depends on the Orthotropic ply objects you pass to this class) is computed at + * the upper and lower surface of the panel and at the tip of the stiffener, + * this calculation is performed for every ply angle present in the panel and + * stiffener laminate. Additionally buckling criteria are computed for combined + * shear and axial buckling for both a global buckling mode (i.e the entire + * panel buckles) and a local buckling mode (i.e. the panel buckles between a + * pair of stiffeners). These buckling failure values are aggregated along with + * the material failure values into a single failure value using KS aggregation. + * The smoothness and conservatism of this aggregation can be controlled using + * the `setKSWeight` method. + * + * The panel length design variables do not directly affect the stiffness or + * stresses computed by the model, their only role is to allow the computation + * of the critical buckling loads used in the buckling failure criteria. When + * using this constitutive model, you must also add a set of + * PanelLengthConstraints to force the panel length design variables to be equal + * to the true physical panel length. Despite seeming needlessly complex, this + * approach is necessary because this constitutive model has no information + * about the geometry of your finite element model and so cannot compute the + * panel length itself. + * + * WARNING: If you use ply fractions as design variables, it is currently up to + * you to add DVConstraints to ensure that the sum of the fractions is equal + * to 1.0. This is not done automatically (yet). + */ +class TACSBladeStiffenedShellConstitutive : public TACSShellConstitutive { + public: + /** + * @brief Construct a new TACSBladeStiffenedShellConstitutive object + * + * @param _panelPly Orthotropic ply object for the panel + * @param _stiffenerPly Orthotropic ply object for the stiffener + * @param _kcorr Shear correction factor + * @param _panelLength Panel length value + * @param _panelLengthNum Panel length design variable number + * @param _stiffenerPitch Stiffener pitch value + * @param _stiffenerPitchNum Stiffener pitch design variable number + * @param _panelThick Panel thickness value + * @param _panelThickNum Panel thickness design variable number + * @param _numPanelPlies Number of ply angles in the panel laminate + * @param _panelPlyAngles Panel ply angles + * @param _panelPlyFracs Panel ply fractions + * @param _panelPlyFracNums Panel ply fraction design variable numbers + * @param _stiffenerHeight Stiffener height value + * @param _stiffenerHeightNum Stiffener height design variable number + * @param _stiffenerThick Stiffener thickness value + * @param _stiffenerThickNum Stiffener thickness design variable number + * @param _numStiffenerPlies Number of ply angles in the stiffener laminate + * @param _stiffenerPlyAngles Stiffener ply angles + * @param _stiffenerPlyFracs Stiffener ply fractions + * @param _stiffenerPlyFracNums Stiffener ply fraction design variable numbers + * @param _flangeFraction Stiffener base width as a fraction of the stiffener + * height + */ + TACSBladeStiffenedShellConstitutive( + TACSOrthotropicPly* _panelPly, TACSOrthotropicPly* _stiffenerPly, + TacsScalar _kcorr, TacsScalar _panelLength, int _panelLengthNum, + TacsScalar _stiffenerPitch, int _stiffenerPitchNum, + TacsScalar _panelThick, int _panelThickNum, int _numPanelPlies, + TacsScalar _panelPlyAngles[], TacsScalar _panelPlyFracs[], + int _panelPlyFracNums[], TacsScalar _stiffenerHeight, + int _stiffenerHeightNum, TacsScalar _stiffenerThick, + int _stiffenerThickNum, int _numStiffenerPlies, + TacsScalar _stiffenerPlyAngles[], TacsScalar _stiffenerPlyFracs[], + int _stiffenerPlyFracNums[], TacsScalar _flangeFraction = 1.0); + + ~TACSBladeStiffenedShellConstitutive(); + + // ============================================================================== + // Set non-default values + // ============================================================================== + /** + * @brief Set the Stiffener Pitch DV Bounds + * + * @param lowerBound Lower bound + * @param upperBound Upper bound + */ + void setStiffenerPitchBounds(TacsScalar lowerBound, TacsScalar upperBound); + + /** + * @brief Set the Stiffener Height DV Bounds + * + * @param lowerBound Lower bound + * @param upperBound Upper bound + */ + void setStiffenerHeightBounds(TacsScalar lowerBound, TacsScalar upperBound); + + /** + * @brief Set the Stiffener Thickness DV Bounds + * + * @param lowerBound Lower bound + * @param upperBound Upper bound + */ + void setStiffenerThicknessBounds(TacsScalar lowerBound, + TacsScalar upperBound); + + /** + * @brief Set the Panel Pitch DV Bounds + * + * @param lowerBound Lower bound + * @param upperBound Upper bound + */ + void setPanelThicknessBounds(TacsScalar lowerBound, TacsScalar upperBound); + + /** + * @brief Set the Stiffener Ply Fraction DV Bounds + * + * @param lowerBounds Lower bounds for each ply fraction + * @param upperBounds Upper bounds for each ply fraction + */ + void setStiffenerPlyFractionBounds(TacsScalar lowerBounds[], + TacsScalar upperBounds[]); + + /** + * @brief Set the Panel Ply Fraction DV Bounds + * + * @param lowerBounds Lower bounds for each ply fraction + * @param upperBounds Upper bounds for each ply fraction + */ + void setPanelPlyFractionBounds(TacsScalar lowerBounds[], + TacsScalar upperBounds[]); + + /** + * @brief Set the Stiffener Ply Fractions + * + * @param plyFractions Ply fractions + */ + void setStiffenerPlyFractions(TacsScalar plyFractions[]); + + /** + * @brief Set the Panel Ply Fractions + * + * @param plyFractions Ply fractions + */ + void setPanelPlyFractions(TacsScalar plyFractions[]); + + /** + * @brief Set the weight used for aggregating the failure criteria through the + * shell thickness + * + * @param _ksWeight + */ + inline void setKSWeight(double _ksWeight) { this->ksWeight = _ksWeight; } + + // ============================================================================== + // Setting/getting design variable information + // ============================================================================== + // Retrieve the global design variable numbers + int getDesignVarNums(int elemIndex, int dvLen, int dvNums[]); + + // Set the element design variable from the design vector + int setDesignVars(int elemIndex, int dvLen, const TacsScalar dvs[]); + + // Get the element design variables values + int getDesignVars(int elemIndex, int dvLen, TacsScalar dvs[]); + + // Get the lower and upper bounds for the design variable values + int getDesignVarRange(int elemIndex, int dvLen, TacsScalar lb[], + TacsScalar ub[]); + + // ============================================================================== + // Evaluate mass properties + // ============================================================================== + // Evaluate the mass per unit area + TacsScalar evalDensity(int elemIndex, const double pt[], + const TacsScalar X[]); + + // Add the derivative of the density w.r.t. the design variables + void addDensityDVSens(int elemIndex, TacsScalar scale, const double pt[], + const TacsScalar X[], int dvLen, TacsScalar dfdx[]); + + // Evaluate the mass moments + void evalMassMoments(int elemIndex, const double pt[], const TacsScalar X[], + TacsScalar moments[]); + + // Add the sensitivity of the mass moments + void addMassMomentsDVSens(int elemIndex, const double pt[], + const TacsScalar X[], const TacsScalar scale[], + int dvLen, TacsScalar dfdx[]); + + // ============================================================================== + // Evaluate thermal properties + // ============================================================================== + // Evaluate the specific heat, Not implemented for this class + TacsScalar evalSpecificHeat(int elemIndex, const double pt[], + const TacsScalar X[]); + + // ============================================================================== + // Compute stress/strain/stiffness + // ============================================================================== + // Evaluate the stress + void evalStress(int elemIndex, const double pt[], const TacsScalar X[], + const TacsScalar e[], TacsScalar s[]); + + // Add the derivative of the product of stress with a vector psi to dfdx + void addStressDVSens(int elemIndex, TacsScalar scale, const double pt[], + const TacsScalar X[], const TacsScalar strain[], + const TacsScalar psi[], int dvLen, TacsScalar dfdx[]); + + // Evaluate the tangent stiffness + void evalTangentStiffness(int elemIndex, const double pt[], + const TacsScalar X[], TacsScalar C[]); + + // ============================================================================== + // Compute failure criteria + // ============================================================================== + // Calculate the point-wise failure criteria + TacsScalar evalFailure(int elemIndex, const double pt[], const TacsScalar X[], + const TacsScalar e[]); + + // Evaluate the derivative of the failure criteria w.r.t. the strain + TacsScalar evalFailureStrainSens(int elemIndex, const double pt[], + const TacsScalar X[], const TacsScalar e[], + TacsScalar sens[]); + + // Add the derivative of the failure criteria w.r.t. the design variables + void addFailureDVSens(int elemIndex, TacsScalar scale, const double pt[], + const TacsScalar X[], const TacsScalar strain[], + int dvLen, TacsScalar dfdx[]); + + // ============================================================================== + // Compute output quantities + // ============================================================================== + // Get the object name + const char* getObjectName() { return constName; } + + // Retrieve the design variable for plotting purposes + TacsScalar evalDesignFieldValue(int elemIndex, const double pt[], + const TacsScalar X[], int index); + + /** + * @brief Compute the effective tensile thickness of the stiffened shell + * + * This is the thickness of an unstiffened shell with the same tensile + * stiffness and density as the stiffened shell + * + * @return TacsScalar The effective thickness + */ + inline TacsScalar computeEffectiveThickness() { + return this->panelThick + + this->computeStiffenerArea() / this->stiffenerPitch; + } + + /** + * @brief Compute the effective bending thickness of the stiffened shell + * + * This is the thickness of an unstiffened shell with the same bending + * stiffness as the stiffened shell. Note this calculation does not currently + * account for any difference in the modulii of the stiffener and panel. + * + * @return TacsScalar The effective thickness + */ + TacsScalar computeEffectiveBendingThickness(); + + // ============================================================================== + // Tests + // ============================================================================== + + /** + * @brief Test `computeCriticalGlobalBucklingStiffnessSens` against finite + * difference/complex-step + * + */ + void testGlobalBucklingStiffnessSens(); + + /** + * @brief Test `computeCriticalShearLoadSens` against finite difference + */ + static bool testCriticalShearLoadSens(const TacsScalar D1, + const TacsScalar D2, + const TacsScalar D3, + const TacsScalar L); + + /** + * @brief Test `bucklingEnvelopeSens` against finite difference + */ + static bool testBucklingEnvelopeSens(const TacsScalar N1, + const TacsScalar N1Crit, + const TacsScalar N12, + const TacsScalar N12Crit); + + protected: + /** + * @brief Compute the stiffness matrix of the stiffened shell + * + * @param C Array to store the stiffness matrix in (will be zeroed out within + * this function) + */ + void computeStiffness(TacsScalar C[]); + + /** + * @brief Compute the Q and ABar Matrices for a laminate based on the Q and + * ABar matrices for each ply + * + * @param numPlies Number of plies in the laminate + * @param QMats The Q matrices for each ply, stored as a flattened 6*numPlies + * entry array + * @param AbarMats The Abar matrices for each ply, stored as a flattened + * 3*numPlies entry array + * @param plyFractions Ply fractions for each ply angle + * @param Q The Q matrix for the laminate, stored as a flattened 6 entry array + * ([Q11, Q12, Q16, Q22, Q26, Q66]) + * @param ABar The ABar matrix for the laminate, stored as a flattened 3 entry + * array ([Q44, Q45, Q55]) + */ + void computeSmearedStiffness(const int numPlies, + const TacsScalar* const QMats, + const TacsScalar* const AbarMats, + const TacsScalar plyFractions[], TacsScalar Q[], + TacsScalar ABar[]); + + /** + * @brief Compute the Q matrix for a laminate based on the Q matrices for each + * ply + * + * @param numPlies Number of plies in the laminate + * @param QMats The Q matrices for each ply, stored as a flattened 6*numPlies + * entry array + * @param plyFractions Ply fractions for each ply angle + * @param Q The Q matrix for the laminate, stored as a flattened 6 entry array + * ([Q11, Q12, Q16, Q22, Q26, Q66]) + */ + void computeSmearedStiffness(const int numPlies, + const TacsScalar* const QMats, + const TacsScalar plyFractions[], TacsScalar Q[]); + + /** + * @brief Compute the failure values for each failure mode of the stiffened + * panel + * + * @param e Shell strains + * @param fail Array to store the failure values in + * @return TacsScalar The aggregated failure value + */ + TacsScalar computeFailureValues(const TacsScalar e[], TacsScalar fail[]); + + // ============================================================================== + // Helper functions for transforming strains/stresses/stiffnesses between the + // panel and stiffener + // ============================================================================== + /** + * @brief Given the shell mid-plane strains, compute the equivalent beam + * strains at the stiffener centroid + * + * The transformation can be written as [eb] = [Te] [es], or in full: + * [e11b] [1, 0, 0, zc, 0, 0, 0, 0] [e11s] + * [xi1b] [0, 0, 0, 0, 0, -1/2, 0, 0] [e22s] + * [xi2b] = [0, 0, 0, 1, 0, 0, 0, 0] [y12s] + * [xi3b] [0, 0, 0, 0, 0, 0, 0, 0] [k11s] + * [y13b] [0, 0, 0, 0, 0, 0, 0, 1] [k22s] + * [y12b] [0, 0, 1/2, 0, 0, zc/2, 0, 0] [k12s] + * [y23s] + * [y13s] + * + * Where: + * - eb is the beam strain vector + * - es is the shell strain vector + * - zc is the distance from the shell mid-plane to the stiffener centroid + * + * @param panelStrain The shell mid-plane strains [e11, e22, y12, k11, k22, + * k12, y23, y13] + * @param stiffenerStrain The stiffener centroid strains [e11, xi1, xi2, xi3, + * y13, y12] + */ + void transformStrain(const TacsScalar panelStrain[], + TacsScalar stiffenerStrain[]); + + /** + * @brief Transform a sensitivity w.r.t the stiffener centroid strains to a + * sensitivity w.r.t the shell mid-plane strains + * + * This transformation can be written as [df/des] = [df/deb] * [deb/des] = + * [df/deb] * [Te], or in full: + * [df/de11s] [df/de11b] [1, 0, 0, zc, 0, 0, 0, 0] + * [df/de22s] [df/dxi1b] [0, 0, 0, 0, 0, -1/2, 0, 0] + * [df/dy12s] = [df/dxi2b] * [0, 0, 0, 1, 0, 0, 0, 0] + * [df/dk11s] [df/dxi3b] [0, 0, 0, 0, 0, 0, 0, 0] + * [df/dk22s] [df/dy13b] [0, 0, 0, 0, 0, 0, 0, 1] + * [df/dk12s] [df/dy12b] [0, 0, 1/2, 0, 0, zc/2, 0, 0] + * [df/dy23s] + * [df/dy13s] + * + * Where: + * - df/des is the sensitivity w.r.t the shell mid-plane strains + * - df/deb is the sensitivity w.r.t the stiffener centroid strains + * - deb/des = Te is the strain transformation matrix + * + * @param stiffenerStrainSens Array containing sensitivity of an output w.r.t + * beam strains + * @param panelStrainSens Array to store the sensitivity of the output w.r.t + * shell mid-plane strains + */ + void transformStrainSens(const TacsScalar stiffenerStrainSens[], + TacsScalar panelStrainSens[]); + + /** + * @brief Add the DV sensitivity of the product of the strain + * transformation matrix with two vectors + * + * This can be written as dfdx += scale * [lhs] * d/dx([Te]) * [rhs] + * + * A common use for this function is to convert the derivative of a quantity + * w.r.t the stiffener centroid strain to a derivative w.r.t the design + * variables, since the stiffener centroid strains depend on the offset of the + * stiffener centroid from the shell mid-plane, which depends on the design + * variables. + * + * This operation can be written as [df/dx] += scale * [df/deBeam] * + * d/dx([Te]) * [eShell] + * + * @param lhs The left-hand-side vector, should be as long as a beam strain + * array + * @param rhs The right hand side vector, should be as long as a shell strain + * array + * @param scale The scaling factor + * @param dfdx The sensitivities of the output w.r.t the design variables to + * be added to + */ + void addStrainTransformProductDVsens(const TacsScalar lhs[], + const TacsScalar rhs[], + const TacsScalar scale, + TacsScalar dfdx[]); + + /** + * @brief Add the contribution of the stiffener stress to the panel stress + * + * The transformation of stiffener to panel stress consists of two steps: + * 1. Transform the stiffener forces to the panel mid-plane, this is the + * transpose of the strain transformation + * 2. Add the transformed stiffener forces to the panel mid-plane forces, + * divided by the stiffener pitch to account for the stiffener spacing + * + * This can be written as [ss] += 1/pitch * [Te]^{T} [sb] + * where: + * - [Te] is the strain transformation matrix + * - [ss] is the shell mid-plane stress vector + * - [sb] is the stiffener beam stress vector + * + * @param stiffenerStress Stiffener beam stresses [F1, M1, M2, M3, V13, V12] + * @param panelStress The shell mid-plane stresses to be added to [N11, N22, + * N12, M11, M22, M12, Q23, Q13] + */ + void addStiffenerStress(const TacsScalar stiffenerStress[], + TacsScalar panelStress[]); + + /** + * @brief Add the contribution of the stiffener stiffness to the panel + * stiffness + * + * This operation can be written as: [Cs] += 1 / pitch * [Te]^{T} * [Cb] * + * [Te] Where: + * - [Te] is the strain transformation matrix + * - [Cs] is the shell stiffness matrix + * - [Cb] is the stiffener beam stiffness matrix + * + * @param stiffenerStiffness The stiffener stiffness matrix, computed by + * `computeStiffenerStiffness` + * @param panelStiffness The panel stiffness matrix to be added to + */ + void addStiffenerStiffness(const TacsScalar stiffenerStiffness[], + TacsScalar panelStiffness[]); + + // ============================================================================== + // Helper functions for computing the panel stress/stiffness/failure + // ============================================================================== + // In future, these methods should be replaced by calls to another shell + // constitutive model + + /** + * @brief Compute the stiffness matrix of the panel (without stiffeners) + * + * @param C Array to store the stiffness matrix in (will be zeroed out within + * this function) + */ + void computePanelStiffness(TacsScalar C[]); + + /** + * @brief Compute the panel stress given the panel strains + * + * @param strain Shell strains [e11, e22, y12, k11, k22, k12, y23, y13] + * @param stress Shell stresses [N11, N22, N12, M11, M22, M12, Q23, Q13] + */ + void computePanelStress(const TacsScalar strain[], TacsScalar stress[]); + + /** + * @brief Add the derivative of the product of panel stresses with a vector + * psi to dfdx + * + * @param scale Scale factor to apply to the derivatives + * @param strain SHell mid-plane strains + * @param psi Array multiplying stresses + * @param dfdx Design variable sensitivity array to add to + */ + void addPanelStressDVSens(const TacsScalar scale, const TacsScalar strain[], + const TacsScalar psi[], TacsScalar dfdx[]); + + /** + * @brief Compute the failure criteria in the panel + * + * @param strain Shell strains [e11, e22, y12, k11, k22, k12, y23, y13] + * @return TacsScalar The aggregated failure value for the panel + */ + TacsScalar computePanelFailure(const TacsScalar strain[]); + + /** + * @brief Compute the sensitivity of the panel failure w.r.t the panel strains + * + * @param strain Shell strains [e11, e22, y12, k11, k22, k12, y23, y13] + * @param sens Array to store the sensitivity of the failure w.r.t the strains + * @return TacsScalar The aggregated failure value for the panel + */ + TacsScalar evalPanelFailureStrainSens(const TacsScalar strain[], + TacsScalar sens[]); + + /** + * @brief Add the derivative of the panel's failure w.r.t it's DVs + * + * @param strain Shell strains [e11, e22, y12, k11, k22, k12, y23, y13] + * @param scale The scale factor to apply to the derivatives + * @param dfdx The array to add the derivative to + */ + void addPanelFailureDVSens(const TacsScalar strain[], const TacsScalar scale, + TacsScalar dfdx[]); + + // ============================================================================== + // Helper functions for computing the stiffner's strain/stress/stiffness + // ============================================================================== + // In future, these methods should be replaced by calls to a beam constitutive + // model + + /** + * @brief Compute the stiffener stress given the stiffener strains + * + * @param stiffenerStrain The stiffener centroid strains [e11, xi1, xi2, xi3, + * y13, y12] + * @param stiffenerStress The stiffener stresses/forces [N11, M1, M2, M3, V12, + * V13] + */ + void computeStiffenerStress(const TacsScalar stiffenerStrain[], + TacsScalar stiffenerStress[]); + + /** + * @brief Add the derivative of the product of stiffener stresses with a + * vector w.r.t the design variables + * + * @param scale Scale factor to apply to the derivatives + * @param strain Stiffener centroid beam strains + * @param psi Array multiplying stresses + * @param dfdx Design variable sensitivity array to add to + */ + void addStiffenerStressDVSens(const TacsScalar scale, + const TacsScalar strain[], + const TacsScalar psi[], TacsScalar dfdx[]); + + /** + * @brief Compute the stiffener's stiffness matrix + * + * @param C The stiffener local stiffness matrix (The derivative of the beam + * stresses w.r.t the beam strains) + */ + void computeStiffenerStiffness(TacsScalar C[]); + + static void computeEffectiveModulii(const int numPlies, + const TacsScalar QMats[], + const TacsScalar plyFracs[], + TacsScalar* E, TacsScalar* G); + + /** + * @brief Compute the failure criterion for the stiffener in a given strain + * state + * + * @param stiffenerStrain The stiffener centroid strains [e11, xi1, xi2, xi3, + * y13, y12] + * @return TacsScalar The failure criterion for the stiffener + */ + TacsScalar computeStiffenerFailure(const TacsScalar stiffenerStrain[]); + + /** + * @brief Compute the sensitivity of the stiffener failure w.r.t the stiffener + * strains + * + * @param strain Beam strains [e11, xi1, xi2, xi3, y13, y12] + * @param sens Array to store the sensitivity of the failure w.r.t the strains + * @return TacsScalar The aggregated failure value for the stiffener + */ + TacsScalar evalStiffenerFailureStrainSens(const TacsScalar strain[], + TacsScalar sens[]); + + /** + * @brief Add the derivative of the stiffener's failure w.r.t it's DVs + * + * @param strain Beam strains [e11, e22, y12, k11, k22, k12, y23, y13] + * @param scale The scale factor to apply to the derivatives + * @param dvLen The number of stiffener design variables + * @param dfdx The array to add the derivative to + */ + void addStiffenerFailureDVSens(const TacsScalar strain[], + const TacsScalar scale, TacsScalar dfdx[]); + + // ============================================================================== + // Helper functions for computing stiffener cross-section properties + // ============================================================================== + /** + * @brief Compute the stiffener area, + * + * @return TacsScalar Stiffener area + */ + TacsScalar computeStiffenerArea(); + + /** + * @brief Compute the derivative of the stiffener's cross-sectional area with + * respect to the stiffener thickness and height + * + * @param dAdt Derivative of the stiffener's cross-sectional area with respect + * to the stiffener thickness + * @param dAdh Derivative of the stiffener's cross-sectional area with respect + * to the stiffener height + */ + void computeStiffenerAreaSens(TacsScalar& dAdt, TacsScalar& dAdh); + + /** + * @brief Compute the stiffener centroid height, this is the height relative + * to the bottom surface of the stiffener, NOT the mid-plane of the panel. + * + * @return TacsScalar The stiffener centroid height + */ + TacsScalar computeStiffenerCentroidHeight(); + + /** + * @brief Compute the derivative of the stiffener centroid height with respect + * to the stiffener thickness and height + * + * @param dzdt Derivative of the stiffener centroid height with respect to the + * stiffener thickness + * @param dzdh Derivative of the stiffener centroid height with respect to the + * stiffener height + */ + void computeStiffenerCentroidHeightSens(TacsScalar& dzdt, TacsScalar& dzdh); + + /** + * @brief Compute the second moment of area about the stiffener centroid + * + * @return TacsScalar Second moment of area about the stiffener centroid + */ + TacsScalar computeStiffenerIzz(); + + /** + * @brief Compute the derivative of the stiffener's second moment of area + * about the stiffener centroid with respect to the stiffener thickness and + * height + * + * @param dIdt Derivative of Izz with respect to the stiffener thickness + * @param dIdh Derivative of Izz with respect to the stiffener height + */ + void computeStiffenerIzzSens(TacsScalar& dIdt, TacsScalar& dIdh); + /** + * @brief Compute the torsion constant of the stiffener cross section + * + * The equation used is taken from page 9 of "TORSIONAL SECTION PROPERTIES OF + * STEEL SHAPES" by the Canadian institute of steel construction + * (http://dir.cisc-icca.ca/files/technical/techdocs/updates/torsionprop.pdf). + * The use of this equation is obviously a little suspect for a composite + * stiffener, but it is the best we have for now. + * + * @return TacsScalar The stiffener torsion constant + */ + TacsScalar computeStiffenerJxx(); + + /** + * @brief Compute the derivative of the stiffener's torsion constant with + * respect to the stiffener thickness and height + * + * @param dJdt Derivative of Jxx with respect to the stiffener thickness + * @param dJdh Derivative of Jxx with respect to the stiffener height + */ + void computeStiffenerJxxSens(TacsScalar& dJdt, TacsScalar& dJdh); + + /** + * @brief Compute the moment of inertia of the stiffener cross section about + * it's centroid, NOT the shell mid-plane + * + * @return TacsScalar The stiffener moment of inertia (Iyy) about it's + * centroid + */ + TacsScalar computeStiffenerMOI(); + + /** + * @brief Compute the derivative of the stiffener's moment of inertia about + * its centroid with respect to the stiffener thickness and height + * + * @param dMOIdt Derivative of Iyy with respect to the stiffener thickness + * @param dMOIdh Derivative of Iyy with respect to the stiffener height + */ + void computeStiffenerMOISens(TacsScalar& dMOIdt, TacsScalar& dMOIdh); + + // ============================================================================== + // Buckling functions + // ============================================================================== + + /** + * @brief Compute the panel + stiffener stiffness values used to compute the + * global buckling loads + * + * @output D1 1-direction bending stiffness + * @output D2 2-direction bending stiffness + * @output D3 Twisting stiffness + */ + void computeCriticalGlobalBucklingStiffness(TacsScalar* D1, TacsScalar* D2, + TacsScalar* D3); + + /** + * @brief Compute the sensitivities of the panel + stiffener stiffness values + * used to compute the global buckling loads + * + * @param dfdD1 Sensitivity of the output to the 1-direction bending stiffness + * @param dfdD2 Sensitivity of the output to the 2-direction bending stiffness + * @param dfdD3 Sensitivity of the output to the twisting stiffness + * @output spSens Sensitivity of the output w.r.t the stiffener pitch + * @output tpSens Sensitivity of the output w.r.t the panel thickness + * @output hsSens Sensitivity of the output w.r.t the stiffener height + * @output tsSens Sensitivity of the output w.r.t the stiffener thickness + * @output QstiffSens Sensitivity of the output w.r.t the stiffener stiffener + * Q matrix entries + * @output QpanelSens Sensitivity of the output w.r.t the stiffener panel Q + * matrix entries + */ + void computeCriticalGlobalBucklingStiffnessSens( + const TacsScalar dfdD1, const TacsScalar dfdD2, const TacsScalar dfdD3, + TacsScalar* spSens, TacsScalar* tpSens, TacsScalar* hsSens, + TacsScalar* tsSens, TacsScalar QstiffSens[], TacsScalar QpanelSens[]); + + /** + * @brief Compute the critical axial load for the global buckling of the + * stiffened panel + * + * @param D1 1-direction bending stiffness, computed by + * `computeCriticalGlobalBucklingStiffness` + * @param L Panel length + * @return TacsScalar The critical load + */ + static inline TacsScalar computeCriticalGlobalAxialLoad(const TacsScalar D1, + const TacsScalar L) { + return M_PI * M_PI * D1 / (L * L); + } + + /** + * @brief Compute the critical axial load for local buckling of the panel + * + * @param D11 D11 stiffness + * @param D22 D22 stiffness + * @param D12 D12 stiffness + * @param D66 D66 stiffness + * @param L Length (in this case, the stiffener pitch) + * @return TacsScalar The critical load + */ + static inline TacsScalar computeCriticalLocalAxialLoad(const TacsScalar D11, + const TacsScalar D22, + const TacsScalar D12, + const TacsScalar D66, + const TacsScalar L) { + return 2.0 * M_PI * M_PI / (L * L) * (sqrt(D11 * D22) + D12 + 2.0 * D66); + } + + /** + * @brief Compute the sensitivity of the critical axial load for local + * buckling of the panel + * + * @param D11 D11 stiffness + * @param D22 D22 stiffness + * @param D12 D12 stiffness + * @param D66 D66 stiffness + * @param L Length (in this case, the stiffener pitch) + * @param D11Sens Sensitivity w.r.t the D11 stiffness + * @param D22Sens Sensitivity w.r.t the D22 stiffness + * @param D12Sens Sensitivity w.r.t the D12 stiffness + * @param D66Sens Sensitivity w.r.t the D66 stiffness + * @param LSens Sensitivity w.r.t the Length + * @return TacsScalar The critical load + */ + static TacsScalar computeCriticalLocalAxialLoadSens( + const TacsScalar D11, const TacsScalar D22, const TacsScalar D12, + const TacsScalar D66, const TacsScalar L, TacsScalar* D11Sens, + TacsScalar* D22Sens, TacsScalar* D12Sens, TacsScalar* D66Sens, + TacsScalar* LSens); + + /** + * @brief Compute the critical shear load for either local or global buckling + * + * The shear buckling loads are calculated based on an infinite-plate + * solution simply supported along the panel sides. For the local skin + * buckling calculations we use the infinite plate solution along edges + * supported by the blade stiffeners, therefore the panel width is + * equal to the stiffener pitch (sp). For the global-level + * calculations, we use the panel length equal to the rib pitch, thus + * the panel width is equal to the local panel length (Lx). + * + * In Stroud and Arganoff, the following formula are suggested for the + * calculation of the buckling loads: + * + * xi = sqrt(D1*D2)/D3 + * + * if xi > 1.0: + * Nxy,crit = (4.0/Ly^2)*(D2*D1^3)^(1/4)*(8.125 + 5.05/xi) + * else: + * Nxy,crit = (4.0/Ly^2)*sqrt(D1*D3)*(11.7 + 0.532*xi + 0.938*xi^2) + * + * Note that if xi = 1, then D3 = sqrt(D1*D2) and so + * (4.0/Ly^2)*sqrt(D1*D3) = (4.0/Ly^2)*(D1*D1^3)^(1/4) + * + * However, when xi = 1, the two terms inside the brackets are not + * equal. As a result, there is a discontinuity between the two + * expressions. To avoid this, we adjust the first formula in a + * conservative manner. As shown in Lekhnitskii, the limit for xi -> + * infty is 8.125, while for xi = 1 is 13.17 and for xi = 0, 11.71. + * + * The formula in Stroud and Arganoff do not meet these end conditions. + * We adjust the formula as follows: + * + * if xi > 1.0: + * Nxy,crit = (4.0/Ly^2)*(D2*D1^3)^(1/4)*(8.125 + 5.045/xi) + * else: + * Nxy,crit = (4.0/Ly^2)*sqrt(D1*D3)*(11.7 + 0.532*xi + 0.938*xi^2) + * + * input: + * @param D1 the longitudinal bending stiffness + * @param D2 the transverse bending stiffness + * @param D3 the shear bending stiffness + * @param L the side-length of the panel + * + * returns: + * @return N12Crit the approximate critical buckling load + */ + static TacsScalar computeCriticalShearLoad(TacsScalar D1, TacsScalar D2, + TacsScalar D3, TacsScalar L); + + /** + * @brief Compute the sensitivity of the critical shear buckling load + * + * @param D1 the longitudinal bending stiffness + * @param D2 the transverse bending stiffness + * @param D3 the shear bending stiffness + * @param L the side-length of the panel + * @param sD1 Sensitivity of the critical load w.r.t the longitudinal bending + * stiffness + * @param sD2 Sensitivity of the critical load w.r.t the transverse bending + * stiffness + * @param sD3 Sensitivity of the critical load w.r.t the shear bending + * stiffness + * @param sL Sensitivity of the critical load w.r.t the side-length of the + * panel + * @return TacsScalar The critical shear buckling load + */ + static TacsScalar computeCriticalShearLoadSens( + const TacsScalar D1, const TacsScalar D2, const TacsScalar D3, + const TacsScalar L, TacsScalar* D1Sens, TacsScalar* D2Sens, + TacsScalar* D3Sens, TacsScalar* LSens); + + /** + * @brief Compute the buckling failure criterion + * + * The failure criterion is: f = N1/N1Crit + (N12/N12Crit)^2 + * + * @param N1 Axial load + * @param N1Crit Critical axial load + * @param N12 Shear load + * @param N12Crit Critical shear load + * @return TacsScalar The failure criterion + */ + static TacsScalar bucklingEnvelope(const TacsScalar N1, + const TacsScalar N1Crit, + const TacsScalar N12, + const TacsScalar N12Crit); + + /** + * @brief Compute the sensitivity of the buckling failure criterion w.r.t the + * loads and critical loads + * + * @param N1 Axial load + * @param N1Crit Critical axial load + * @param N12 Shear load + * @param N12Crit Critical shear load + * @param N1Sens Sensitivity of the failure criterion w.r.t the axial load + * @param N1CritSens Sensitivity of the failure criterion w.r.t the critical + * axial load + * @param N12Sens Sensitivity of the failure criterion w.r.t the shear load + * @param N12CritSens Sensitivity of the failure criterion w.r.t the critical + * shear load + */ + static TacsScalar bucklingEnvelopeSens( + const TacsScalar N1, const TacsScalar N1Crit, const TacsScalar N12, + const TacsScalar N12Crit, TacsScalar* N1Sens, TacsScalar* N1CritSens, + TacsScalar* N12Sens, TacsScalar* N12CritSens); + + // ============================================================================== + // Attributes + // ============================================================================== + + // --- General attributes --- + int numPanelPlies; ///< Number of plies in the panel laminate + int numStiffenerPlies; ///< Number of plies in the stiffener laminate + double ksWeight = 80.0; ///< Failure criteria KS aggregation weight + int numDesignVars; ///< Number of design variables + int numGeneralDV; ///< Number of general DVs + int numPanelDV; ///< Number of panel DVs + int numStiffenerDV; ///< Number of stiffener DVs + + // --- Material properties --- + TACSOrthotropicPly* panelPly; ///< Orthotropic ply for the panel + TACSOrthotropicPly* stiffenerPly; ///< Orthotropic ply for the stiffener + TacsScalar kcorr; ///< Shear correction factor + + // --- Design variable values --- + TacsScalar panelLength; ///< Panel length + TacsScalar stiffenerPitch; ///< Stiffener pitch + TacsScalar stiffenerHeight; ///< Stiffener height + TacsScalar stiffenerThick; ///< Stiffener thickness + TacsScalar panelThick; ///< Panel thickness + TacsScalar* panelPlyFracs; ///< Panel ply Fracs + TacsScalar* stiffenerPlyFracs; ///< Stiffener ply Fracs + + // --- Fixed parameters --- + TacsScalar* panelPlyAngles; ///< Panel ply angles + TacsScalar* stiffenerPlyAngles; ///< Stiffener ply angles + TacsScalar flangeFraction; ///< Flange fraction (stiffener base width as a + ///< fraction of stiffener height) + TacsScalar* panelQMats; ///< Panel Q-matrices (they are constant since the + ///< ply angles are fixed) + TacsScalar* stiffenerQMats; ///< Panel Q-matrices (they are constant since + ///< the ply angles are fixed) + TacsScalar* panelAbarMats; + TacsScalar* stiffenerAbarMats; + + // --- Design variable bounds --- + TacsScalar panelLengthLowerBound = 0.0; + TacsScalar panelLengthUpperBound = 1e20; + TacsScalar stiffenerPitchLowerBound = 1e-3; + TacsScalar stiffenerPitchUpperBound = 1e20; + TacsScalar stiffenerHeightLowerBound = 1e-3; + TacsScalar stiffenerHeightUpperBound = 1e20; + TacsScalar stiffenerThickLowerBound = 1e-4; + TacsScalar stiffenerThickUpperBound = 1e20; + TacsScalar panelThickLowerBound = 1e-4; + TacsScalar panelThickUpperBound = 1e20; + TacsScalar* panelPlyFracLowerBounds; + TacsScalar* panelPlyFracUpperBounds; + TacsScalar* stiffenerPlyFracLowerBounds; + TacsScalar* stiffenerPlyFracUpperBounds; + + // --- Design variable numbers --- + int panelLengthNum; ///< Panel length DV number + int stiffenerPitchNum; ///< Stiffener pitch DV number + int stiffenerHeightNum; ///< Stiffener height DV number + int stiffenerThickNum; ///< Stiffener thickness DV number + int panelThickNum; ///< Panel thickness DV number + int* panelPlyFracNums; ///< Panel ply fraction DV numbers + int* stiffenerPlyFracNums; ///< Stiffener ply fraction DV numbers + + // --- Local design variable numbers, these are useful when returning + // sensitivity values --- + int panelLengthLocalNum; ///< Panel length local DV number + int panelThickLocalNum; ///< Panel thickness local DV number + int* panelPlyFracLocalNums; ///< Panel ply fraction local DV numbers + int stiffenerPitchLocalNum; ///< Stiffener pitch local DV number + int stiffenerHeightLocalNum; ///< Stiffener height local DV number + int stiffenerThickLocalNum; ///< Stiffener thickness local DV number + int* stiffenerPlyFracLocalNums; ///< Stiffener ply fraction local DV numbers + int panelDVStartNum; ///< Panel DV start number + int stiffenerDVStartNum; ///< Stiffener DV start number + + // --- Arrays for storing failure values and their + // sensitivities --- + TacsScalar* panelPlyFailValues; + TacsScalar* stiffenerPlyFailValues; + TacsScalar** panelPlyFailStrainSens; + TacsScalar** stiffenerPlyFailStrainSens; + TacsScalar* panelPlyFailSens; + TacsScalar* stiffenerPlyFailSens; + + static const char* constName; ///< Constitutive model name + static const int NUM_Q_ENTRIES = 6; ///< Number of entries in the Q matrix + static const int NUM_ABAR_ENTRIES = + 3; ///< Number of entries in the ABar matrix + static const int NUM_FAILURES = 4; ///< Number of failure modes +}; diff --git a/src/constitutive/TACSIsoRectangleBeamConstitutive.cpp b/src/constitutive/TACSIsoRectangleBeamConstitutive.cpp index 168c062e6..950ae9d0c 100644 --- a/src/constitutive/TACSIsoRectangleBeamConstitutive.cpp +++ b/src/constitutive/TACSIsoRectangleBeamConstitutive.cpp @@ -336,7 +336,7 @@ TacsScalar TACSIsoRectangleBeamConstitutive::evalFailureStrainSens( const TacsScalar e[], TacsScalar sens[]) { // Check the cross-section for failure at the four corners TacsScalar e0[6], s0[6]; - TacsScalar e0d[6], s0d[6]; + TacsScalar dfde0[6], dfds0[6]; TacsScalar fail_checks[4]; TacsScalar fail_checks_sens[4][6]; TacsScalar max_fail = -1e20, ks_sum = 0.0; @@ -360,14 +360,15 @@ TacsScalar TACSIsoRectangleBeamConstitutive::evalFailureStrainSens( props->evalStress3D(e0, s0); // Compute the von Mises stress - fail_checks[count] = props->vonMisesFailure3DStressSens(s0, s0d); - props->evalStress3D(s0d, e0d); - fail_checks_sens[count][0] = e0d[0]; - fail_checks_sens[count][2] = -y_lim[i] * e0d[0]; - fail_checks_sens[count][3] = -z_lim[j] * e0d[0]; - fail_checks_sens[count][1] = y_lim[i] * e0d[4] - z_lim[j] * e0d[5]; - fail_checks_sens[count][5] = e0d[4]; - fail_checks_sens[count][4] = e0d[5]; + fail_checks[count] = props->vonMisesFailure3DStressSens(s0, dfds0); + + props->evalStress3D(dfds0, dfde0); + fail_checks_sens[count][0] = dfde0[0]; + fail_checks_sens[count][2] = -y_lim[i] * dfde0[0]; + fail_checks_sens[count][3] = -z_lim[j] * dfde0[0]; + fail_checks_sens[count][1] = y_lim[i] * dfde0[4] - z_lim[j] * dfde0[5]; + fail_checks_sens[count][5] = dfde0[4]; + fail_checks_sens[count][4] = dfde0[5]; if (TacsRealPart(fail_checks[count]) > TacsRealPart(max_fail)) { max_fail = fail_checks[count]; @@ -375,16 +376,16 @@ TacsScalar TACSIsoRectangleBeamConstitutive::evalFailureStrainSens( } } - for (int i = 0; i < count; i++) { - ks_sum += exp(ks_weight * (fail_checks[i] - max_fail)); - } - - for (int i = 0; i < count; i++) { - for (int k = 0; k < NUM_STRESSES; k++) { - sens[k] += exp(ks_weight * (fail_checks[i] - max_fail)) * - fail_checks_sens[i][k] / ks_sum; + for (int ii = 0; ii < count; ii++) { + TacsScalar val = exp(ks_weight * (fail_checks[ii] - max_fail)); + ks_sum += val; + for (int kk = 0; kk < NUM_STRESSES; kk++) { + sens[kk] += val * fail_checks_sens[ii][kk]; } } + for (int kk = 0; kk < NUM_STRESSES; kk++) { + sens[kk] /= ks_sum; + } return max_fail + log(ks_sum) / ks_weight; } diff --git a/src/constitutive/TACSMaterialProperties.cpp b/src/constitutive/TACSMaterialProperties.cpp index aedce8b33..bdb8423d6 100644 --- a/src/constitutive/TACSMaterialProperties.cpp +++ b/src/constitutive/TACSMaterialProperties.cpp @@ -1288,7 +1288,7 @@ void TACSOrthotropicPly::testFailSens(double dh, TacsScalar angle) { TacsRealPart(angle)); for (int k = 0; k < 3; k++) { - strain[k] = -1.0; + strain[k] = -1.0e-3; // Calculate the failure load TacsScalar p = failure(angle, strain); diff --git a/src/constitutive/TACSShellConstitutive.h b/src/constitutive/TACSShellConstitutive.h index 4fa937bdf..fe267682e 100644 --- a/src/constitutive/TACSShellConstitutive.h +++ b/src/constitutive/TACSShellConstitutive.h @@ -39,7 +39,7 @@ class TACSShellConstitutive : public TACSConstitutive { // Get the number of stresses int getNumStresses(); - /* + /** Get the integrals of the density through the thickness moments = int_{-t/2}^{t/2} [1, z, z^2] rho(z) dz @@ -53,7 +53,15 @@ class TACSShellConstitutive : public TACSConstitutive { const TacsScalar X[], TacsScalar moments[]) = 0; /** - Add the derivative of the pointwise mass times the given scalar + Add the contribution of the mass moment sensitivities to the derivative of a + function + + Given the sensitivity of some function, f, with respect to the mass moments, + this function adds the sensitivity of the function the design variables due + to the dependence of the mass moments on the design variables. + + e.g dfdx[0] += scale[0]*dm0/dx1 + scale[1]*dm1/dx1 + scale[2]*dm2/dx1 + dfdx[1] += scale[0]*dm0/dx2 + scale[1]*dm1/dx2 + scale[2]*dm2/dx2 @param elemIndex The local element index @param pt The parametric location diff --git a/src/constitutive/bladeFSDTStiffness.cpp b/src/constitutive/bladeFSDTStiffness.cpp deleted file mode 100644 index 54275f15f..000000000 --- a/src/constitutive/bladeFSDTStiffness.cpp +++ /dev/null @@ -1,2605 +0,0 @@ -#include "bladeFSDTStiffness.h" - -#include "FElibrary.h" -#include "tacslapack.h" - -/* - Copyright (c) 2011 Graeme Kennedy. All rights reserved. - Not for commercial purposes. -*/ - -/* - The bladeFSDTStiffness object - - This is the constitutive class for a blade-stiffened panel. The - contribution of the stiffeners to the panel thickness are handled - using a smeared-stiffener approach - see Brush and Almroth: Buckling - of bars, plates and shells. - - This method requires the initial values and the design variable - numbers for: - - sp: the stiffener spacing - sh: the stiffener height - st: the stiffener thickness - t: the panel thickness - pf_nums: the ply fraction numbers - stiff_pf_nums: the ply fraction numbers for the stiffeners - - The failure calculations are based on a failure envelope that - includes both material failure and buckling constraints. The - buckling constraints can only be used when a "PanelDimensions" - object is passed into the object. This is required in order to - obtain the effective panel dimensions. -*/ -bladeFSDTStiffness::bladeFSDTStiffness(OrthoPly* _ortho_ply, TacsScalar _kcorr, - TacsScalar _Lx, int _Lx_num, - TacsScalar _sp, int _sp_num, - TacsScalar _sh, int _sh_num, - TacsScalar _st, int _st_num, - TacsScalar _t, int _t_num, - int _pf_nums[], int _stiff_pf_nums[]) { - ortho_ply = _ortho_ply; - ortho_ply->incref(); - kcorr = _kcorr; - - // Record the panel length and design variable number - Lx = _Lx; - Lx_num = _Lx_num; - - // Record the stiffener information - // Note that the default low/high bounds can be changed - sp = _sp; - sp_num = _sp_num; - sp_low = 0.1; // 10 cm - sp_high = 0.2; // 20 cm - - sh = _sh; - sh_num = _sh_num; - sh_low = 0.04; // 4cm - sh_high = 0.05; // 5cm - - st = _st; - st_num = _st_num; - st_low = 0.002; // 2 mm - st_high = 0.01; // 1 cm - - sf_fraction = 1.0; // Flange length fraction - - for (int k = 0; k < NUM_PLIES; k++) { - stiff_ply_angles[k] = -0.5 * M_PI + ((k + 1) * M_PI) / NUM_PLIES; - } - - for (int k = 0; k < NUM_PLIES; k++) { - stiff_pf[k] = 1.0 / NUM_PLIES; - stiff_pf_nums[k] = _stiff_pf_nums[k]; - stiff_pf_low[k] = 0.15; // 15 % - stiff_pf_high[k] = 0.70; // 70 % - } - - // Record the panel thickness information - t = _t; - t_num = _t_num; - t_low = 0.002; // 2 mm - t_high = 0.01; // 1 cm - - for (int k = 0; k < NUM_PLIES; k++) { - ply_angles[k] = -0.5 * M_PI + ((k + 1) * M_PI) / NUM_PLIES; - } - - for (int k = 0; k < NUM_PLIES; k++) { - pf[k] = 1.0 / NUM_PLIES; - pf_nums[k] = _pf_nums[k]; - pf_low[k] = 0.15; // 15 % - pf_high[k] = 0.70; // 70 % - } - - if (sp_num < 0) { - fprintf(stderr, "bladeFSDTStiffness: sp_num must be non-negative\n"); - } - if (sh_num < 0) { - fprintf(stderr, "bladeFSDTStiffness: sh_num must be non-negative\n"); - } - if (st_num < 0) { - fprintf(stderr, "bladeFSDTStiffness: st_num must be non-negative\n"); - } - if (t_num < 0) { - fprintf(stderr, "bladeFSDTStiffness: t_num must be non-negative\n"); - } - - // Calculate additional information about the design variables - for (int k = 0; k < NUM_PLIES; k++) { - pf_unique[k] = pf_nums[k]; - stiff_pf_unique[k] = stiff_pf_nums[k]; - } - - num_pf_unique = FElibrary::uniqueSort(pf_unique, NUM_PLIES); - num_stiff_pf_unique = FElibrary::uniqueSort(stiff_pf_unique, NUM_PLIES); - - num_pf_con = 0; - if (num_pf_unique > 0) { - num_pf_con++; - } - if (num_stiff_pf_unique > 0) { - num_pf_con++; - } - - // Initialize the stiffness and failure properties - ks_weight = 80.0; // Default value of the ks weight parameter - updateStiffness(); - calcBucklingProps(); -} - -bladeFSDTStiffness::~bladeFSDTStiffness() { ortho_ply->decref(); } - -const char* bladeFSDTStiffness::constName = "bladeFSDTStiffness"; - -/* - Set non-default values into the class -*/ - -void bladeFSDTStiffness::setStiffenerPitchBounds(TacsScalar _sp_low, - TacsScalar _sp_high) { - sp_low = _sp_low; - sp_high = _sp_high; -} - -void bladeFSDTStiffness::setStiffenerHeightBounds(TacsScalar _sh_low, - TacsScalar _sh_high) { - sh_low = _sh_low; - sh_high = _sh_high; -} - -void bladeFSDTStiffness::setStiffenerThicknessBounds(TacsScalar _st_low, - TacsScalar _st_high) { - st_low = _st_low; - st_high = _st_high; -} - -void bladeFSDTStiffness::setStiffenerPlyFractionBounds(TacsScalar _pf_low[], - TacsScalar _pf_high[]) { - for (int k = 0; k < NUM_PLIES; k++) { - pf_low[k] = _pf_low[k]; - pf_high[k] = _pf_high[k]; - } -} - -void bladeFSDTStiffness::setStiffenerPlyFractions(TacsScalar _pf[]) { - for (int k = 0; k < NUM_PLIES; k++) { - stiff_pf[k] = _pf[k]; - } -} - -void bladeFSDTStiffness::setThicknessBounds(TacsScalar _t_low, - TacsScalar _t_high) { - t_low = _t_low; - t_high = _t_high; -} - -void bladeFSDTStiffness::setPlyFractionBounds(TacsScalar _pf_low[], - TacsScalar _pf_high[]) { - for (int k = 0; k < NUM_PLIES; k++) { - stiff_pf_low[k] = _pf_low[k]; - stiff_pf_high[k] = _pf_high[k]; - } -} - -void bladeFSDTStiffness::setPlyFractions(TacsScalar _pf[]) { - for (int k = 0; k < NUM_PLIES; k++) { - pf[k] = _pf[k]; - } -} - -void bladeFSDTStiffness::setKSWeight(double _ks_weight) { - ks_weight = _ks_weight; -} - -/* - Retrieve the critical panel loads for the given set of design variables -*/ -void bladeFSDTStiffness::getCriticalGlobalLoads(TacsScalar* Nx, - TacsScalar* Nxy) { - *Nx = Nx_global_crit; - *Nxy = Nxy_global_crit; -} - -void bladeFSDTStiffness::getCriticalPanelLoads(TacsScalar* Nx, - TacsScalar* Nxy) { - *Nx = Nx_panel_crit; - *Nxy = Nxy_panel_crit; -} - -void bladeFSDTStiffness::getCriticalStiffenerLoads(TacsScalar* Nx_weak, - TacsScalar* Nx_strong) { - *Nx_weak = Nx_weak_stiff_crit; - *Nx_strong = Nx_strong_stiff_crit; -} - -/* - Retrieve the failure criteria for panel-only optimization - purposes (without the use of a structural analysis in TACS). -*/ - -TacsScalar bladeFSDTStiffness::getFailureCriterion(const TacsScalar stress[8]) { - TacsScalar strain[8]; - memcpy(strain, stress, 8 * sizeof(TacsScalar)); - - double gpt[2] = {0.0, 0.0}; - TacsScalar A[6], B[6], D[6], As[3]; - getStiffness(gpt, A, B, D, As); - - int ipiv[8]; - TacsScalar C[8 * 8]; - memset(C, 0, 64 * sizeof(TacsScalar)); - - // Copy the A/B matrices to C - C[0] = A[0]; - C[8] = A[1]; - C[16] = A[2]; - C[1] = A[1]; - C[9] = A[3]; - C[17] = A[4]; - C[2] = A[2]; - C[10] = A[4]; - C[18] = A[5]; - - C[3] = B[0]; - C[11] = B[1]; - C[19] = B[2]; - C[4] = B[1]; - C[12] = B[3]; - C[20] = B[4]; - C[5] = B[2]; - C[13] = B[4]; - C[21] = B[5]; - - // Copy the B/D matrices to C - C[24] = B[0]; - C[32] = B[1]; - C[40] = B[2]; - C[25] = B[1]; - C[33] = B[3]; - C[41] = B[4]; - C[26] = B[2]; - C[34] = B[4]; - C[42] = B[5]; - - C[27] = D[0]; - C[35] = D[1]; - C[43] = D[2]; - C[28] = D[1]; - C[36] = D[3]; - C[44] = D[4]; - C[29] = D[2]; - C[37] = D[4]; - C[45] = D[5]; - - C[54] = As[0]; - C[62] = As[1]; - C[55] = As[1]; - C[63] = As[2]; - - int nstress = 8, one = 1, info = 0; - LAPACKgesv(&nstress, &one, C, &nstress, ipiv, strain, &nstress, &info); - - TacsScalar fail = 0.0; - failure(gpt, strain, &fail); - return fail; -} - -TacsScalar bladeFSDTStiffness::getBucklingCriterion( - const TacsScalar stress[8]) { - TacsScalar strain[8]; - memcpy(strain, stress, 8 * sizeof(TacsScalar)); - - double gpt[2] = {0.0, 0.0}; - TacsScalar A[6], B[6], D[6], As[3]; - getStiffness(gpt, A, B, D, As); - - int ipiv[8]; - TacsScalar C[8 * 8]; - memset(C, 0, 64 * sizeof(TacsScalar)); - - // Copy the A/B matrices to C - C[0] = A[0]; - C[8] = A[1]; - C[16] = A[2]; - C[1] = A[1]; - C[9] = A[3]; - C[17] = A[4]; - C[2] = A[2]; - C[10] = A[4]; - C[18] = A[5]; - - C[3] = B[0]; - C[11] = B[1]; - C[19] = B[2]; - C[4] = B[1]; - C[12] = B[3]; - C[20] = B[4]; - C[5] = B[2]; - C[13] = B[4]; - C[21] = B[5]; - - // Copy the B/D matrices to C - C[24] = B[0]; - C[32] = B[1]; - C[40] = B[2]; - C[25] = B[1]; - C[33] = B[3]; - C[41] = B[4]; - C[26] = B[2]; - C[34] = B[4]; - C[42] = B[5]; - - C[27] = D[0]; - C[35] = D[1]; - C[43] = D[2]; - C[28] = D[1]; - C[36] = D[3]; - C[44] = D[4]; - C[29] = D[2]; - C[37] = D[4]; - C[45] = D[5]; - - C[54] = As[0]; - C[62] = As[1]; - C[55] = As[1]; - C[63] = As[2]; - - int nstress = 8, one = 1, info = 0; - LAPACKgesv(&nstress, &one, C, &nstress, ipiv, strain, &nstress, &info); - - TacsScalar fail = 0.0; - buckling(&fail, strain); - return fail; -} - -void bladeFSDTStiffness::getPanelLoads(const TacsScalar stress[], - TacsScalar* _Nx, TacsScalar* _Nxy) { - TacsScalar strain[8]; - memcpy(strain, stress, 8 * sizeof(TacsScalar)); - - double gpt[2] = {0.0, 0.0}; - TacsScalar A[6], B[6], D[6], As[3]; - getStiffness(gpt, A, B, D, As); - - int ipiv[8]; - TacsScalar C[8 * 8]; - memset(C, 0, 64 * sizeof(TacsScalar)); - - // Copy the A/B matrices to C - C[0] = A[0]; - C[8] = A[1]; - C[16] = A[2]; - C[1] = A[1]; - C[9] = A[3]; - C[17] = A[4]; - C[2] = A[2]; - C[10] = A[4]; - C[18] = A[5]; - - C[3] = B[0]; - C[11] = B[1]; - C[19] = B[2]; - C[4] = B[1]; - C[12] = B[3]; - C[20] = B[4]; - C[5] = B[2]; - C[13] = B[4]; - C[21] = B[5]; - - // Copy the B/D matrices to C - C[24] = B[0]; - C[32] = B[1]; - C[40] = B[2]; - C[25] = B[1]; - C[33] = B[3]; - C[41] = B[4]; - C[26] = B[2]; - C[34] = B[4]; - C[42] = B[5]; - - C[27] = D[0]; - C[35] = D[1]; - C[43] = D[2]; - C[28] = D[1]; - C[36] = D[3]; - C[44] = D[4]; - C[29] = D[2]; - C[37] = D[4]; - C[45] = D[5]; - - C[54] = As[0]; - C[62] = As[1]; - C[55] = As[1]; - C[63] = As[2]; - - int nstress = 8, one = 1, info = 0; - LAPACKgesv(&nstress, &one, C, &nstress, ipiv, strain, &nstress, &info); - - TacsScalar Nx = (Qbar_panel[0] * strain[0] + Qbar_panel[1] * strain[1]); - *_Nx = (TacsRealPart(Nx) < 0.0 ? -Nx : TacsScalar(0.0)); - - *_Nxy = Qbar_panel[5] * strain[2]; -} - -void bladeFSDTStiffness::getStiffenerLoads(const TacsScalar stress[], - TacsScalar* _Nx, TacsScalar* _Nxy) { - TacsScalar strain[8]; - memcpy(strain, stress, 8 * sizeof(TacsScalar)); - - double gpt[2] = {0.0, 0.0}; - TacsScalar A[6], B[6], D[6], As[3]; - getStiffness(gpt, A, B, D, As); - - int ipiv[8]; - TacsScalar C[8 * 8]; - memset(C, 0, 64 * sizeof(TacsScalar)); - - // Copy the A/B matrices to C - C[0] = A[0]; - C[8] = A[1]; - C[16] = A[2]; - C[1] = A[1]; - C[9] = A[3]; - C[17] = A[4]; - C[2] = A[2]; - C[10] = A[4]; - C[18] = A[5]; - - C[3] = B[0]; - C[11] = B[1]; - C[19] = B[2]; - C[4] = B[1]; - C[12] = B[3]; - C[20] = B[4]; - C[5] = B[2]; - C[13] = B[4]; - C[21] = B[5]; - - // Copy the B/D matrices to C - C[24] = B[0]; - C[32] = B[1]; - C[40] = B[2]; - C[25] = B[1]; - C[33] = B[3]; - C[41] = B[4]; - C[26] = B[2]; - C[34] = B[4]; - C[42] = B[5]; - - C[27] = D[0]; - C[35] = D[1]; - C[43] = D[2]; - C[28] = D[1]; - C[36] = D[3]; - C[44] = D[4]; - C[29] = D[2]; - C[37] = D[4]; - C[45] = D[5]; - - C[54] = As[0]; - C[62] = As[1]; - C[55] = As[1]; - C[63] = As[2]; - - int nstress = 8, one = 1, info = 0; - LAPACKgesv(&nstress, &one, C, &nstress, ipiv, strain, &nstress, &info); - - // Calculate the stiffener buckling criteria - TacsScalar Nx = (Qbar_stiff[0] * (strain[0] - 0.5 * sh * strain[3]) + - Qbar_stiff[1] * (strain[1] - 0.5 * sh * strain[4])); - *_Nx = (TacsRealPart(Nx) < 0.0 ? -Nx : TacsScalar(0.0)); - - // Qxz: strain[6] = gamma_{xz} - *_Nxy = Qbar_stiff[5] * strain[6]; -} - -/* - Get information about the constraints - here just the ply fraction - constraints. -*/ -int bladeFSDTStiffness::isLinear() { return 1; } - -// The ply fractions must add up to one -int bladeFSDTStiffness::getNumCon() { return num_pf_con; } - -int bladeFSDTStiffness::getConCSRSize() { - return num_pf_unique + num_stiff_pf_unique; -} - -int bladeFSDTStiffness::getConRange(int offset, TacsScalar lb[], - TacsScalar ub[]) { - if (num_pf_unique > 0) { - lb[offset] = 1.0; - ub[offset] = 1.0; - offset++; - } - - if (num_stiff_pf_unique > 0) { - lb[offset] = 1.0; - ub[offset] = 1.0; - } - - return num_pf_con; -} - -int bladeFSDTStiffness::addConCSR(int offset, int rowp[], int cols[]) { - int start = rowp[offset]; - if (num_pf_unique > 0) { - for (int k = 0; k < num_pf_unique; k++, start++) { - cols[start] = pf_unique[k]; - } - offset++; - rowp[offset] = start; - } - - if (num_stiff_pf_unique > 0) { - for (int k = 0; k < num_stiff_pf_unique; k++, start++) { - cols[start] = stiff_pf_unique[k]; - } - offset++; - rowp[offset] = start; - } - - return num_pf_con; -} - -int bladeFSDTStiffness::evalCon(int offset, TacsScalar con[]) { - if (num_pf_unique > 0) { - con[offset] = 0.0; - for (int k = 0; k < NUM_PLIES; k++) { - con[offset] += pf[k]; - } - offset++; - } - - if (num_stiff_pf_unique > 0) { - con[offset] = 0.0; - for (int k = 0; k < NUM_PLIES; k++) { - con[offset] += stiff_pf[k]; - } - } - - return num_pf_con; -} - -int bladeFSDTStiffness::evalConDVSens(int offset, TacsScalar Acol[], - const int rowp[], const int cols[]) { - int start = rowp[offset]; - - if (num_pf_unique > 0) { - for (int k = 0; k < num_pf_unique; k++, start++) { - Acol[start] = 0.0; - for (int j = 0; j < NUM_PLIES; j++) { - if (pf_unique[k] == pf_nums[j]) { - Acol[start] += 1.0; - } - } - } - } - - if (num_stiff_pf_unique > 0) { - for (int k = 0; k < num_stiff_pf_unique; k++, start++) { - Acol[start] = 0.0; - for (int j = 0; j < NUM_PLIES; j++) { - if (stiff_pf_unique[k] == stiff_pf_nums[j]) { - Acol[start] += 1.0; - } - } - } - } - - return num_pf_con; -} - -// Design variable information set up -// ---------------------------------- -int bladeFSDTStiffness::ownsDesignVar(const int dvNum) const { - if (Lx_num == dvNum) { - return 1; - } else if (sp_num == dvNum) { - return 1; - } else if (sh_num == dvNum) { - return 1; - } else if (st_num == dvNum) { - return 1; - } else if (t_num == dvNum) { - return 1; - } - - for (int k = 0; k < NUM_PLIES; k++) { - if (pf_nums[k] == dvNum || stiff_pf_nums[k] == dvNum) { - return 1; - } - } - return 0; -} - -void bladeFSDTStiffness::setDesignVars(const TacsScalar dvs[], int numDVs) { - if (Lx_num >= 0 && Lx_num < numDVs) { - Lx = dvs[Lx_num]; - } - if (sp_num < numDVs) { - sp = dvs[sp_num]; - } - if (sh_num < numDVs) { - sh = dvs[sh_num]; - } - if (st_num < numDVs) { - st = dvs[st_num]; - } - if (t_num < numDVs) { - t = dvs[t_num]; - } - - for (int k = 0; k < NUM_PLIES; k++) { - if (pf_nums[k] >= 0 && pf_nums[k] < numDVs) { - pf[k] = dvs[pf_nums[k]]; - } - if (stiff_pf_nums[k] >= 0 && stiff_pf_nums[k] < numDVs) { - stiff_pf[k] = dvs[stiff_pf_nums[k]]; - } - } - - updateStiffness(); -} - -/* - Set the stiffness properties -*/ -void bladeFSDTStiffness::updateStiffness() { - // Zero the stiffness properties - for (int j = 0; j < 6; j++) { - Qbar_panel[j] = Qbar_stiff[j] = 0.0; - } - - for (int j = 0; j < 3; j++) { - Abar_panel[j] = Abar_stiff[j] = 0.0; - } - - // Calculate the constitutive properties of the panel - for (int k = 0; k < NUM_PLIES; k++) { - TacsScalar Qp[6], Ap[3]; - - // Calculate the stiffness contribution from the panel - ortho_ply->calculateQbar(Qp, ply_angles[k]); - ortho_ply->calculateAbar(Ap, ply_angles[k]); - - for (int j = 0; j < 6; j++) { - Qbar_panel[j] += pf[k] * Qp[j]; - } - - for (int j = 0; j < 3; j++) { - Abar_panel[j] += pf[k] * Ap[j]; - } - - // Calculate the stiffness contribution from the stiffener - ortho_ply->calculateQbar(Qp, stiff_ply_angles[k]); - ortho_ply->calculateAbar(Ap, stiff_ply_angles[k]); - - for (int j = 0; j < 6; j++) { - Qbar_stiff[j] += stiff_pf[k] * Qp[j]; - } - - for (int j = 0; j < 3; j++) { - Abar_stiff[j] += stiff_pf[k] * Ap[j]; - } - } - - A[0] = A[1] = A[2] = A[3] = A[4] = A[5] = 0.0; - B[0] = B[1] = B[2] = B[3] = B[4] = B[5] = 0.0; - D[0] = D[1] = D[2] = D[3] = D[4] = D[5] = 0.0; - As[0] = As[1] = As[2] = 0.0; - - // Add the contributions from the panel - TacsScalar It = (t * t * t) / 12.0; - - for (int k = 0; k < 6; k++) { - A[k] = t * Qbar_panel[k]; - B[k] = 0.0; - D[k] = It * Qbar_panel[k]; - } - - As[0] = t * kcorr * Abar_panel[0]; - As[1] = t * kcorr * Abar_panel[1]; - As[2] = t * kcorr * Abar_panel[2]; - - k_penalty = DRILLING_REGULARIZATION * Qbar_panel[5] * t; - - // Add the contributions from the stiffener - // st == stiffener thickness - // sh == stiffener height - // sf_fraction == stiffener flange fraction - TacsScalar Area = st * sh * (1.0 + sf_fraction); - TacsScalar es = -0.5 * sh; - - // The moment of inertia of the stiffener about the neutral axis of - // the plate - TacsScalar Is = st * (sh * sh * sh / 12.0); - TacsScalar Js = sh * (st * st * st / 3.0); - - // The effective Young's modulus of the stiffener - TacsScalar Es = - (Qbar_stiff[0] - (Qbar_stiff[1] * Qbar_stiff[1]) / Qbar_stiff[3]); - TacsScalar Gs = Qbar_stiff[5]; - - // Add the contributions to the stiffness - TacsScalar sfact = 1.0 / sp; - A[0] += (Es * Area) * sfact; - B[0] += (es * Es * Area) * sfact; - D[0] += Es * (Area * es * es + Is) * sfact; - D[5] += Js * Gs * sfact; - As[0] += kcorr * Gs * sh * st * sfact; - - if (TacsRealPart(B[0] * B[0]) > TacsRealPart(A[0] * D[0])) { - fprintf(stderr, "bladeFSDTStiffness: A11*D11 - B11^2 < 0\n"); - fprintf(stderr, "t = %8.3f sh = %8.3f st = %8.3f sp = %8.3f\n", - TacsRealPart(t), TacsRealPart(sh), TacsRealPart(st), - TacsRealPart(sp)); - fprintf(stderr, "A11 = %10.3e B11 = %10.3e D11 = %10.3e\n", - TacsRealPart(A[0]), TacsRealPart(B[0]), TacsRealPart(D[0])); - } - - calcBucklingProps(); -} - -int bladeFSDTStiffness::getLxNum() { return Lx_num; } - -void bladeFSDTStiffness::getDesignVars(TacsScalar dvs[], int numDVs) { - if (Lx_num >= 0 && Lx_num < numDVs) { - dvs[Lx_num] = Lx; - } - if (sp_num >= 0 && sp_num < numDVs) { - dvs[sp_num] = sp; - } - if (sh_num >= 0 && sh_num < numDVs) { - dvs[sh_num] = sh; - } - if (st_num >= 0 && st_num < numDVs) { - dvs[st_num] = st; - } - if (t_num >= 0 && t_num < numDVs) { - dvs[t_num] = t; - } - - for (int k = 0; k < NUM_PLIES; k++) { - if (pf_nums[k] >= 0 && pf_nums[k] < numDVs) { - dvs[pf_nums[k]] = pf[k]; - } - if (stiff_pf_nums[k] >= 0 && stiff_pf_nums[k] < numDVs) { - dvs[stiff_pf_nums[k]] = stiff_pf[k]; - } - } -} - -void bladeFSDTStiffness::getDesignVarRange(TacsScalar lb[], TacsScalar ub[], - int numDVs) { - if (Lx_num >= 0 && Lx_num < numDVs) { - lb[Lx_num] = 0.0; - ub[Lx_num] = 1e20; - } - if (sp_num < numDVs) { - lb[sp_num] = sp_low; - ub[sp_num] = sp_high; - } - if (sh_num < numDVs) { - lb[sh_num] = sh_low; - ub[sh_num] = sh_high; - } - if (st_num < numDVs) { - lb[st_num] = st_low; - ub[st_num] = st_high; - } - if (t_num < numDVs) { - lb[t_num] = t_low; - ub[t_num] = t_high; - } - - for (int k = 0; k < NUM_PLIES; k++) { - if (pf_nums[k] >= 0 && pf_nums[k] < numDVs) { - lb[pf_nums[k]] = pf_low[k]; - ub[pf_nums[k]] = pf_high[k]; - } - } - - for (int k = 0; k < NUM_PLIES; k++) { - if (stiff_pf_nums[k] >= 0 && stiff_pf_nums[k] < numDVs) { - lb[stiff_pf_nums[k]] = stiff_pf_low[k]; - ub[stiff_pf_nums[k]] = stiff_pf_high[k]; - } - } -} - -/* - Calculate the mass per unit area and the moment of inertia per unit - area of the plate. -*/ -void bladeFSDTStiffness::getPointwiseMass(const double gpt[], - TacsScalar mass[]) { - mass[0] = ortho_ply->getRho() * t; - mass[1] = 0.0; - mass[2] = ortho_ply->getRho() * t * t * t / 12.0; - - TacsScalar Area = st * sh * (1.0 + sf_fraction); - TacsScalar sfact = 1.0 / sp; - - // Add the contribution to the mass - mass[0] += ortho_ply->getRho() * Area * sfact; - mass[2] += 0.25 * ortho_ply->getRho() * st * st * Area * sfact; -} - -/* - Calculate the sensitivity of the pointwise mass -*/ -void bladeFSDTStiffness::pointwiseMassDVSens(int dvNum, const double gpt[], - TacsScalar massDVSens[]) { - massDVSens[0] = massDVSens[1] = massDVSens[2] = 0.0; - if (dvNum >= 0) { - if (t_num == dvNum) { - massDVSens[0] = ortho_ply->getRho(); - massDVSens[2] = ortho_ply->getRho() * t * t / 4.0; - } else if (sp_num == dvNum) { - TacsScalar Area = st * sh * (1.0 + sf_fraction); - TacsScalar sfact_sens = -1.0 / (sp * sp); - - massDVSens[0] = ortho_ply->getRho() * Area * sfact_sens; - massDVSens[2] = 0.25 * ortho_ply->getRho() * st * st * Area * sfact_sens; - } else if (sh_num == dvNum) { - TacsScalar Area_sens = st * (1.0 + sf_fraction); - TacsScalar sfact = 1.0 / sp; - - massDVSens[0] = ortho_ply->getRho() * Area_sens * sfact; - massDVSens[2] = 0.25 * ortho_ply->getRho() * st * st * Area_sens * sfact; - } else if (st_num == dvNum) { - TacsScalar Area_sens = sh * (1.0 + sf_fraction); - TacsScalar sfact = 1.0 / sp; - - massDVSens[0] += ortho_ply->getRho() * Area_sens * sfact; - massDVSens[2] = - (3.0 / 4.0) * ortho_ply->getRho() * st * st * Area_sens * sfact; - } - } -} - -TacsScalar bladeFSDTStiffness::getDensity() { return ortho_ply->getRho(); } - -/* - Add the derivative of the pointwise mass times alpha to each component -*/ -void bladeFSDTStiffness::addPointwiseMassDVSens(const double pt[], - const TacsScalar alpha[], - TacsScalar dvSens[], - int dvLen) { - TacsScalar rho = ortho_ply->getRho(); - - if (t_num >= 0 && t_num < dvLen) { - dvSens[t_num] += alpha[0] * rho; - } - if (sp_num >= 0 && sp_num < dvLen) { - TacsScalar Area = st * sh * (1.0 + sf_fraction); - TacsScalar sfact_sens = -1.0 / (sp * sp); - - dvSens[sp_num] += alpha[0] * rho * Area * sfact_sens; - } - if (sh_num >= 0 && sh_num < dvLen) { - TacsScalar Area_sens = st * (1.0 + sf_fraction); - TacsScalar sfact = 1.0 / sp; - - dvSens[sh_num] += alpha[0] * rho * Area_sens * sfact; - } - if (st_num >= 0 && st_num < dvLen) { - TacsScalar Area_sens = sh * (1.0 + sf_fraction); - TacsScalar sfact = 1.0 / sp; - - dvSens[st_num] += alpha[0] * rho * Area_sens * sfact; - } -} - -/* - Calculate the stiffness properties of the panel -*/ -TacsScalar bladeFSDTStiffness::getStiffness(const double gpt[], TacsScalar _A[], - TacsScalar _B[], TacsScalar _D[], - TacsScalar _As[]) { - for (int k = 0; k < 6; k++) { - _A[k] = A[k]; - _B[k] = B[k]; - _D[k] = D[k]; - } - - for (int k = 0; k < 3; k++) { - _As[k] = As[k]; - } - - return k_penalty; -} - -/* - Calculate the derivative w.r.t. one of the design variables: - - sp: the stiffener pitch - sh: the stiffener height - st: the stiffener thickness - t: the panel thickness - - Note that sensitivities w.r.t. the ply fractions are handled - elsewhere. -*/ -TacsScalar bladeFSDTStiffness::getStiffnessDVSens(int dvNum, const double gpt[], - TacsScalar sA[], - TacsScalar sB[], - TacsScalar sD[], - TacsScalar sAs[]) { - sA[0] = sA[1] = sA[2] = sA[3] = sA[4] = sA[5] = 0.0; - sB[0] = sB[1] = sB[2] = sB[3] = sB[4] = sB[5] = 0.0; - sD[0] = sD[1] = sD[2] = sD[3] = sD[4] = sD[5] = 0.0; - sAs[0] = sAs[1] = sAs[2] = 0.0; - - TacsScalar k_penalty_sens = 0.0; - - if (dvNum >= 0 && ownsDesignVar(dvNum)) { - if (t_num == dvNum) { - // Calcualte the senstivity w.r.t. the panel thickness - TacsScalar It = (t * t) / 4.0; - - for (int k = 0; k < 6; k++) { - sA[k] = Qbar_panel[k]; - sB[k] = 0.0; - sD[k] = It * Qbar_panel[k]; - } - - sAs[0] = kcorr * Abar_panel[0]; - sAs[1] = kcorr * Abar_panel[1]; - sAs[2] = kcorr * Abar_panel[2]; - - k_penalty_sens = DRILLING_REGULARIZATION * Qbar_panel[5]; - } else if (sp_num == dvNum) { - // Calculate the derivative of the stiffness w.r.t. stiffener pitch - TacsScalar Area = st * sh * (1.0 + sf_fraction); - TacsScalar es = -0.5 * sh; - TacsScalar Is = st * (sh * sh * sh / 12.0); - TacsScalar Js = sh * (st * st * st / 3.0); - - // The effective Young's modulus of the stiffener - TacsScalar Es = - (Qbar_stiff[0] - (Qbar_stiff[1] * Qbar_stiff[1]) / Qbar_stiff[3]); - TacsScalar Gs = Qbar_stiff[5]; - - // Add the contributions to the stiffness - TacsScalar sfact_sens = -1.0 / (sp * sp); - sA[0] += (Es * Area) * sfact_sens; - sB[0] += (es * Es * Area) * sfact_sens; - sD[0] += Es * (Area * es * es + Is) * sfact_sens; - sD[5] += Js * Gs * sfact_sens; - sAs[0] += kcorr * Gs * sh * st * sfact_sens; - } else if (sh_num == dvNum) { - // Calculate the derivative of the stiffness w.r.t. stiffener height - TacsScalar Area = st * sh * (1.0 + sf_fraction); - TacsScalar es = -0.5 * sh; - - TacsScalar Area_sens = st * (1.0 + sf_fraction); - TacsScalar es_sens = -0.5; - TacsScalar Is_sens = st * sh * sh / 4.0; - TacsScalar Js_sens = (st * st * st / 3.0); - - // The effective Young's modulus of the stiffener - TacsScalar Es = - (Qbar_stiff[0] - (Qbar_stiff[1] * Qbar_stiff[1]) / Qbar_stiff[3]); - TacsScalar Gs = Qbar_stiff[5]; - - // Add the contributions to the stiffness - TacsScalar sfact = 1.0 / sp; - sA[0] += (Es * Area_sens) * sfact; - sB[0] += Es * (es_sens * Area + es * Area_sens) * sfact; - sD[0] += Es * - (Area_sens * es * es + 2.0 * Area * es * es_sens + Is_sens) * - sfact; - sD[5] += Js_sens * Gs * sfact; - sAs[0] += kcorr * Gs * st * sfact; - } else if (st_num == dvNum) { - // calculate the derivative of the stiffness w.r.t. - // the stiffener thickness - TacsScalar es = -0.5 * sh; - - TacsScalar Area_sens = sh * (1.0 + sf_fraction); - TacsScalar Is_sens = (sh * sh * sh / 12.0); - TacsScalar Js_sens = sh * st * st; - - // The effective Young's modulus of the stiffener - TacsScalar Es = - (Qbar_stiff[0] - (Qbar_stiff[1] * Qbar_stiff[1]) / Qbar_stiff[3]); - TacsScalar Gs = Qbar_stiff[5]; - - // Add the contributions to the stiffness - TacsScalar sfact = 1.0 / sp; - sA[0] += (Es * Area_sens) * sfact; - sB[0] += (es * Es * Area_sens) * sfact; - sD[0] += Es * (Area_sens * es * es + Is_sens) * sfact; - sD[5] += Js_sens * Gs * sfact; - sAs[0] += kcorr * Gs * sh * sfact; - } else { - TacsScalar sAbar_panel[3], sQbar_panel[6]; - TacsScalar sAbar_stiff[3], sQbar_stiff[6]; - sAbar_panel[0] = sAbar_panel[1] = sAbar_panel[2] = 0.0; - sAbar_stiff[0] = sAbar_stiff[1] = sAbar_stiff[2] = 0.0; - - sQbar_panel[0] = sQbar_panel[1] = sQbar_panel[2] = 0.0; - sQbar_panel[3] = sQbar_panel[4] = sQbar_panel[5] = 0.0; - - sQbar_stiff[0] = sQbar_stiff[1] = sQbar_stiff[2] = 0.0; - sQbar_stiff[3] = sQbar_stiff[4] = sQbar_stiff[5] = 0.0; - - for (int k = 0; k < NUM_PLIES; k++) { - if (pf_nums[k] == dvNum) { - TacsScalar Qp[6], Ap[3]; - ortho_ply->calculateQbar(Qp, ply_angles[k]); - ortho_ply->calculateAbar(Ap, ply_angles[k]); - - for (int j = 0; j < 6; j++) { - sQbar_panel[j] += Qp[j]; - } - - for (int j = 0; j < 3; j++) { - sAbar_panel[j] += Ap[j]; - } - } - } - - // Add the contributions from the panel - TacsScalar It = (t * t * t) / 12.0; - - for (int k = 0; k < 6; k++) { - sA[k] = t * sQbar_panel[k]; - sB[k] = 0.0; - sD[k] = It * sQbar_panel[k]; - } - - sAs[0] = t * kcorr * sAbar_panel[0]; - sAs[1] = t * kcorr * sAbar_panel[1]; - sAs[2] = t * kcorr * sAbar_panel[2]; - - for (int k = 0; k < NUM_PLIES; k++) { - if (stiff_pf_nums[k] == dvNum) { - TacsScalar Qp[6], Ap[3]; - ortho_ply->calculateQbar(Qp, stiff_ply_angles[k]); - ortho_ply->calculateAbar(Ap, stiff_ply_angles[k]); - - for (int j = 0; j < 6; j++) { - sQbar_stiff[j] += Qp[j]; - } - - for (int j = 0; j < 3; j++) { - sAbar_stiff[j] += Ap[j]; - } - } - } - - TacsScalar Area = st * sh * (1.0 + sf_fraction); - TacsScalar es = -0.5 * sh; - TacsScalar Is = st * (sh * sh * sh / 12.0); - TacsScalar Js = sh * (st * st * st / 3.0); - - TacsScalar Es_sens = - (sQbar_stiff[0] - - 2.0 * (Qbar_stiff[1] * sQbar_stiff[1]) / Qbar_stiff[3] + - sQbar_stiff[3] * (Qbar_stiff[1] * Qbar_stiff[1]) / - (Qbar_stiff[3] * Qbar_stiff[3])); - TacsScalar Gs_sens = sQbar_stiff[5]; - - TacsScalar sfact = 1.0 / sp; - sA[0] += (Es_sens * Area) * sfact; - sB[0] += (es * Es_sens * Area) * sfact; - sD[0] += Es_sens * (Area * es * es + Is) * sfact; - sD[5] += Js * Gs_sens * sfact; - sAs[0] += kcorr * Gs_sens * sh * st * sfact; - - k_penalty_sens = DRILLING_REGULARIZATION * sQbar_panel[5] * t; - } - } - - return k_penalty_sens; -} - -/* - Add the derivative of the product of the stress to the design - derivative array -*/ -void bladeFSDTStiffness::addStiffnessDVSens(const double pt[], - const TacsScalar e[], - const TacsScalar psi[], - TacsScalar rotPsi, - TacsScalar fdvSens[], int dvLen) { - int panel_nums[5] = {t_num, sp_num, sh_num, st_num, Lx_num}; - int dvNum; - // Store the derivative of the stress values - TacsScalar s[8], ksens; - - for (int k = 0; k < 5 + 2 * NUM_PLIES; k++) { - if (k < 5) { - dvNum = panel_nums[k]; - } else if (5 <= k && k < NUM_PLIES + 5) { - dvNum = pf_nums[k - 5]; - } else { - dvNum = stiff_pf_nums[k - (NUM_PLIES + 5)]; - } - - if (dvNum >= 0 && dvNum < dvLen) { - ksens = calculateStressDVSens(pt, e, s, dvNum); - - // Add the result to the design variable vector - fdvSens[dvNum] += (s[0] * psi[0] + s[1] * psi[1] + s[2] * psi[2] + - s[3] * psi[3] + s[4] * psi[4] + s[5] * psi[5] + - s[6] * psi[6] + s[7] * psi[7] + rotPsi * ksens); - } - } -} - -/* - Add the derivative of the product of the stress to the design - derivative array -*/ -TacsScalar bladeFSDTStiffness::calculateStressDVSens(const double pt[], - const TacsScalar strain[], - TacsScalar s_sens[], - int dvNum) { - // Store the derivative of the stress values - TacsScalar A_sens[6], B_sens[6], D_sens[6], As_sens[3]; - TacsScalar ksens; - - ksens = getStiffnessDVSens(dvNum, pt, A_sens, B_sens, D_sens, As_sens); - - // Compute the in-plane resultants - s_sens[0] = A_sens[0] * strain[0] + A_sens[1] * strain[1] + - A_sens[2] * strain[2] + B_sens[0] * strain[3] + - B_sens[1] * strain[4] + B_sens[2] * strain[5]; - s_sens[1] = A_sens[1] * strain[0] + A_sens[3] * strain[1] + - A_sens[4] * strain[2] + B_sens[1] * strain[3] + - B_sens[3] * strain[4] + B_sens[4] * strain[5]; - s_sens[2] = A_sens[2] * strain[0] + A_sens[4] * strain[1] + - A_sens[5] * strain[2] + B_sens[2] * strain[3] + - B_sens[4] * strain[4] + B_sens[5] * strain[5]; - - // Compute the bending moments - s_sens[3] = B_sens[0] * strain[0] + B_sens[1] * strain[1] + - B_sens[2] * strain[2] + D_sens[0] * strain[3] + - D_sens[1] * strain[4] + D_sens[2] * strain[5]; - s_sens[4] = B_sens[1] * strain[0] + B_sens[3] * strain[1] + - B_sens[4] * strain[2] + D_sens[1] * strain[3] + - D_sens[3] * strain[4] + D_sens[4] * strain[5]; - s_sens[5] = B_sens[2] * strain[0] + B_sens[4] * strain[1] + - B_sens[5] * strain[2] + D_sens[2] * strain[3] + - D_sens[4] * strain[4] + D_sens[5] * strain[5]; - - // Compute the shear resultants - s_sens[6] = As_sens[0] * strain[6] + As_sens[1] * strain[7]; - s_sens[7] = As_sens[1] * strain[6] + As_sens[2] * strain[7]; - - return ksens; -} - -/* - The shear buckling loads are calculated based on an infinite-plate - solution simply supported along the panel sides. For the local skin - buckling calculations we use the infinite plate solution along edges - supported by the blade stiffeners, therefore the panel width is - equal to the stiffener pitch (sp). For the global-level - calculations, we use the panel length equal to the rib pitch, thus - the panel width is equal to the local panel length (Lx). - - In Stroud and Arganoff, the following formula are suggested for the - calculation of the buckling loads: - - xi = sqrt(D1*D2)/D3 - - if xi > 1.0: - Nxy,crit = (4.0/Ly^2)*(D2*D1^3)^(1/4)*(8.125 + 5.05/xi) - else: - Nxy,crit = (4.0/Ly^2)*sqrt(D1*D3)*(11.7 + 0.532*xi + 0.938*xi^2) - - Note that if xi = 1, then D3 = sqrt(D1*D2) and so - (4.0/Ly^2)*sqrt(D1*D3) = (4.0/Ly^2)*(D1*D1^3)^(1/4) - - However, when xi = 1, the two terms inside the brackets are not - equal. As a result, there is a discontinuity between the two - expressions. To avoid this, we adjust the first formula in a - conservative manner. As shown in Lekhnitskii, the limit for xi -> - infty is 8.125, while for xi = 1 is 13.17 and for xi = 0, 11.71. - - The formula in Stroud and Arganoff do not meet these end conditions. - We adjust the formula as follows: - - if xi > 1.0: - Nxy,crit = (4.0/Ly^2)*(D2*D1^3)^(1/4)*(8.125 + 5.045/xi) - else: - Nxy,crit = (4.0/Ly^2)*sqrt(D1*D3)*(11.7 + 0.532*xi + 0.938*xi^2) - - input: - D1: the longitudinal bending stiffness - D2: the transverse bending stiffness - D3: the shear bending stiffness - L: the side-length of the panel - - returns: - Nxy_crit: the approximate critical buckling load -*/ -TacsScalar bladeFSDTStiffness::calcCriticalShearLoad(TacsScalar D1, - TacsScalar D2, - TacsScalar D3, - TacsScalar L) { - TacsScalar xi = sqrt(D1 * D2) / D3; - - double ks = 50.0; - TacsScalar Nxy_crit_1 = - (4.0 / (L * L)) * sqrt(D3 * D1 * xi) * (8.125 + 5.045 / xi); - TacsScalar Nxy_crit_2 = - (4.0 / (L * L)) * sqrt(D1 * D3) * (11.7 + 0.532 * xi + 0.938 * xi * xi); - - TacsScalar Nxy_min = 0.0; - if (TacsRealPart(Nxy_crit_1) < TacsRealPart(Nxy_crit_2)) { - Nxy_min = Nxy_crit_1; - } else { - Nxy_min = Nxy_crit_2; - } - - TacsScalar Nxy_diff = fabs(Nxy_crit_1 - Nxy_crit_2); - TacsScalar Nxy_crit = Nxy_min - log(1.0 + exp(-ks * Nxy_diff)) / ks; - - return Nxy_crit; -} - -/* - Calculate the sensitivity of the shear buckling load w.r.t. the - inputs. This is the differentiated version of the above code. -*/ -TacsScalar bladeFSDTStiffness::calcCriticalShearLoadSens( - TacsScalar D1, TacsScalar D2, TacsScalar D3, TacsScalar L, TacsScalar sD1, - TacsScalar sD2, TacsScalar sD3, TacsScalar sL) { - TacsScalar xi = sqrt(D1 * D2) / D3; - TacsScalar sxi = - (0.5 * (D1 * sD2 + D2 * sD1) - xi * xi * D3 * sD3) / (xi * D3 * D3); - - double ks = 50.0; - TacsScalar Nxy_crit_1 = - (4.0 / (L * L)) * sqrt(D3 * D1 * xi) * (8.125 + 5.045 / xi); - TacsScalar Nxy_crit_2 = - (4.0 / (L * L)) * sqrt(D1 * D3) * (11.7 + 0.532 * xi + 0.938 * xi * xi); - - TacsScalar Nxy_min = 0.0; - if (TacsRealPart(Nxy_crit_1) < TacsRealPart(Nxy_crit_2)) { - Nxy_min = Nxy_crit_1; - } else { - Nxy_min = Nxy_crit_2; - } - - TacsScalar Nxy_diff = fabs(Nxy_crit_1 - Nxy_crit_2); - TacsScalar sum = 1.0 + exp(-ks * Nxy_diff); - - // Compute the derivative w.r.t. the first critical load - TacsScalar y = sqrt(D3 * D1 * xi); - TacsScalar sy = 0.5 * (sD3 * D1 * xi + sD1 * D3 * xi + sxi * D1 * D3) / y; - TacsScalar cb = (8.125 + 5.045 / xi); - - TacsScalar Nxy_crit_1_sens = - (4.0 / (L * L)) * (sy * cb - 5.045 * sxi * y / (xi * xi)); - if (sL != 0.0) { - Nxy_crit_1_sens -= 8.0 * sL / (L * L * L) * y * cb; - } - - // Compute the derivative w.r.t. the second critical load - y = sqrt(D1 * D3); - sy = 0.5 * (sD1 * D3 + sD3 * D1) / y; - cb = (11.7 + 0.532 * xi + 0.938 * xi * xi); - - TacsScalar Nxy_crit_2_sens = - (4.0 / (L * L)) * (sy * cb + y * (0.532 * sxi + 2.0 * 0.938 * xi * sxi)); - if (sL != 0.0) { - Nxy_crit_2_sens -= 8.0 * sL / (L * L * L) * y * cb; - } - - // Compute the derivative due to the KS function - TacsScalar Nxy_crit_sens = 0.0; - if (TacsRealPart(Nxy_crit_1) < TacsRealPart(Nxy_crit_2)) { - Nxy_crit_sens = - (Nxy_crit_1_sens + Nxy_crit_2_sens * exp(-ks * Nxy_diff)) / sum; - } else { - Nxy_crit_sens = - (Nxy_crit_1_sens * exp(-ks * Nxy_diff) + Nxy_crit_2_sens) / sum; - } - - return Nxy_crit_sens; -} - -/* - Calculate the buckling properties of the panel - - The global buckling loads for the smeared panel: - Nx_global_crit: The critical axial buckling load - Nxy_global_crit: The critical shear buckling load - - The buckling loads for the skin in between stiffeners: - Nx_panel_crit: The critical buckling load of the panel - Nxy_panel_crit: The critical shear buckling load of the panel - - The buckling load of the stiffener: - Nx_weak_stiff_crit: The critical lower buckling load of the stiffener - Nx_strong_stiff_crit: The criticial higher buckling load of the stiffener -*/ -void bladeFSDTStiffness::calcBucklingProps() { - // Calculate the global buckling mode - // ---------------------------------- - // Compute the neutral axis location: - TacsScalar Ep = - Qbar_panel[0] - (Qbar_panel[1] * Qbar_panel[1]) / Qbar_panel[3]; - TacsScalar Es = - Qbar_stiff[0] - (Qbar_stiff[1] * Qbar_stiff[1]) / Qbar_stiff[3]; - - // The modulus-weighted area: - TacsScalar An = (Ep * sp * t + Es * sh * st * (1.0 + sf_fraction)); - - // The modulus-weighted moment of area - TacsScalar Cn = 0.5 * Es * sh * sh * st; - - // The modulus-weighted centroid - TacsScalar zn = Cn / An; - - // The bending stiffness - TacsScalar EI = (zn * zn * (t * sp * Ep + st * sh * sf_fraction * Es) + - Es * (st * (sh * sh * sh) / 12.0 + - st * sh * (zn - 0.5 * sh) * (zn - 0.5 * sh))); - - // Compute the unit EI stiffness for the buckling - TacsScalar D1 = EI / sp; - Nx_global_crit = (M_PI * M_PI * D1) / (Lx * Lx); - - // Compute the required data for the shear loading - // The transverse bending stiffness - TacsScalar D12_panel = (t * t * t * Qbar_panel[1]) / 12.0; - TacsScalar D12_stiff = ((t + 0.5 * st) * (t + 0.5 * st) * (t + 0.5 * st) * - (Qbar_panel[1] + Qbar_stiff[1])) / - 6.0; - - TacsScalar D2 = sp / ((sp - sh * sf_fraction) / D12_panel + - (sh * sf_fraction) / D12_stiff); - - // The twisting stiffness - TacsScalar D66_panel = (t * t * t * Qbar_panel[5]) / 12.0; - TacsScalar D66_stiff = ((t + 0.5 * st) * (t + 0.5 * st) * (t + 0.5 * st) * - (Qbar_panel[5] + Qbar_stiff[5])) / - 6.0; - - TacsScalar D3 = sp / ((sp - sh * sf_fraction) / D66_panel + - (sh * sf_fraction) / D66_stiff); - Nxy_global_crit = calcCriticalShearLoad(D1, D2, D3, Lx); - - // Compute the critical buckling loads for the panel - // ------------------------------------------------- - TacsScalar I = (t * t * t) / 12.0; - TacsScalar D11 = I * Qbar_panel[0]; - TacsScalar D12 = I * Qbar_panel[1]; - TacsScalar D22 = I * Qbar_panel[3]; - TacsScalar D66 = I * Qbar_panel[5]; - - Nx_panel_crit = - (2.0 * M_PI * M_PI / (sp * sp)) * (sqrt(D11 * D22) + D12 + 2.0 * D66); - Nxy_panel_crit = calcCriticalShearLoad(D11, D22, D12 + 2.0 * D66, sp); - - // Compute the critical loads for the stiffener - // -------------------------------------------- - TacsScalar Is_weak = sh * st * st * st / 12.0; - TacsScalar Is_strong = st * sh * sh * sh / 12.0; - - Nx_weak_stiff_crit = (M_PI * M_PI * Es * Is_weak) / (Lx * Lx); - Nx_strong_stiff_crit = (M_PI * M_PI * Es * Is_strong) / (Lx * Lx); -} - -/* - Calculate the derivative of the critical buckling loads w.r.t. the - design variables - - This function computes the derivative w.r.t: - - t_num: the panel thickness - sh_num: the stiffener height - st_num: the stiffener thickness - sp_num: the stiffener pitch - Lx_num: the length of the panel - - And... any remaining ply fraction variables through sQbar_panel and - sQbar_stiff -*/ -void bladeFSDTStiffness::calcBucklingPropsDVSens( - int dvNum, TacsScalar* sNx_global_crit, TacsScalar* sNxy_global_crit, - TacsScalar* sNx_panel_crit, TacsScalar* sNxy_panel_crit, - TacsScalar* sNx_weak_stiff_crit, TacsScalar* sNx_strong_stiff_crit) { - if (dvNum == t_num) { - // Compute the neutral axis location: - TacsScalar Ep = - Qbar_panel[0] - (Qbar_panel[1] * Qbar_panel[1]) / Qbar_panel[3]; - TacsScalar Es = - Qbar_stiff[0] - (Qbar_stiff[1] * Qbar_stiff[1]) / Qbar_stiff[3]; - - // The modulus-weighted area: - TacsScalar An = (Ep * sp * t + Es * sh * st + Es * sh * st * sf_fraction); - TacsScalar An_sens = Ep * sp; - - // The modulus-weighted centroid - TacsScalar Cn = 0.5 * Es * sh * sh * st; - - // The modulus-weighted centroid - TacsScalar zn = Cn / An; - TacsScalar zn_sens = -Cn / (An * An) * An_sens; - - // The bending stiffness - TacsScalar EI = (zn * zn * (t * sp * Ep + st * sh * sf_fraction * Es) + - Es * (st * (sh * sh * sh) / 12.0 + - st * sh * (zn - 0.5 * sh) * (zn - 0.5 * sh))); - TacsScalar EI_sens = - (2.0 * zn * zn_sens * (t * sp * Ep + st * sh * sf_fraction * Es) + - zn * zn * sp * Ep + Es * (2.0 * st * sh * (zn - 0.5 * sh) * zn_sens)); - - // Compute the unit EI stiffness for the buckling - TacsScalar D1 = EI / sp; - TacsScalar D1_sens = EI_sens / sp; - - // Compute the sensitivity of the global axial load - *sNx_global_crit = (M_PI * M_PI * D1_sens) / (Lx * Lx); - - // Compute the required data for the shear loading - // The transverse bending stiffness - TacsScalar D12_panel = (t * t * t * Qbar_panel[1]) / 12.0; - TacsScalar D12_stiff = ((t + 0.5 * st) * (t + 0.5 * st) * (t + 0.5 * st) * - (Qbar_panel[1] + Qbar_stiff[1])) / - 6.0; - - TacsScalar D2 = sp / ((sp - sh * sf_fraction) / D12_panel + - (sh * sf_fraction) / D12_stiff); - - TacsScalar D12_panel_sens = (t * t * Qbar_panel[1]) / 4.0; - TacsScalar D12_stiff_sens = - ((t + 0.5 * st) * (t + 0.5 * st) * (Qbar_panel[1] + Qbar_stiff[1])) / - 2.0; - - TacsScalar D2_sens = - (D2 * D2 / sp) * - ((sp - sh * sf_fraction) / (D12_panel * D12_panel) * D12_panel_sens + - (sh * sf_fraction) / (D12_stiff * D12_stiff) * D12_stiff_sens); - - // The twisting stiffness - TacsScalar D66_panel = (t * t * t * Qbar_panel[5]) / 12.0; - TacsScalar D66_stiff = ((t + 0.5 * st) * (t + 0.5 * st) * (t + 0.5 * st) * - (Qbar_panel[5] + Qbar_stiff[5])) / - 6.0; - - TacsScalar D3 = sp / ((sp - sh * sf_fraction) / D66_panel + - (sh * sf_fraction) / D66_stiff); - - TacsScalar D66_panel_sens = (t * t * Qbar_panel[5]) / 4.0; - TacsScalar D66_stiff_sens = - ((t + 0.5 * st) * (t + 0.5 * st) * (Qbar_panel[5] + Qbar_stiff[5])) / - 2.0; - - TacsScalar D3_sens = - (D3 * D3 / sp) * - ((sp - sh * sf_fraction) / (D66_panel * D66_panel) * D66_panel_sens + - (sh * sf_fraction) / (D66_stiff * D66_stiff) * D66_stiff_sens); - - *sNxy_global_crit = calcCriticalShearLoadSens(D1, D2, D3, Lx, D1_sens, - D2_sens, D3_sens, 0.0); - - // Compute the remaining critical loads - TacsScalar I = (t * t * t) / 12.0; - TacsScalar D11 = I * Qbar_panel[0]; - TacsScalar D12 = I * Qbar_panel[1]; - TacsScalar D22 = I * Qbar_panel[3]; - TacsScalar D66 = I * Qbar_panel[5]; - - TacsScalar I_sens = (t * t) / 4.0; - TacsScalar D11_sens = I_sens * Qbar_panel[0]; - TacsScalar D12_sens = I_sens * Qbar_panel[1]; - TacsScalar D22_sens = I_sens * Qbar_panel[3]; - TacsScalar D66_sens = I_sens * Qbar_panel[5]; - - TacsScalar sqrtD11D22 = sqrt(D11 * D22); - - *sNx_panel_crit = (2.0 * M_PI * M_PI / (sp * sp)) * - (0.5 * (D11 * D22_sens + D11_sens * D22) / sqrtD11D22 + - D12_sens + 2.0 * D66_sens); - - *sNxy_panel_crit = - calcCriticalShearLoadSens(D11, D22, D12 + 2.0 * D66, sp, D11_sens, - D22_sens, D12_sens + 2.0 * D66_sens, 0.0); - - *sNx_weak_stiff_crit = 0.0; - *sNx_strong_stiff_crit = 0.0; - } else if (dvNum == sp_num) { - // Calculate the derivative w.r.t. the stiffener spacing - TacsScalar Ep = - Qbar_panel[0] - (Qbar_panel[1] * Qbar_panel[1]) / Qbar_panel[3]; - TacsScalar Es = - Qbar_stiff[0] - (Qbar_stiff[1] * Qbar_stiff[1]) / Qbar_stiff[3]; - - // The modulus-weighted area: - TacsScalar An = (Ep * sp * t + Es * sh * st + Es * sh * st * sf_fraction); - TacsScalar An_sens = Ep * t; - - // The modulus-weighted centroid - TacsScalar Cn = 0.5 * Es * sh * sh * st; - - // The modulus-weighted centroid - TacsScalar zn = Cn / An; - TacsScalar zn_sens = -Cn / (An * An) * An_sens; - - // The bending stiffness - TacsScalar EI = (zn * zn * (t * sp * Ep + st * sh * sf_fraction * Es) + - Es * (st * (sh * sh * sh) / 12.0 + - st * sh * (zn - 0.5 * sh) * (zn - 0.5 * sh))); - TacsScalar EI_sens = - (2.0 * zn * zn_sens * (t * sp * Ep + st * sh * sf_fraction * Es) + - Es * (2.0 * st * sh * (zn - 0.5 * sh) * zn_sens) + zn * zn * (t * Ep)); - - // Compute the unit EI stiffness for the buckling - TacsScalar D1 = EI / sp; - TacsScalar D1_sens = EI_sens / sp - EI / (sp * sp); - *sNx_global_crit = (M_PI * M_PI * D1_sens) / (Lx * Lx); - - // Compute the required data for the shear loading - // The transverse bending stiffness - TacsScalar D12_panel = (t * t * t * Qbar_panel[1]) / 12.0; - TacsScalar D12_stiff = ((t + 0.5 * st) * (t + 0.5 * st) * (t + 0.5 * st) * - (Qbar_panel[1] + Qbar_stiff[1])) / - 6.0; - - TacsScalar D2 = sp / ((sp - sh * sf_fraction) / D12_panel + - (sh * sf_fraction) / D12_stiff); - TacsScalar D2_sens = (D2 / sp) - ((D2 * D2) / sp) * (1.0 / D12_panel); - - // The twisting stiffness - TacsScalar D66_panel = (t * t * t * Qbar_panel[5]) / 12.0; - TacsScalar D66_stiff = ((t + 0.5 * st) * (t + 0.5 * st) * (t + 0.5 * st) * - (Qbar_panel[5] + Qbar_stiff[5])) / - 6.0; - - TacsScalar D3 = sp / ((sp - sh * sf_fraction) / D66_panel + - (sh * sf_fraction) / D66_stiff); - TacsScalar D3_sens = (D3 / sp) - ((D3 * D3) / sp) * (1.0 / D66_panel); - - *sNxy_global_crit = calcCriticalShearLoadSens(D1, D2, D3, Lx, D1_sens, - D2_sens, D3_sens, 0.0); - - // Compute the critical buckling loads for the panel - TacsScalar I = (t * t * t) / 12.0; - TacsScalar D11 = I * Qbar_panel[0]; - TacsScalar D12 = I * Qbar_panel[1]; - TacsScalar D22 = I * Qbar_panel[3]; - TacsScalar D66 = I * Qbar_panel[5]; - - *sNx_panel_crit = (-4.0 * M_PI * M_PI / (sp * sp * sp)) * - (sqrt(D11 * D22) + D12 + 2.0 * D66); - *sNxy_panel_crit = calcCriticalShearLoadSens(D11, D22, D12 + 2.0 * D66, sp, - 0.0, 0.0, 0.0, 1.0); - - *sNx_weak_stiff_crit = 0.0; - *sNx_strong_stiff_crit = 0.0; - } else if (dvNum == sh_num) { - // Calculate the derivative w.r.t. stiffener height - TacsScalar Ep = - Qbar_panel[0] - (Qbar_panel[1] * Qbar_panel[1]) / Qbar_panel[3]; - TacsScalar Es = - Qbar_stiff[0] - (Qbar_stiff[1] * Qbar_stiff[1]) / Qbar_stiff[3]; - - // The modulus-weighted area: - TacsScalar An = (Ep * sp * t + Es * sh * st * (1.0 + sf_fraction)); - TacsScalar An_sens = Es * st * (1.0 + sf_fraction); - - // The modulus-weighted centroid - TacsScalar Cn = 0.5 * Es * sh * sh * st; - TacsScalar Cn_sens = Es * sh * st; - - // The modulus-weighted centroid - TacsScalar zn = Cn / An; - TacsScalar zn_sens = (Cn_sens * An - Cn * An_sens) / (An * An); - - // The bending stiffness - TacsScalar EI = (zn * zn * (t * sp * Ep + st * sh * sf_fraction * Es) + - Es * (st * (sh * sh * sh) / 12.0 + - st * sh * (zn - 0.5 * sh) * (zn - 0.5 * sh))); - TacsScalar EI_sens = - (2.0 * zn * zn_sens * (t * sp * Ep + st * sh * sf_fraction * Es) + - zn * zn * st * sf_fraction * Es + - Es * (st * (sh * sh) / 4.0 + st * (zn - 0.5 * sh) * (zn - 0.5 * sh) + - 2.0 * st * sh * (zn - 0.5 * sh) * (zn_sens - 0.5))); - - // Compute the unit EI stiffness for the buckling - TacsScalar D1 = EI / sp; - TacsScalar D1_sens = EI_sens / sp; - *sNx_global_crit = (M_PI * M_PI * D1_sens) / (Lx * Lx); - - // Compute the required data for the shear loading - // The transverse bending stiffness - TacsScalar D12_panel = (t * t * t * Qbar_panel[1]) / 12.0; - TacsScalar D12_stiff = ((t + 0.5 * st) * (t + 0.5 * st) * (t + 0.5 * st) * - (Qbar_panel[1] + Qbar_stiff[1])) / - 6.0; - - TacsScalar D2 = sp / ((sp - sh * sf_fraction) / D12_panel + - (sh * sf_fraction) / D12_stiff); - TacsScalar D2_sens = - -((D2 * D2) / sp) * (sf_fraction / D12_stiff - sf_fraction / D12_panel); - - // The twisting stiffness - TacsScalar D66_panel = (t * t * t * Qbar_panel[5]) / 12.0; - TacsScalar D66_stiff = ((t + 0.5 * st) * (t + 0.5 * st) * (t + 0.5 * st) * - (Qbar_panel[5] + Qbar_stiff[5])) / - 6.0; - - TacsScalar D3 = sp / ((sp - sh * sf_fraction) / D66_panel + - (sh * sf_fraction) / D66_stiff); - TacsScalar D3_sens = - -((D3 * D3) / sp) * (sf_fraction / D66_stiff - sf_fraction / D66_panel); - - *sNxy_global_crit = calcCriticalShearLoadSens(D1, D2, D3, Lx, D1_sens, - D2_sens, D3_sens, 0.0); - - *sNx_panel_crit = 0.0; - *sNxy_panel_crit = 0.0; - - TacsScalar Is_weak = st * st * st / 12.0; - TacsScalar Is_strong = st * sh * sh / 4.0; - - *sNx_weak_stiff_crit = (M_PI * M_PI * Es * Is_weak) / (Lx * Lx); - *sNx_strong_stiff_crit = (M_PI * M_PI * Es * Is_strong) / (Lx * Lx); - } else if (dvNum == st_num) { - // Compute the derivative w.r.t. the stiffener thickness - TacsScalar Ep = - Qbar_panel[0] - (Qbar_panel[1] * Qbar_panel[1]) / Qbar_panel[3]; - TacsScalar Es = - Qbar_stiff[0] - (Qbar_stiff[1] * Qbar_stiff[1]) / Qbar_stiff[3]; - - // The modulus-weighted area: - TacsScalar An = (Ep * sp * t + Es * sh * st * (1.0 + sf_fraction)); - TacsScalar An_sens = Es * sh * (1.0 + sf_fraction); - - // The modulus-weighted centroid - TacsScalar Cn = 0.5 * Es * sh * sh * st; - TacsScalar Cn_sens = 0.5 * Es * sh * sh; - - // The modulus-weighted centroid - TacsScalar zn = Cn / An; - TacsScalar zn_sens = (Cn_sens * An - Cn * An_sens) / (An * An); - - // The bending stiffness - TacsScalar EI = (zn * zn * (t * sp * Ep + st * sh * sf_fraction * Es) + - Es * (st * (sh * sh * sh) / 12.0 + - st * sh * (zn - 0.5 * sh) * (zn - 0.5 * sh))); - TacsScalar EI_sens = - (2.0 * zn * zn_sens * (t * sp * Ep + st * sh * sf_fraction * Es) + - zn * zn * sh * sf_fraction * Es + - Es * ((sh * sh * sh) / 12.0 + sh * (zn - 0.5 * sh) * (zn - 0.5 * sh) + - 2.0 * st * sh * (zn - 0.5 * sh) * zn_sens)); - - // Compute the unit EI stiffness for the buckling - TacsScalar D1 = EI / sp; - TacsScalar D1_sens = EI_sens / sp; - *sNx_global_crit = (M_PI * M_PI * D1_sens) / (Lx * Lx); - - // Compute the required data for the shear loading - // The transverse bending stiffness - TacsScalar D12_panel = (t * t * t * Qbar_panel[1]) / 12.0; - TacsScalar D12_stiff = ((t + 0.5 * st) * (t + 0.5 * st) * (t + 0.5 * st) * - (Qbar_panel[1] + Qbar_stiff[1])) / - 6.0; - TacsScalar D12_stiff_sens = - 1.5 * - ((t + 0.5 * st) * (t + 0.5 * st) * (Qbar_panel[1] + Qbar_stiff[1])) / - 6.0; - - TacsScalar D2 = sp / ((sp - sh * sf_fraction) / D12_panel + - (sh * sf_fraction) / D12_stiff); - TacsScalar D2_sens = - (D2 * D2) / sp * - ((sh * sf_fraction) / (D12_stiff * D12_stiff) * D12_stiff_sens); - - // The twisting stiffness - TacsScalar D66_panel = (t * t * t * Qbar_panel[5]) / 12.0; - TacsScalar D66_stiff = ((t + 0.5 * st) * (t + 0.5 * st) * (t + 0.5 * st) * - (Qbar_panel[5] + Qbar_stiff[5])) / - 6.0; - TacsScalar D66_stiff_sens = - 1.5 * - ((t + 0.5 * st) * (t + 0.5 * st) * (Qbar_panel[5] + Qbar_stiff[5])) / - 6.0; - - TacsScalar D3 = sp / ((sp - sh * sf_fraction) / D66_panel + - (sh * sf_fraction) / D66_stiff); - TacsScalar D3_sens = - (D3 * D3) / sp * - ((sh * sf_fraction) / (D66_stiff * D66_stiff) * D66_stiff_sens); - - *sNxy_global_crit = calcCriticalShearLoadSens(D1, D2, D3, Lx, D1_sens, - D2_sens, D3_sens, 0.0); - - *sNx_panel_crit = 0.0; - *sNxy_panel_crit = 0.0; - - TacsScalar Is_weak = sh * st * st / 4.0; - TacsScalar Is_strong = sh * sh * sh / 12.0; - - *sNx_weak_stiff_crit = (M_PI * M_PI * Es * Is_weak) / (Lx * Lx); - *sNx_strong_stiff_crit = (M_PI * M_PI * Es * Is_strong) / (Lx * Lx); - } else if (dvNum == Lx_num) { - // Compute the neutral axis location: - TacsScalar Ep = - Qbar_panel[0] - (Qbar_panel[1] * Qbar_panel[1]) / Qbar_panel[3]; - TacsScalar Es = - Qbar_stiff[0] - (Qbar_stiff[1] * Qbar_stiff[1]) / Qbar_stiff[3]; - - // The modulus-weighted area: - TacsScalar An = (Ep * sp * t + Es * sh * st * (1.0 + sf_fraction)); - - // The modulus-weighted centroid - TacsScalar Cn = 0.5 * Es * sh * sh * st; - - // The modulus-weighted centroid - TacsScalar zn = Cn / An; - - // The bending stiffness - TacsScalar EI = (zn * zn * (t * sp * Ep + st * sh * sf_fraction * Es) + - Es * (st * (sh * sh * sh) / 12.0 + - st * sh * (zn - 0.5 * sh) * (zn - 0.5 * sh))); - - // Compute the unit EI stiffness for the buckling - TacsScalar D1 = EI / sp; - *sNx_global_crit = -2.0 * (M_PI * M_PI * D1) / (Lx * Lx * Lx); - - // Compute the required data for the shear loading - // The transverse bending stiffness - TacsScalar D12_panel = (t * t * t * Qbar_panel[1]) / 12.0; - TacsScalar D12_stiff = ((t + 0.5 * st) * (t + 0.5 * st) * (t + 0.5 * st) * - (Qbar_panel[1] + Qbar_stiff[1])) / - 6.0; - - TacsScalar D2 = sp / ((sp - sh * sf_fraction) / D12_panel + - (sh * sf_fraction) / D12_stiff); - - // The twisting stiffness - TacsScalar D66_panel = (t * t * t * Qbar_panel[5]) / 12.0; - TacsScalar D66_stiff = ((t + 0.5 * st) * (t + 0.5 * st) * (t + 0.5 * st) * - (Qbar_panel[5] + Qbar_stiff[5])) / - 6.0; - - TacsScalar D3 = sp / ((sp - sh * sf_fraction) / D66_panel + - (sh * sf_fraction) / D66_stiff); - - *sNxy_global_crit = - calcCriticalShearLoadSens(D1, D2, D3, Lx, 0.0, 0.0, 0.0, 1.0); - - *sNx_panel_crit = 0.0; - *sNxy_panel_crit = 0.0; - - TacsScalar Is_weak = sh * st * st * st / 12.0; - TacsScalar Is_strong = st * sh * sh * sh / 12.0; - - *sNx_weak_stiff_crit = -2.0 * (M_PI * M_PI * Es * Is_weak) / (Lx * Lx * Lx); - *sNx_strong_stiff_crit = - -2.0 * (M_PI * M_PI * Es * Is_strong) / (Lx * Lx * Lx); - } else if (dvNum >= 0) { - TacsScalar sQbar_panel[6], sQbar_stiff[6]; - sQbar_panel[0] = sQbar_panel[1] = sQbar_panel[2] = 0.0; - sQbar_panel[3] = sQbar_panel[4] = sQbar_panel[5] = 0.0; - - sQbar_stiff[0] = sQbar_stiff[1] = sQbar_stiff[2] = 0.0; - sQbar_stiff[3] = sQbar_stiff[4] = sQbar_stiff[5] = 0.0; - - for (int k = 0; k < NUM_PLIES; k++) { - if (pf_nums[k] == dvNum) { - TacsScalar Qp[6]; - ortho_ply->calculateQbar(Qp, ply_angles[k]); - - for (int j = 0; j < 6; j++) { - sQbar_panel[j] += Qp[j]; - } - } - } - - for (int k = 0; k < NUM_PLIES; k++) { - if (stiff_pf_nums[k] == dvNum) { - TacsScalar Qp[6]; - ortho_ply->calculateQbar(Qp, stiff_ply_angles[k]); - - for (int j = 0; j < 6; j++) { - sQbar_stiff[j] += Qp[j]; - } - } - } - - // Compute the neutral axis location: - TacsScalar Ep = - Qbar_panel[0] - (Qbar_panel[1] * Qbar_panel[1]) / Qbar_panel[3]; - TacsScalar Ep_sens = - (sQbar_panel[0] - - 2.0 * (Qbar_panel[1] * sQbar_panel[1]) / Qbar_panel[3] + - sQbar_panel[3] * (Qbar_panel[1] * Qbar_panel[1]) / - (Qbar_panel[3] * Qbar_panel[3])); - - TacsScalar Es = - Qbar_stiff[0] - (Qbar_stiff[1] * Qbar_stiff[1]) / Qbar_stiff[3]; - TacsScalar Es_sens = - (sQbar_stiff[0] - - 2.0 * (Qbar_stiff[1] * sQbar_stiff[1]) / Qbar_stiff[3] + - sQbar_stiff[3] * (Qbar_stiff[1] * Qbar_stiff[1]) / - (Qbar_stiff[3] * Qbar_stiff[3])); - - // The modulus-weighted area: - TacsScalar An = (Ep * sp * t + Es * sh * st * (1.0 + sf_fraction)); - TacsScalar An_sens = - (Ep_sens * sp * t + Es_sens * sh * st * (1.0 + sf_fraction)); - - // The modulus-weighted centroid - TacsScalar Cn = 0.5 * Es * sh * sh * st; - TacsScalar Cn_sens = 0.5 * Es_sens * sh * sh * st; - - // The modulus-weighted centroid - TacsScalar zn = Cn / An; - TacsScalar zn_sens = (Cn_sens * An - Cn * An_sens) / (An * An); - - // The bending stiffness - TacsScalar EI = (zn * zn * (t * sp * Ep + st * sh * sf_fraction * Es) + - Es * (st * (sh * sh * sh) / 12.0 + - st * sh * (zn - 0.5 * sh) * (zn - 0.5 * sh))); - - TacsScalar EI_sens = - (zn * zn * (t * sp * Ep_sens + st * sh * sf_fraction * Es_sens) + - Es_sens * (st * (sh * sh * sh) / 12.0 + - st * sh * (zn - 0.5 * sh) * (zn - 0.5 * sh)) + - 2.0 * zn * zn_sens * (t * sp * Ep + st * sh * sf_fraction * Es) + - Es * (2.0 * st * sh * (zn - 0.5 * sh) * zn_sens)); - - // Compute the unit EI stiffness for the buckling - TacsScalar D1 = EI / sp; - TacsScalar D1_sens = EI_sens / sp; - *sNx_global_crit = (M_PI * M_PI * D1_sens) / (Lx * Lx); - - // Compute the required data for the shear loading - // The transverse bending stiffness - TacsScalar D12_panel = (t * t * t * Qbar_panel[1]) / 12.0; - TacsScalar D12_stiff = ((t + 0.5 * st) * (t + 0.5 * st) * (t + 0.5 * st) * - (Qbar_panel[1] + Qbar_stiff[1])) / - 6.0; - TacsScalar D2 = sp / ((sp - sh * sf_fraction) / D12_panel + - (sh * sf_fraction) / D12_stiff); - - TacsScalar D12_panel_sens = (t * t * t * sQbar_panel[1]) / 12.0; - TacsScalar D12_stiff_sens = - ((t + 0.5 * st) * (t + 0.5 * st) * (t + 0.5 * st) * - (sQbar_panel[1] + sQbar_stiff[1])) / - 6.0; - TacsScalar D2_sens = - (D2 * D2 / sp) * - ((sp - sh * sf_fraction) / (D12_panel * D12_panel) * D12_panel_sens + - (sh * sf_fraction) / (D12_stiff * D12_stiff) * D12_stiff_sens); - - // The twisting stiffness - TacsScalar D66_panel = (t * t * t * Qbar_panel[5]) / 12.0; - TacsScalar D66_stiff = ((t + 0.5 * st) * (t + 0.5 * st) * (t + 0.5 * st) * - (Qbar_panel[5] + Qbar_stiff[5])) / - 6.0; - - TacsScalar D3 = sp / ((sp - sh * sf_fraction) / D66_panel + - (sh * sf_fraction) / D66_stiff); - - TacsScalar D66_panel_sens = (t * t * t * sQbar_panel[5]) / 12.0; - TacsScalar D66_stiff_sens = - ((t + 0.5 * st) * (t + 0.5 * st) * (t + 0.5 * st) * - (sQbar_panel[5] + sQbar_stiff[5])) / - 6.0; - - TacsScalar D3_sens = - (D3 * D3 / sp) * - ((sp - sh * sf_fraction) / (D66_panel * D66_panel) * D66_panel_sens + - (sh * sf_fraction) / (D66_stiff * D66_stiff) * D66_stiff_sens); - - *sNxy_global_crit = calcCriticalShearLoadSens(D1, D2, D3, Lx, D1_sens, - D2_sens, D3_sens, 0.0); - - // Compute the critical buckling loads for the panel - // ------------------------------------------------- - TacsScalar I = (t * t * t) / 12.0; - TacsScalar D11 = I * Qbar_panel[0]; - TacsScalar D12 = I * Qbar_panel[1]; - TacsScalar D22 = I * Qbar_panel[3]; - TacsScalar D66 = I * Qbar_panel[5]; - - TacsScalar D11_sens = I * sQbar_panel[0]; - TacsScalar D12_sens = I * sQbar_panel[1]; - TacsScalar D22_sens = I * sQbar_panel[3]; - TacsScalar D66_sens = I * sQbar_panel[5]; - - TacsScalar sqrtD11D22 = sqrt(D11 * D22); - - *sNx_panel_crit = (2.0 * M_PI * M_PI / (sp * sp)) * - (0.5 * (D11 * D22_sens + D11_sens * D22) / sqrtD11D22 + - D12_sens + 2.0 * D66_sens); - - *sNxy_panel_crit = - calcCriticalShearLoadSens(D11, D22, D12 + 2.0 * D66, sp, D11_sens, - D22_sens, D12_sens + 2.0 * D66_sens, 0.0); - - // Compute the critical loads for the stiffener - // -------------------------------------------- - TacsScalar Is_weak = sh * st * st * st / 12.0; - TacsScalar Is_strong = st * sh * sh * sh / 12.0; - - *sNx_weak_stiff_crit = (M_PI * M_PI * Es_sens * Is_weak) / (Lx * Lx); - *sNx_strong_stiff_crit = (M_PI * M_PI * Es_sens * Is_strong) / (Lx * Lx); - } -} - -/* - Print information to stdout about this stiffener class. - - This is useful for debugging purposes. This prints the design - variable values and the critical buckling loads for the stiffener - class. -*/ -void bladeFSDTStiffness::printBucklingInfo() { - double gpt[2] = {0.0, 0.0}; - TacsScalar mass[3]; - getPointwiseMass(gpt, mass); - - printf("%s properties\n", constName); - printf("Lx panel dimension: %15.6f\n", TacsRealPart(Lx)); - printf("stiffener pitch: %15.6f\n", TacsRealPart(sp)); - printf("stiffener height: %15.6f\n", TacsRealPart(sh)); - printf("stiffener thickness: %15.6f\n", TacsRealPart(st)); - printf("panel thickness: %15.6f\n", TacsRealPart(t)); - printf("mass per unit area: %15.6f\n", TacsRealPart(mass[0])); - printf("global Nx,cr: %15.6f\n", TacsRealPart(Nx_global_crit)); - printf("global Nxy,cr: %15.6f\n", TacsRealPart(Nxy_global_crit)); - printf("panel Nx,cr: %15.6f\n", TacsRealPart(Nx_panel_crit)); - printf("panel Nxy,cr: %15.6f\n", TacsRealPart(Nxy_panel_crit)); - printf("stiffener Nx,cr %15.6f\n", TacsRealPart(Nx_weak_stiff_crit)); - printf("stiffener Nx,cr %15.6f\n", TacsRealPart(Nx_strong_stiff_crit)); -} - -/* - Compute all the failure criteria for each ply, for each of the - top/bottom plies and the plies in the stiffeners. -*/ -int bladeFSDTStiffness::calcFail(const TacsScalar strain[], TacsScalar fail[], - TacsScalar* _max) { - // Keep track of the maximum value of the failure criteria and the - // total number of load numbers - TacsScalar max = 0.0; - int load_num = 0; - - TacsScalar e[3]; - // Compute the strain at the upper panel surface - e[0] = strain[0] + 0.5 * t * strain[3]; - e[1] = strain[1] + 0.5 * t * strain[4]; - e[2] = strain[2] + 0.5 * t * strain[5]; - - for (int k = 0; k < NUM_PLIES; k++) { - fail[load_num] = ortho_ply->failure(ply_angles[k], e); - if (TacsRealPart(fail[load_num]) > TacsRealPart(max)) { - max = fail[load_num]; - } - load_num++; - } - - // Compute the strain at the lower panel sufrace - e[0] = strain[0] - 0.5 * t * strain[3]; - e[1] = strain[1] - 0.5 * t * strain[4]; - e[2] = strain[2] - 0.5 * t * strain[5]; - - for (int k = 0; k < NUM_PLIES; k++) { - fail[load_num] = ortho_ply->failure(ply_angles[k], e); - if (TacsRealPart(fail[load_num]) > TacsRealPart(max)) { - max = fail[load_num]; - } - load_num++; - } - - // Compute the strain at the furthest fiber of the stiffener - e[0] = strain[0] - sh * strain[3]; - e[1] = 0.0; - e[2] = 0.0; - - // Compute the failure criteria for the stiffener - for (int k = 0; k < NUM_PLIES; k++) { - fail[load_num] = ortho_ply->failure(stiff_ply_angles[k], e); - if (TacsRealPart(fail[load_num]) > TacsRealPart(max)) { - max = fail[load_num]; - } - load_num++; - } - - *_max = max; - - return load_num; -} - -/* - Compute the derivative of each of the failure -*/ -void bladeFSDTStiffness::calcFailStrainSens(const TacsScalar strain[], - const TacsScalar weights[], - TacsScalar sens[]) { - sens[0] = sens[1] = sens[2] = sens[3] = 0.0; - sens[4] = sens[5] = sens[6] = sens[7] = 0.0; - - int load_num = 0; - - for (int k = 0; k < NUM_PLIES; k++) { - TacsScalar e[3], e_sens[3]; - // Compute the strain at the upper surface - e[0] = strain[0] + 0.5 * t * strain[3]; - e[1] = strain[1] + 0.5 * t * strain[4]; - e[2] = strain[2] + 0.5 * t * strain[5]; - - ortho_ply->failureStrainSens(e_sens, ply_angles[k], e); - - sens[0] += weights[load_num] * e_sens[0]; - sens[1] += weights[load_num] * e_sens[1]; - sens[2] += weights[load_num] * e_sens[2]; - - sens[3] += 0.5 * t * weights[load_num] * e_sens[0]; - sens[4] += 0.5 * t * weights[load_num] * e_sens[1]; - sens[5] += 0.5 * t * weights[load_num] * e_sens[2]; - load_num++; - } - - for (int k = 0; k < NUM_PLIES; k++) { - TacsScalar e[3], e_sens[3]; - // Compute the strain at the lower sufrace - e[0] = strain[0] - 0.5 * t * strain[3]; - e[1] = strain[1] - 0.5 * t * strain[4]; - e[2] = strain[2] - 0.5 * t * strain[5]; - - ortho_ply->failureStrainSens(e_sens, ply_angles[k], e); - - sens[0] += weights[load_num] * e_sens[0]; - sens[1] += weights[load_num] * e_sens[1]; - sens[2] += weights[load_num] * e_sens[2]; - - sens[3] -= 0.5 * t * weights[load_num] * e_sens[0]; - sens[4] -= 0.5 * t * weights[load_num] * e_sens[1]; - sens[5] -= 0.5 * t * weights[load_num] * e_sens[2]; - load_num++; - } - - // Compute the failure criteria for the stiffener - for (int k = 0; k < NUM_PLIES; k++) { - TacsScalar e[3], e_sens[3]; - // Compute the strain at the upper surface - e[0] = strain[0] - sh * strain[3]; - e[1] = 0.0; - e[2] = 0.0; - - ortho_ply->failureStrainSens(e_sens, stiff_ply_angles[k], e); - - sens[0] += weights[load_num] * e_sens[0]; - sens[3] -= sh * weights[load_num] * e_sens[0]; - load_num++; - } -} - -TacsScalar bladeFSDTStiffness::calcFailDVSens(int dvNum, - const TacsScalar strain[], - const TacsScalar weights[]) { - int load_num = 0; - TacsScalar failSens = 0.0; - - if (dvNum == t_num) { - for (int k = 0; k < NUM_PLIES; k++) { - TacsScalar e[3], e_sens[3]; - // Compute the strain at the upper surface - e[0] = strain[0] + 0.5 * t * strain[3]; - e[1] = strain[1] + 0.5 * t * strain[4]; - e[2] = strain[2] + 0.5 * t * strain[5]; - - ortho_ply->failureStrainSens(e_sens, ply_angles[k], e); - failSens += 0.5 * weights[load_num] * - (strain[3] * e_sens[0] + strain[4] * e_sens[1] + - strain[5] * e_sens[2]); - load_num++; - } - - for (int k = 0; k < NUM_PLIES; k++) { - TacsScalar e[3], e_sens[3]; - // Compute the strain at the lower sufrace - e[0] = strain[0] - 0.5 * t * strain[3]; - e[1] = strain[1] - 0.5 * t * strain[4]; - e[2] = strain[2] - 0.5 * t * strain[5]; - - ortho_ply->failureStrainSens(e_sens, ply_angles[k], e); - failSens -= 0.5 * weights[load_num] * - (strain[3] * e_sens[0] + strain[4] * e_sens[1] + - strain[5] * e_sens[2]); - load_num++; - } - } else if (dvNum == sh_num) { - load_num = 2 * NUM_PLIES; - - // Compute the failure criteria for the stiffener - for (int k = 0; k < NUM_PLIES; k++) { - TacsScalar e[3], e_sens[3]; - // Compute the strain at the upper surface - e[0] = strain[0] - sh * strain[3]; - e[1] = 0.0; - e[2] = 0.0; - - ortho_ply->failureStrainSens(e_sens, stiff_ply_angles[k], e); - failSens -= weights[load_num] * strain[3] * e_sens[0]; - load_num++; - } - } - - return failSens; -} - -/* - Functions to determine the failure load in terms of the strain and - derivatives of the failure load in terms of the strain components. -*/ -void bladeFSDTStiffness::failure(const double pt[], const TacsScalar strain[], - TacsScalar* fval) { - TacsScalar fail[MAX_NUM_FAIL], max; - int num_fail = calcFail(strain, fail, &max); - TacsScalar ks_sum = 0.0; - for (int k = 0; k < num_fail; k++) { - ks_sum += exp(ks_weight * (fail[k] - max)); - } - - *fval = max + log(ks_sum) / ks_weight; -} - -void bladeFSDTStiffness::failureStrainSens(const double pt[], - const TacsScalar strain[], - TacsScalar sens[]) { - TacsScalar fail[MAX_NUM_FAIL], sens_weights[MAX_NUM_FAIL], max; - int num_fail = calcFail(strain, fail, &max); - TacsScalar ks_sum = 0.0; - for (int k = 0; k < num_fail; k++) { - ks_sum += exp(ks_weight * (fail[k] - max)); - } - - for (int k = 0; k < num_fail; k++) { - sens_weights[k] = exp(ks_weight * (fail[k] - max)) / ks_sum; - } - - calcFailStrainSens(strain, sens_weights, sens); -} - -/* - Functions to determine the derivative of the failure - load w.r.t. the design variables -*/ -void bladeFSDTStiffness::failureDVSens(int dvNum, const double pt[], - const TacsScalar strain[], - TacsScalar* failSens) { - TacsScalar fail[MAX_NUM_FAIL], sens_weights[MAX_NUM_FAIL], max; - int num_fail = calcFail(strain, fail, &max); - TacsScalar ks_sum = 0.0; - for (int k = 0; k < num_fail; k++) { - ks_sum += exp(ks_weight * (fail[k] - max)); - } - - for (int k = 0; k < num_fail; k++) { - sens_weights[k] = exp(ks_weight * (fail[k] - max)) / ks_sum; - } - - *failSens = calcFailDVSens(dvNum, strain, sens_weights); -} - -/* - Add the derivative of the failure load times alpha -*/ -void bladeFSDTStiffness::addFailureDVSens(const double pt[], - const TacsScalar strain[], - TacsScalar alpha, TacsScalar dvSens[], - int dvLen) { - TacsScalar fail[MAX_NUM_FAIL], sens_weights[MAX_NUM_FAIL], max; - int num_fail = calcFail(strain, fail, &max); - TacsScalar ks_sum = 0.0; - for (int k = 0; k < num_fail; k++) { - ks_sum += exp(ks_weight * (fail[k] - max)); - } - - // Compute the sensitivities of the arrays - for (int k = 0; k < num_fail; k++) { - sens_weights[k] = exp(ks_weight * (fail[k] - max)) / ks_sum; - } - - // Add the scaled multiple of the derivatives - if (Lx_num >= 0 && Lx_num < dvLen) { - dvSens[Lx_num] += alpha * calcFailDVSens(Lx_num, strain, sens_weights); - } - if (sp_num >= 0 && sp_num < dvLen) { - dvSens[sp_num] += alpha * calcFailDVSens(sp_num, strain, sens_weights); - } - if (sh_num >= 0 && sh_num < dvLen) { - dvSens[sh_num] += alpha * calcFailDVSens(sh_num, strain, sens_weights); - } - if (st_num >= 0 && st_num < dvLen) { - dvSens[st_num] += alpha * calcFailDVSens(st_num, strain, sens_weights); - } - if (t_num >= 0 && t_num < dvLen) { - dvSens[t_num] += alpha * calcFailDVSens(t_num, strain, sens_weights); - } - - // Add the derivatives from the ply fraction variables - for (int k = 0; k < num_pf_unique; k++) { - if (pf_unique[k] < dvLen) { - dvSens[pf_unique[k]] += - alpha * calcFailDVSens(pf_unique[k], strain, sens_weights); - } - } - for (int k = 0; k < num_stiff_pf_unique; k++) { - if (stiff_pf_unique[k] < dvLen) { - dvSens[stiff_pf_unique[k]] += - alpha * calcFailDVSens(stiff_pf_unique[k], strain, sens_weights); - } - } -} - -/* - Compute the buckling criteria for every component of the stiffened - panel. -*/ -int bladeFSDTStiffness::calcBuckling(const TacsScalar strain[], - TacsScalar bval[], TacsScalar* _max) { - TacsScalar max = 0.0; - int load_num = 0; - - // Compute the buckling contributions to the failure load. - // These use the interaction criterion: - // bval = (Nxy/Nxy,crit)^2 + Nx/Nx,crit <= 1 - // ------------------------------------------------------- - // Calculate the global buckling criteria - TacsScalar stress[8]; - calculateStress(A, B, D, As, strain, stress); - - TacsScalar Nx = -stress[0]; - TacsScalar Nxy = stress[2]; - - bval[load_num] = ((Nx / Nx_global_crit) + - (Nxy / Nxy_global_crit) * (Nxy / Nxy_global_crit)); - max = bval[load_num]; - load_num++; - - // Calculate the panel buckling criteria - // This is for the inter-stiffener portion of the panel - Nx = -t * (Qbar_panel[0] * strain[0] + Qbar_panel[1] * strain[1]); - Nxy = t * Qbar_panel[5] * strain[2]; - - bval[load_num] = - ((Nx / Nx_panel_crit) + (Nxy / Nxy_panel_crit) * (Nxy / Nxy_panel_crit)); - if (TacsRealPart(bval[load_num]) > TacsRealPart(max)) { - max = bval[load_num]; - } - load_num++; - - *_max = max; - - return load_num; -} - -void bladeFSDTStiffness::calcBucklingStrainSens(const TacsScalar strain[], - const TacsScalar weights[], - TacsScalar sens[]) { - sens[0] = sens[1] = sens[2] = sens[3] = 0.0; - sens[4] = sens[5] = sens[6] = sens[7] = 0.0; - - int load_num = 0; - - // Compute the buckling contributions to the failure load. - // These use the interaction criterion: - // (Nxy/Nxy,crit)^2 + Nx/Nx,crit <= 1 - // ------------------------------------------------------- - - // Calculate the global buckling criteria - TacsScalar stress[8], s_sens[8]; - calculateStress(A, B, D, As, strain, stress); - - s_sens[0] = -weights[load_num] / Nx_global_crit; - s_sens[2] = - 2.0 * weights[load_num] * stress[2] / (Nxy_global_crit * Nxy_global_crit); - s_sens[1] = s_sens[3] = s_sens[4] = s_sens[5] = s_sens[6] = s_sens[7] = 0.0; - - calculateStress(A, B, D, As, s_sens, stress); - - for (int j = 0; j < 8; j++) { - sens[j] += stress[j]; - } - load_num++; - - // Calculate the panel buckling criteria - // This is for the inter-stiffener portion of the panel - TacsScalar Nxy = t * Qbar_panel[5] * strain[2]; - - sens[0] -= (weights[load_num] * t * Qbar_panel[0]) / Nx_panel_crit; - sens[1] -= (weights[load_num] * t * Qbar_panel[1]) / Nx_panel_crit; - sens[2] += 2.0 * (weights[load_num] * t * Qbar_panel[5] * Nxy) / - (Nxy_panel_crit * Nxy_panel_crit); - load_num++; -} - -TacsScalar bladeFSDTStiffness::calcBucklingDVSens(int dvNum, - const TacsScalar strain[], - const TacsScalar weights[]) { - int load_num = 0; - TacsScalar bvalSens = 0.0; - - TacsScalar sNx_global_crit, sNxy_global_crit; - TacsScalar sNx_panel_crit, sNxy_panel_crit; - TacsScalar sNx_weak_stiff_crit, sNx_strong_stiff_crit; - calcBucklingPropsDVSens(dvNum, &sNx_global_crit, &sNxy_global_crit, - &sNx_panel_crit, &sNxy_panel_crit, - &sNx_weak_stiff_crit, &sNx_strong_stiff_crit); - - TacsScalar sQbar_panel[6], sQbar_stiff[6]; - sQbar_panel[0] = sQbar_panel[1] = sQbar_panel[2] = 0.0; - sQbar_panel[3] = sQbar_panel[4] = sQbar_panel[5] = 0.0; - - sQbar_stiff[0] = sQbar_stiff[1] = sQbar_stiff[2] = 0.0; - sQbar_stiff[3] = sQbar_stiff[4] = sQbar_stiff[5] = 0.0; - - for (int k = 0; k < NUM_PLIES; k++) { - if (pf_nums[k] == dvNum) { - TacsScalar Qp[6]; - ortho_ply->calculateQbar(Qp, ply_angles[k]); - - for (int j = 0; j < 6; j++) { - sQbar_panel[j] += Qp[j]; - } - } - } - - for (int k = 0; k < NUM_PLIES; k++) { - if (stiff_pf_nums[k] == dvNum) { - TacsScalar Qp[6]; - ortho_ply->calculateQbar(Qp, stiff_ply_angles[k]); - - for (int j = 0; j < 6; j++) { - sQbar_stiff[j] += Qp[j]; - } - } - } - - // Calculate the global buckling criteria - TacsScalar stress[8], stress_sens[8]; - calculateStress(A, B, D, As, strain, stress); - - const double gpt[2] = {0.0, 0.0}; - calculateStressDVSens(gpt, strain, stress_sens, dvNum); - - TacsScalar Nx = 0.0, Nxy = 0.0, sNx = 0.0, sNxy = 0.0; - Nx = -stress[0]; - sNx = -stress_sens[0]; - - Nxy = stress[2]; - sNxy = stress_sens[2]; - - bvalSens += weights[load_num] * - ((sNx / Nx_global_crit) - - (Nx / (Nx_global_crit * Nx_global_crit)) * sNx_global_crit + - 2.0 * (Nxy * sNxy) / (Nxy_global_crit * Nxy_global_crit) - - 2.0 * (Nxy * Nxy) / - (Nxy_global_crit * Nxy_global_crit * Nxy_global_crit) * - sNxy_global_crit); - load_num++; - - // Add the panel buckling failure contribution - Nx = -t * (Qbar_panel[0] * strain[0] + Qbar_panel[1] * strain[1]); - Nxy = t * Qbar_panel[5] * strain[2]; - - if (dvNum == t_num) { - sNxy = (t * sQbar_panel[5] + Qbar_panel[5]) * strain[2]; - } else { - sNxy = t * sQbar_panel[5] * strain[2]; - } - - // Compute the axial contribution - if (dvNum == t_num) { - sNx = -(t * (sQbar_panel[0] * strain[0] + sQbar_panel[1] * strain[1]) + - (Qbar_panel[0] * strain[0] + Qbar_panel[1] * strain[1])); - } else { - sNx = -t * (sQbar_panel[0] * strain[0] + sQbar_panel[1] * strain[1]); - } - - bvalSens += weights[load_num] * - (sNx / Nx_panel_crit - - (sNx_panel_crit * Nx) / (Nx_panel_crit * Nx_panel_crit) + - 2.0 * (Nxy * sNxy) / (Nxy_panel_crit * Nxy_panel_crit) - - 2.0 * (sNxy_panel_crit * Nxy * Nxy) / - (Nxy_panel_crit * Nxy_panel_crit * Nxy_panel_crit)); - load_num++; - - // Calculate the contribution from the stiffeners - Nx = -st * sh * - (Qbar_stiff[0] * (strain[0] - 0.5 * sh * strain[3]) + - Qbar_stiff[1] * (strain[1] - 0.5 * sh * strain[4])); - - sNx = -st * sh * - (sQbar_stiff[0] * (strain[0] - 0.5 * sh * strain[3]) + - sQbar_stiff[1] * (strain[1] - 0.5 * sh * strain[4])); - - if (dvNum == sh_num) { - sNx = -st * (Qbar_stiff[0] * (strain[0] - sh * strain[3]) + - Qbar_stiff[1] * (strain[1] - sh * strain[4])); - } else if (dvNum == st_num) { - sNx = -sh * (Qbar_stiff[0] * (strain[0] - 0.5 * sh * strain[3]) + - Qbar_stiff[1] * (strain[1] - 0.5 * sh * strain[4])); - } - - return bvalSens; -} - -/* - Functions to determine the critical buckling function in terms of the - strain. -*/ -void bladeFSDTStiffness::buckling(const TacsScalar strain[], TacsScalar* bval) { - TacsScalar bfuncs[NUM_BUCKLING], max; - int num_buckling = calcBuckling(strain, bfuncs, &max); - TacsScalar ks_sum = 0.0; - for (int k = 0; k < num_buckling; k++) { - ks_sum += exp(ks_weight * (bfuncs[k] - max)); - } - - *bval = max + log(ks_sum) / ks_weight; -} - -void bladeFSDTStiffness::bucklingStrainSens(const TacsScalar strain[], - TacsScalar sens[]) { - TacsScalar bfuncs[NUM_BUCKLING], sens_weights[NUM_BUCKLING], max; - int num_buckling = calcBuckling(strain, bfuncs, &max); - TacsScalar ks_sum = 0.0; - for (int k = 0; k < num_buckling; k++) { - ks_sum += exp(ks_weight * (bfuncs[k] - max)); - } - - for (int k = 0; k < num_buckling; k++) { - sens_weights[k] = exp(ks_weight * (bfuncs[k] - max)) / ks_sum; - } - - calcBucklingStrainSens(strain, sens_weights, sens); -} - -/* - Functions to determine the derivative of the buckling criteria - load w.r.t. the design variables -*/ -void bladeFSDTStiffness::bucklingDVSens(int dvNum, const TacsScalar strain[], - TacsScalar* failSens) { - TacsScalar bfuncs[NUM_BUCKLING], sens_weights[NUM_BUCKLING], max; - int num_buckling = calcBuckling(strain, bfuncs, &max); - TacsScalar ks_sum = 0.0; - for (int k = 0; k < num_buckling; k++) { - ks_sum += exp(ks_weight * (bfuncs[k] - max)); - } - - for (int k = 0; k < num_buckling; k++) { - sens_weights[k] = exp(ks_weight * (bfuncs[k] - max)) / ks_sum; - } - - *failSens = calcBucklingDVSens(dvNum, strain, sens_weights); -} - -/* - Add the derivative of the buckling load times alpha to the array - dvSens -*/ -void bladeFSDTStiffness::addBucklingDVSens(const TacsScalar strain[], - TacsScalar alpha, - TacsScalar dvSens[], int dvLen) { - TacsScalar bfuncs[NUM_BUCKLING], sens_weights[NUM_BUCKLING], max; - int num_buckling = calcBuckling(strain, bfuncs, &max); - TacsScalar ks_sum = 0.0; - for (int k = 0; k < num_buckling; k++) { - ks_sum += exp(ks_weight * (bfuncs[k] - max)); - } - - for (int k = 0; k < num_buckling; k++) { - sens_weights[k] = exp(ks_weight * (bfuncs[k] - max)) / ks_sum; - } - - // Add the scaled multiple of the derivatives - if (Lx_num >= 0 && Lx_num < dvLen) { - dvSens[Lx_num] += alpha * calcBucklingDVSens(Lx_num, strain, sens_weights); - } - if (sp_num >= 0 && sp_num < dvLen) { - dvSens[sp_num] += alpha * calcBucklingDVSens(sp_num, strain, sens_weights); - } - if (sh_num >= 0 && sh_num < dvLen) { - dvSens[sh_num] += alpha * calcBucklingDVSens(sh_num, strain, sens_weights); - } - if (st_num >= 0 && st_num < dvLen) { - dvSens[st_num] += alpha * calcBucklingDVSens(st_num, strain, sens_weights); - } - if (t_num >= 0 && t_num < dvLen) { - dvSens[t_num] += alpha * calcBucklingDVSens(t_num, strain, sens_weights); - } - - // Add the derivatives from the ply fraction variables - for (int k = 0; k < num_pf_unique; k++) { - if (pf_unique[k] < dvLen) { - dvSens[pf_unique[k]] += - alpha * calcBucklingDVSens(pf_unique[k], strain, sens_weights); - } - } - for (int k = 0; k < num_stiff_pf_unique; k++) { - if (stiff_pf_unique[k] < dvLen) { - dvSens[stiff_pf_unique[k]] += - alpha * calcBucklingDVSens(stiff_pf_unique[k], strain, sens_weights); - } - } -} - -const char* bladeFSDTStiffness::constitutiveName() const { return constName; } - -// Retrieve design variable information ... -TacsScalar bladeFSDTStiffness::getDVOutputValue(int dv_index, - const double gpt[]) { - if (dv_index == 0) { - return t + sh * st * (1.0 + sf_fraction) / sp; - } else if (dv_index - 1 < NUM_PLIES) { - return pf[dv_index - 1]; - } - - return 0.0; -} - -/* - Get the maximum number of design variables ownable by this constitutive class -*/ -int bladeFSDTStiffness::getNumDesignVars() { return 5 + 2 * NUM_PLIES; } - -int bladeFSDTStiffness::getDesignVarNums(int dvNums[], int dvLen) { - if (Lx_num >= 0) { - dvNums[0] = Lx_num; - } else { - dvNums[0] = -1; - } - - if (sp_num >= 0) { - dvNums[1] = sp_num; - } else { - dvNums[1] = -1; - } - - if (sh_num >= 0) { - dvNums[2] = sh_num; - } else { - dvNums[2] = -1; - } - - if (st_num >= 0) { - dvNums[3] = st_num; - } else { - dvNums[3] = -1; - } - - if (t_num >= 0) { - dvNums[4] = t_num; - } else { - dvNums[4] = -1; - } - - for (int i = 0; i < NUM_PLIES; i++) { - if (pf_nums[i] >= 0) { - dvNums[i + 5] = pf_nums[i]; - } else { - dvNums[i + 5] = -1; - } - - if (stiff_pf_nums[i] >= 0) { - dvNums[i + NUM_PLIES + 5] = stiff_pf_nums[i]; - } else { - dvNums[i + NUM_PLIES + 5] = -1; - } - } - return 1; -} diff --git a/src/constitutive/bladeFSDTStiffness.h b/src/constitutive/bladeFSDTStiffness.h deleted file mode 100644 index 8a657e9b5..000000000 --- a/src/constitutive/bladeFSDTStiffness.h +++ /dev/null @@ -1,273 +0,0 @@ -#ifndef TACS_BLADE_FSDT_STIFFNESS_H -#define TACS_BLADE_FSDT_STIFFNESS_H - -/*! - Copyright (c) 2011 Graeme Kennedy. All rights reserved. - Not for commercial purposes. -*/ - -#include "FSDTStiffness.h" -#include "MaterialProperties.h" - -/* - A blade-stiffened panel - - A class for calculating the stiffness and failure properties of - blade-stiffened panels. The panel stiffness characteristics are - calculated based on smeared though-thicknes properties. - - The following buckling modes are included: - - 1. Global axial/shear buckling of the entire panel - 2. Axial and shear buckling of the skin between stiffeners - 3. Axial and shear buckling of the blade-stiffener - - The following failure modes are included - - 1. Failure of the skin via Tsai--Wu failure envelope - - Calculate the strain at the outer-plies: - \epsilon_{0} +/- t/2*\kappa - - Design variables: - - Ly/Lx = the approximate dimensions of the panel - - sp = stiffener pitch (spacing) = Ly/ny_stiffener (ny_stiffner - the - number of stiffeners in the transverse direction is not an integer - although it should be in reality.) - - ts = skin thickness - - sh = stiffener height - - ply_angles = ply angles included in the optimization - - ply_fractions = ply percentages or ply fractions - the relative - number of plies at a given orientation -*/ -class bladeFSDTStiffness : public FSDTStiffness { - public: - static const int NUM_PLIES = 4; - - bladeFSDTStiffness(OrthoPly* _ortho_ply, TacsScalar _kcorr, TacsScalar _Lx, - int _Lx_num, TacsScalar _sp, int _sp_num, TacsScalar _sh, - int _sh_num, TacsScalar _st, int _st_num, TacsScalar _t, - int _t_num, int _pf_nums[], int _stiff_pf_nums[]); - ~bladeFSDTStiffness(); - - // Set non-default values - // ---------------------- - void setStiffenerPitchBounds(TacsScalar _sp_low, TacsScalar _sp_high); - void setStiffenerHeightBounds(TacsScalar _sh_low, TacsScalar _sh_high); - void setStiffenerThicknessBounds(TacsScalar _st_low, TacsScalar _st_high); - void setStiffenerPlyFractionBounds(TacsScalar _pf_low[], - TacsScalar _pf_high[]); - void setStiffenerPlyFractions(TacsScalar _pf[]); - void setThicknessBounds(TacsScalar _t_low, TacsScalar _t_high); - void setPlyFractionBounds(TacsScalar _pf_low[], TacsScalar _pf_high[]); - void setPlyFractions(TacsScalar _pf[]); - - void setKSWeight(double _ks_weight); - - // Retrieve the critical loads - // --------------------------- - void getCriticalGlobalLoads(TacsScalar* Nx, TacsScalar* Nxy); - void getCriticalPanelLoads(TacsScalar* Nx, TacsScalar* Nxy); - void getCriticalStiffenerLoads(TacsScalar* Nx, TacsScalar* Nxy); - - // Compute the critical shear loads and the sensitivities - // ------------------------------------------------------ - TacsScalar calcCriticalShearLoad(TacsScalar D1, TacsScalar D2, TacsScalar D3, - TacsScalar L); - TacsScalar calcCriticalShearLoadSens(TacsScalar D1, TacsScalar D2, - TacsScalar D3, TacsScalar L, - TacsScalar sD1, TacsScalar sD2, - TacsScalar sD3, TacsScalar sL); - - // Retrieve the local loads - // ------------------------ - void getPanelLoads(const TacsScalar stress[], TacsScalar* Nx, - TacsScalar* Nxy); - void getStiffenerLoads(const TacsScalar stress[], TacsScalar* Nx, - TacsScalar* Nxy); - - // Functions for panel-only optimizations - // -------------------------------------- - TacsScalar getFailureCriterion(const TacsScalar stress[]); - TacsScalar getBucklingCriterion(const TacsScalar stress[]); - - // Additional constraint evaluation functions - // ------------------------------------------ - int isLinear(); - int getNumCon(); - int getConCSRSize(); - int getConRange(int offset, TacsScalar lb[], TacsScalar ub[]); - int addConCSR(int offset, int rowp[], int cols[]); - int evalCon(int offset, TacsScalar con[]); - int evalConDVSens(int offset, TacsScalar Acol[], const int rowp[], - const int cols[]); - - // Design variable information set up - // ---------------------------------- - int ownsDesignVar(const int dvNum) const; - void setDesignVars(const TacsScalar dvs[], int numDVs); - void getDesignVars(TacsScalar dvs[], int numDVs); - void getDesignVarRange(TacsScalar lowerBound[], TacsScalar upperBound[], - int numDVs); - int getLxNum(); - - int getNumDesignVars(); - int getDesignVarNums(int dvNums[], int dvLen); - - // Functions required by FSDTStiffness - // ----------------------------------- - void getPointwiseMass(const double gpt[], TacsScalar mass[]); - void pointwiseMassDVSens(int dvNum, const double gpt[], TacsScalar mass[]); - void addPointwiseMassDVSens(const double pt[], const TacsScalar alpha[], - TacsScalar dvSens[], int dvLen); - TacsScalar getDensity(); - // Get the stiffness matrices and their derivatives - // ------------------------------------------------ - TacsScalar getStiffness(const double gpt[], TacsScalar A[], TacsScalar B[], - TacsScalar D[], TacsScalar As[]); - TacsScalar getStiffnessDVSens(int dvNum, const double gpt[], TacsScalar sA[], - TacsScalar sB[], TacsScalar sD[], - TacsScalar sAs[]); - void addStiffnessDVSens(const double pt[], const TacsScalar e[], - const TacsScalar psi[], TacsScalar rotPsi, - TacsScalar fdvSens[], int dvLen); - TacsScalar calculateStressDVSens(const double pt[], const TacsScalar strain[], - TacsScalar s_sens[], int dvNum); - - // Calculate the point-wise failure criteria - // ----------------------------------------- - void failure(const double gpt[], const TacsScalar strain[], TacsScalar* fail); - void failureStrainSens(const double gpt[], const TacsScalar strain[], - TacsScalar sens[]); - void failureDVSens(int dvNum, const double gpt[], const TacsScalar strain[], - TacsScalar* failSens); - void addFailureDVSens(const double pt[], const TacsScalar strain[], - TacsScalar alpha, TacsScalar dvSens[], int dvLen); - - // Calculate the buckling criteria - // ------------------------------- - void buckling(const TacsScalar strain[], TacsScalar* bval); - void bucklingStrainSens(const TacsScalar strain[], TacsScalar* bvalSens); - void bucklingDVSens(int dvNum, const TacsScalar strain[], - TacsScalar* bvalSens); - void addBucklingDVSens(const TacsScalar strain[], TacsScalar alpha, - TacsScalar dvSens[], int dvLen); - - const char* constitutiveName() const; - - // Retrieve the design variable for plotting purposes - // -------------------------------------------------- - TacsScalar getDVOutputValue(int dv_index, const double gpt[]); - - // Write the buckling properties to stdout - // --------------------------------------- - void printBucklingInfo(); - - private: - // Update the stiffness information A, B, D, As, k_penalty - void updateStiffness(); - - // Calculate the buckling loads - void calcBucklingProps(); - - // Calculate the derivative of the buckling loads - void calcBucklingPropsDVSens(int dvNum, TacsScalar* sNx_global_crit, - TacsScalar* sNxy_global_crit, - TacsScalar* sNx_panel_crit, - TacsScalar* sNxy_panel_crit, - TacsScalar* sNx_weak_stiff_crit, - TacsScalar* sNx_strong_stiff_crit); - - // Calculate the failure criteria - int calcFail(const TacsScalar strain[], TacsScalar fail[], TacsScalar* _max); - void calcFailStrainSens(const TacsScalar strain[], const TacsScalar weights[], - TacsScalar sens[]); - TacsScalar calcFailDVSens(int dvNum, const TacsScalar strain[], - const TacsScalar weights[]); - - // Calculate the buckling criteria - int calcBuckling(const TacsScalar strain[], TacsScalar bval[], - TacsScalar* _max); - void calcBucklingStrainSens(const TacsScalar strain[], - const TacsScalar weights[], TacsScalar sens[]); - TacsScalar calcBucklingDVSens(int dvNum, const TacsScalar strain[], - const TacsScalar weights[]); - - static const int NUM_BUCKLING = 4; - static const int MAX_NUM_FAIL = 3 * NUM_PLIES; - - // Stiffener information - // --------------------- - // Stiffener pitch variables - int sp_num; - TacsScalar sp, sp_low, sp_high; - - // Stiffener height - int sh_num; - TacsScalar sh, sh_low, sh_high; - - // Stiffener thickness - int st_num; - TacsScalar st, st_low, st_high; - - // Flage fraction - the fraction of the length of flange over the - // stiffener height - TacsScalar sf_fraction; - - int num_pf_con; // Number of ply-fraction constraints: 0, 1 or 2 - - // Ply percentage information - // -------------------------- - int num_stiff_pf_unique; - int stiff_pf_nums[NUM_PLIES], stiff_pf_unique[NUM_PLIES]; - TacsScalar stiff_pf[NUM_PLIES], stiff_ply_angles[NUM_PLIES], - stiff_pf_low[NUM_PLIES], stiff_pf_high[NUM_PLIES]; - - // Panel information - // ----------------- - // Panel thickness - int t_num; - TacsScalar t, t_low, t_high; - - // Ply percentage information - int num_pf_unique; - int pf_nums[NUM_PLIES], pf_unique[NUM_PLIES]; - TacsScalar pf[NUM_PLIES], ply_angles[NUM_PLIES], pf_low[NUM_PLIES], - pf_high[NUM_PLIES]; - - // Panel dimension information - TacsScalar Lx; - int Lx_num; - - // Buckling information - // -------------------- - // Critical buckling loads - TacsScalar Nx_global_crit, Nxy_global_crit; - TacsScalar Nx_panel_crit, Nxy_panel_crit; - TacsScalar Nx_weak_stiff_crit, Nx_strong_stiff_crit; - - // Stiffness information - // --------------------- - // Stiffness information for the panel and the blade stiffener - TacsScalar Abar_panel[3], Qbar_panel[6]; - TacsScalar Abar_stiff[3], Qbar_stiff[6]; - - // The stiffness matrices - TacsScalar A[6], B[6], D[6], As[6]; - TacsScalar k_penalty; - - // Information about the stiffeners - OrthoPly* ortho_ply; - - TacsScalar kcorr; // The shear correction factor - double ks_weight; // The ks weight for the failure envelope calculations - - static const char* constName; -}; - -#endif diff --git a/src/elements/TACSElementTypes.cpp b/src/elements/TACSElementTypes.cpp index 77a8cac52..6269b5d1c 100644 --- a/src/elements/TACSElementTypes.cpp +++ b/src/elements/TACSElementTypes.cpp @@ -85,7 +85,7 @@ int TacsGetOutputComponentCount(ElementType etype, int comp) { } else if (comp == TACS_OUTPUT_STRESSES) { return 9; } else if (comp == TACS_OUTPUT_EXTRAS) { - return 4; + return 8; } else if (comp == TACS_OUTPUT_LOADS) { return 6; } @@ -305,6 +305,14 @@ const char *TacsGetOutputComponentName(ElementType etype, int comp, int index) { return "dv2"; case 3: return "dv3"; + case 4: + return "dv4"; + case 5: + return "dv5"; + case 6: + return "dv6"; + case 7: + return "dv7"; default: return NULL; } diff --git a/src/elements/TACSElementVerification.cpp b/src/elements/TACSElementVerification.cpp index c95924525..a13bf3518 100644 --- a/src/elements/TACSElementVerification.cpp +++ b/src/elements/TACSElementVerification.cpp @@ -89,14 +89,15 @@ void TacsPrintErrorComponents(FILE *fp, const char *descript, fprintf(fp, "%*s[ ] %15s %15s %15s %15s\n", (int)strlen(descript), "Val", "Analytic", "Approximate", "Rel. Error", "Abs. Error"); for (int i = 0; i < size; i++) { + double absError = fabs(TacsRealPart(testVals[i] - refVals[i])); if (refVals[i] != 0.0) { fprintf(fp, "%s[%3d] %15.6e %15.6e %15.4e %15.4e\n", descript, i, TacsRealPart(testVals[i]), TacsRealPart(refVals[i]), - fabs(TacsRealPart((testVals[i] - refVals[i]) / refVals[i])), - fabs(TacsRealPart(testVals[i] - refVals[i]))); + fabs(TacsRealPart(absError / refVals[i])), absError); } else { - fprintf(fp, "%s[%3d] %15.6e %15.6e\n", descript, i, - TacsRealPart(testVals[i]), TacsRealPart(refVals[i])); + fprintf(fp, "%s[%3d] %15.6e %15.6e %15s %15.4e\n", descript, i, + TacsRealPart(testVals[i]), TacsRealPart(refVals[i]), "-", + absError); } } } diff --git a/src/elements/TACSElementVerification.h b/src/elements/TACSElementVerification.h index 85690218e..3992a2ad3 100644 --- a/src/elements/TACSElementVerification.h +++ b/src/elements/TACSElementVerification.h @@ -71,6 +71,27 @@ void TacsPrintErrorComponents(FILE *fp, const char *descript, bool TacsAssertAllClose(TacsScalar *testVals, TacsScalar *refVals, int size, double atol, double rtol); +/** + * @brief Assert that the values in testVals are close to the values in refVals. + * The closeness is computed using a hybrid of absolute and relative errors that + * should avoid false positives when the values are close to zero. Basically, it + * computes a relative error for "large" values and an absolute error for + * "small" values. The criterion is identical to numpy's `assert_allclose` + * function: + * + * Failure is raised if:: + * abs(`test` - `ref`) > (`atol` + `rtol` * abs(`ref`)) + * + * @param testVals Array of test values + * @param refVals Array of reference values + * @param size Number of values in each array + * @param atol Absolute tolerance + * @param rtol Relative tolerance + * @return bool True if all values are close, false otherwise + */ +bool TacsAssertAllClose(TacsScalar *testVals, TacsScalar *refVals, int size, + double atol, double rtol); + /* Perturb the input variables in the forward sense */ diff --git a/src/elements/shell/TACSShellElement.h b/src/elements/shell/TACSShellElement.h index 5cfbbeb4d..aafe630a0 100644 --- a/src/elements/shell/TACSShellElement.h +++ b/src/elements/shell/TACSShellElement.h @@ -1308,7 +1308,11 @@ void TACSShellElement::getOutputData( data[1] = con->evalDesignFieldValue(elemIndex, pt, X, 0); data[2] = con->evalDesignFieldValue(elemIndex, pt, X, 1); data[3] = con->evalDesignFieldValue(elemIndex, pt, X, 2); - data += 4; + data[4] = con->evalDesignFieldValue(elemIndex, pt, X, 3); + data[5] = con->evalDesignFieldValue(elemIndex, pt, X, 4); + data[6] = con->evalDesignFieldValue(elemIndex, pt, X, 5); + data[7] = con->evalDesignFieldValue(elemIndex, pt, X, 6); + data += 8; } } } diff --git a/tacs/constitutive.pxd b/tacs/constitutive.pxd index 796e1232c..58ba7c32b 100644 --- a/tacs/constitutive.pxd +++ b/tacs/constitutive.pxd @@ -130,6 +130,43 @@ cdef extern from "TACSLamParamShellConstitutive.h": TacsScalar, TacsScalar, TacsScalar, TacsScalar, TacsScalar, int, int, TacsScalar, TacsScalar) +cdef extern from "TACSBladeStiffenedShellConstitutive.h": + cdef cppclass TACSBladeStiffenedShellConstitutive(TACSShellConstitutive): + TACSBladeStiffenedShellConstitutive( + TACSOrthotropicPly*, # panelPly + TACSOrthotropicPly*, # stiffenerPly + TacsScalar, # kcorr + TacsScalar, # panelLength + int, # panelLengthNum + TacsScalar, # stiffenerPitch + int, # stiffenerPitchNum + TacsScalar, # panelThick + int, # panelThickNum + int, # numPanelPlies + TacsScalar[], # panelPlyAngles + TacsScalar[], # panelPlyFracs + int[], # panelPlyFracNums + TacsScalar, # stiffenerHeight + int, # stiffenerHeightNum + TacsScalar, # stiffenerThick + int, # stiffenerThickNum + int, # numStiffenerPlies + TacsScalar[], # stiffenerPlyAngles + TacsScalar[], # stiffenerPlyFracs + int[], # stiffenerPlyFracNums + TacsScalar # flangeFraction + ) + void setKSWeight(double ksWeight) + void setStiffenerPitchBounds(TacsScalar lowerBound, TacsScalar upperBound) + void setStiffenerHeightBounds(TacsScalar lowerBound, TacsScalar upperBound) + void setStiffenerThicknessBounds(TacsScalar lowerBound, TacsScalar upperBound) + void setPanelThicknessBounds(TacsScalar lowerBound, TacsScalar upperBound) + void setStiffenerPlyFractionBounds(TacsScalar[] lowerBound, TacsScalar[] upperBound) + void setPanelPlyFractionBounds(TacsScalar[] lowerBound, TacsScalar[] upperBound) + +cdef class BladeStiffenedShellConstitutive(ShellConstitutive): + cdef TACSBladeStiffenedShellConstitutive *blade_ptr + cdef extern from "TACSBeamConstitutive.h": cdef cppclass TACSBeamConstitutive(TACSConstitutive): pass diff --git a/tacs/constitutive.pyx b/tacs/constitutive.pyx index cff3d66e8..f2bfc8a89 100644 --- a/tacs/constitutive.pyx +++ b/tacs/constitutive.pyx @@ -764,6 +764,127 @@ cdef class CompositeShellConstitutive(ShellConstitutive): self.props = [prop.getMaterialProperties() for prop in ply_list] +cdef class BladeStiffenedShellConstitutive(ShellConstitutive): + """This constitutive class models a shell stiffened with T-shaped stiffeners. + The stiffeners are not explicitly modelled. + Instead, their stiffness is "smeared" across the shell. + """ + def __cinit__( + self, + OrthotropicPly panelPly, + OrthotropicPly stiffenerPly, + TacsScalar kcorr, + TacsScalar panelLength, + int panelLengthNum, + TacsScalar stiffenerPitch, + int stiffenerPitchNum, + TacsScalar panelThick, + int panelThickNum, + int numPanelPlies, + np.ndarray[TacsScalar, ndim=1, mode='c'] panelPlyAngles, + np.ndarray[TacsScalar, ndim=1, mode='c'] panelPlyFracs, + np.ndarray[int, ndim=1, mode='c'] panelPlyFracNums, + TacsScalar stiffenerHeight, + int stiffenerHeightNum, + TacsScalar stiffenerThick, + int stiffenerThickNum, + int numStiffenerPlies, + np.ndarray[TacsScalar, ndim=1, mode='c'] stiffenerPlyAngles, + np.ndarray[TacsScalar, ndim=1, mode='c'] stiffenerPlyFracs, + np.ndarray[int, ndim=1, mode='c'] stiffenerPlyFracNums, + TacsScalar flangeFraction = 1.0 + ): + + if len(panelPlyAngles) != numPanelPlies: + raise ValueError('panelPlyAngles must have length numPanelPlies') + if len(panelPlyAngles) != numPanelPlies: + raise ValueError('panelPlyNums must have length numPanelPlies') + if len(stiffenerPlyAngles) != numStiffenerPlies: + raise ValueError('stiffenerPlyAngles must have length numStiffenerPlies') + if len(stiffenerPlyAngles) != numStiffenerPlies: + raise ValueError('stiffenerPlyNums must have length numStiffenerPlies') + + # Numpy's default int type is int64, but this is interpreted by Cython as a long. + if panelPlyFracNums.dtype != np.intc: + panelPlyFracNums = panelPlyFracNums.astype(np.intc) + if stiffenerPlyFracNums.dtype != np.intc: + stiffenerPlyFracNums = stiffenerPlyFracNums.astype(np.intc) + # raise ValueError('panelPlyFracNums must be of type int32') + + self.blade_ptr = new TACSBladeStiffenedShellConstitutive( + panelPly.ptr, + stiffenerPly.ptr, + kcorr, + panelLength, + panelLengthNum, + stiffenerPitch, + stiffenerPitchNum, + panelThick, + panelThickNum, + numPanelPlies, + panelPlyAngles.data, + panelPlyFracs.data, + panelPlyFracNums.data, + stiffenerHeight, + stiffenerHeightNum, + stiffenerThick, + stiffenerThickNum, + numStiffenerPlies, + stiffenerPlyAngles.data, + stiffenerPlyFracs.data, + stiffenerPlyFracNums.data, + flangeFraction + ) + self.ptr = self.cptr = self.blade_ptr + self.ptr.incref() + + def setKSWeight(self, double ksWeight): + """ + Update the ks weight used for aggregating the different failure modes + + Args: + ksWeight (float): KS weight + """ + if self.blade_ptr: + self.blade_ptr.setKSWeight(ksWeight) + + def setStiffenerPitchBounds(self, TacsScalar lowerBound, TacsScalar upperBound): + if self.blade_ptr: + self.blade_ptr.setStiffenerPitchBounds(lowerBound, upperBound) + + def setStiffenerHeightBounds(self, TacsScalar lowerBound, TacsScalar upperBound): + + if self.blade_ptr: + self.blade_ptr.setStiffenerHeightBounds(lowerBound, upperBound) + + def setStiffenerThicknessBounds(self, TacsScalar lowerBound, TacsScalar upperBound): + + if self.blade_ptr: + self.blade_ptr.setStiffenerThicknessBounds(lowerBound, upperBound) + + def setPanelThicknessBounds(self, TacsScalar lowerBound, TacsScalar upperBound): + + if self.blade_ptr: + self.blade_ptr.setPanelThicknessBounds(lowerBound, upperBound) + + def setStiffenerPlyFractionBounds( + self, + np.ndarray[TacsScalar, ndim=1, mode='c'] lowerBound, + np.ndarray[TacsScalar, ndim=1, mode='c'] upperBound + ): + + if self.blade_ptr: + self.blade_ptr.setStiffenerPlyFractionBounds(lowerBound.data, upperBound.data) + + def setPanelPlyFractionBounds( + self, + np.ndarray[TacsScalar, ndim=1, mode='c'] lowerBound, + np.ndarray[TacsScalar, ndim=1, mode='c'] upperBound + ): + + if self.blade_ptr: + self.blade_ptr.setPanelPlyFractionBounds(lowerBound.data, upperBound.data) + def generateBDFCard(self): """ Generate pyNASTRAN card class based on current design variable values. @@ -1464,4 +1585,4 @@ def TestConstitutiveFailureStrainSens(Constitutive con, int elem_index, assert len(pt) == 3 assert len(x) == 3 return TacsTestConstitutiveFailureStrainSens(con.ptr, elem_index, pt.data, x.data, - dh, test_print_level, atol, rtol) \ No newline at end of file + dh, test_print_level, atol, rtol) diff --git a/tacs/constraints/__init__.py b/tacs/constraints/__init__.py index ec446b691..6346f1624 100644 --- a/tacs/constraints/__init__.py +++ b/tacs/constraints/__init__.py @@ -1,5 +1,6 @@ from .adjacency import AdjacencyConstraint from .dv import DVConstraint +from .panel_length import PanelLengthConstraint from .volume import VolumeConstraint from .base import TACSConstraint diff --git a/tacs/constraints/base.py b/tacs/constraints/base.py index a26ea170f..2421d01de 100644 --- a/tacs/constraints/base.py +++ b/tacs/constraints/base.py @@ -85,7 +85,7 @@ def addConstraint(self, conName, compIDs=None, lower=-1e20, upper=1e20, **kwargs upper bound for constraint. Defaults to 1e20. """ - raise NotImplemented( + raise NotImplementedError( f"'addConstraint' method is not implemented for class '{type(self).__name__}'" ) @@ -191,7 +191,7 @@ def evalConstraints(self, funcs, evalCons=None, ignoreMissing=False): >>> # Result will look like (if TACSConstraint has name of 'c1'): >>> # {'c1_LE_SPAR': array([12354.10])} """ - raise NotImplemented( + raise NotImplementedError( f"'evalConstraints' method is not implemented for class '{type(self).__name__}'" ) @@ -218,7 +218,7 @@ def evalConstraintsSens(self, funcsSens, evalCons=None): >>> # Result will look like (if TACSConstraint has name of 'c1'): >>> # {'c1_LE_SPAR':{'struct':<50x242 sparse matrix of type '' with 100 stored elements in Compressed Sparse Row format>}} """ - raise NotImplemented( + raise NotImplementedError( f"'evalConstraintsSens' method is not implemented for class '{type(self).__name__}'" ) diff --git a/tacs/constraints/panel_length.py b/tacs/constraints/panel_length.py new file mode 100644 index 000000000..e37a12c9d --- /dev/null +++ b/tacs/constraints/panel_length.py @@ -0,0 +1,794 @@ +""" +============================================================================== +Panel Length Constraint +============================================================================== +@File : panel_length.py +@Date : 2023/04/23 +@Author : Alasdair Christison Gray +@Description : This class implements a constraint which enforces the panel +length design variable values passed to elements using the BladeStiffenedShell +constitutive model to be consistent with the true length of the panel they are +a part of. +""" + +# ============================================================================== +# Standard Python modules +# ============================================================================== + +# ============================================================================== +# External Python modules +# ============================================================================== +from numba import njit +import numpy as np +import scipy as sp + +# ============================================================================== +# Extension modules +# ============================================================================== +from tacs.constraints.base import TACSConstraint + + +@njit(cache=True, fastmath=True) +def computePanelLength(points, direction): + """Given the sorted points around the perimeter of a panel, compute the length of the panel in a given direction + + Note: This function is approximate, it works best when the length direction is close to parallel with the panel + + Parameters + ---------- + points : n x 3 array + Coordinates of the perimeter points of the panel, in sorted order, so that points[i] - points[i-1] is a vector + along the perimeter + direction : length 3 array + Direction in which to compute the panel length + + Returns + ------- + float or complex + The panel length in the given direction + """ + numPoints = points.shape[0] + length = 0.0 + for pointInd in range(numPoints): + for edgeInd in range(numPoints): + startInd = edgeInd + endInd = (edgeInd + 1) % numPoints + # We only need to check edges that are not adjacent to the current point + if not (startInd == pointInd or endInd == pointInd): + # Find the intersection of a line through the point in the given + # direction with a line along the current edge + edge = points[endInd] - points[startInd] + mat = np.stack((direction, -edge), axis=1) + rhs = points[startInd] - points[pointInd] + sol, res, _, _ = np.linalg.lstsq(mat, rhs) + alpha = sol[0] + beta = sol[1] + # Only compute the length if the intersection occurs within the true bounds of the edge + if np.real(beta) - 1e-12 <= 1 and np.real(beta) + 1e-12 >= 0: + # intersectionPoint = points[startInd] + beta * edge + # newLength = np.sqrt(np.sum((intersectionPoint - points[pointInd]) ** 2)) + newLength = np.sqrt(np.sum((alpha * direction) ** 2)) + if ( + np.real(newLength) > np.real(length) + and np.real(newLength) > res + ): + length = newLength + return length + + +@njit(cache=True, fastmath=True) +def computePanelLengthSens(points, direction): + """Given the sorted points around the perimeter of a panel, compute the + sensitivitiy of the length of the panel in a given direction with + respect to the coordinates of the points + + Parameters + ---------- + points : n x 3 array + Coordinates of the perimeter points of the panel, in sorted order, so that points[i] - points[i-1] is a vector + along the perimeter + direction : length 3 array + Direction in which to compute the panel length + + Returns + ------- + n x 3 array + Panel length sensitivities + """ + sens = np.zeros_like(points) + pointsPert = np.zeros_like(points, dtype=np.complex128) + pointsPert[:] = points[:] + for ii in range(points.shape[0]): + for jj in range(points.shape[1]): + pointsPert[ii, jj] += 1e-200j + sens[ii, jj] = np.imag(computePanelLength(pointsPert, direction)) * 1e200 + pointsPert[ii, jj] -= 1e-200j + return sens + + +def simplifyPoly(nodeIDs, nodes, angleTol=18.0): + """ + Take a (closed) chain of nodes and remove any nodes that turn by less than angleTol degrees. + This simplifies the polygon by leaving only "sharp" corners + """ + cont = True + while cont: + newNodes = [] + newNodeIDs = [] + for i in range(len(nodes)): + im1 = i - 1 + ip1 = i + 1 + if i == 0: + im1 = len(nodes) - 1 + if i == len(nodes) - 1: + ip1 = 0 + + v1 = nodes[ip1] - nodes[i] + v2 = nodes[im1] - nodes[i] + # Angle between vectors + arg = np.dot(v1, v2) / (np.linalg.norm(v1) * np.linalg.norm(v2)) + arg = max(-1, arg) + arg = min(1, arg) + theta = np.arccos(arg) + + if theta < np.pi * (1 - angleTol / 180): + newNodes.append(nodes[i]) + newNodeIDs.append(nodeIDs[i]) + + if len(newNodes) == len(nodes): + cont = False + + nodes = np.array(newNodes) + nodeIDs = np.array(newNodeIDs) + + return list(nodeIDs), nodes + + +class PanelLengthConstraint(TACSConstraint): + def __init__( + self, + name, + assembler, + comm, + outputViewer=None, + meshLoader=None, + options=None, + ): + """ + NOTE: This class should not be initialized directly by the user. + Use pyTACS.createPanelLengthConstraint instead. + + Parameters + ---------- + name : str + Name of this tacs problem + + assembler : TACS.Assembler + Cython object responsible for creating and setting tacs objects used to solve problem + + comm : mpi4py.MPI.Intracomm + The comm object on which to create the pyTACS object. + + outputViewer : TACS.TACSToFH5 + Cython object used to write out f5 files that can be converted and used for postprocessing. + + meshLoader : pymeshloader.pyMeshLoader + pyMeshLoader object used to create the assembler. + + options : dict + Dictionary holding problem-specific option parameters (case-insensitive). + """ + + # Problem name + self.name = name + + # Default setup for common constraint class objects, sets up comm and options + TACSConstraint.__init__( + self, assembler, comm, options, outputViewer, meshLoader + ) + + # Create a map from the global DV index to the proc index that owns it and the local index on that proc + self.globalToLocalDVNumsOnProc = self.comm.gather( + self.globalToLocalDVNums, root=0 + ) + self.DVMap = {} + if self.rank == 0: + for procInd in range(self.comm.size): + for globalInd, localInd in self.globalToLocalDVNumsOnProc[ + procInd + ].items(): + self.DVMap[globalInd] = {"proc": procInd, "localInd": localInd} + + # Now create the same thing for the nodes + nodeDict = self.meshLoader.getGlobalToLocalNodeIDDict() + nodeDicts = self.comm.gather(nodeDict, root=0) + self.nodeMap = {} + if self.rank == 0: + for procInd in range(self.comm.size): + for globalInd, localInd in nodeDicts[procInd].items(): + self.nodeMap[globalInd] = {"proc": procInd, "localInd": localInd} + + # Store the number of DVs and nodes on each proc + self.numLocalDVs = self.getNumDesignVars() + + self.computePanelLength = computePanelLength + self.computePanelLengthSens = computePanelLengthSens + + # Store flags for whether or not we need to recompute the constraints and derivatives + self.constraintsUpToDate = {} + self.funcs = {} + self.constraintsSensUpToDate = {} + self.funcsSens = {} + + def setDesignVars(self, x): + """Wrapper around the base class setDesignVars method that also sets + the flag to indicate that the constraints need to be recomputed + """ + TACSConstraint.setDesignVars(self, x) + for key in self.constraintsUpToDate: + self.constraintsUpToDate[key] = False + + def setNodes(self, Xpts): + """Wrapper around the base class setNodes method that also sets + the flag to indicate that the constraints and their derivatives + need to be recomputed + """ + TACSConstraint.setNodes(self, Xpts) + for key in self.constraintsUpToDate: + self.constraintsUpToDate[key] = False + self.constraintsSensUpToDate[key] = False + + def addConstraint(self, conName, compIDs=None, lower=None, upper=None, dvIndex=0): + """ + Generic method to adding a new constraint set for TACS. + + Parameters + ---------- + conName : str + The user-supplied name for the constraint set. This will + typically be a string that is meaningful to the user + + compIDs: list[int] or None + List of compIDs to apply constraints to. If None, all compIDs will be used. Defaults to None. + + lower: float or complex + lower bound for constraint. Not used. + + upper: float or complex + upper bound for constraint. Not used. + + dvIndex : int + Index number of the panel length DV's. Defaults to 0. + + """ + if compIDs is not None: + # Make sure CompIDs is flat and get element numbers on each proc corresponding to specified compIDs + compIDs = self._flatten(compIDs) + else: + nComps = self.meshLoader.getNumComponents() + compIDs = range(nComps) + + dvGlobalInds = [] + dvProcs = [] + dvLocalInds = [] + boundaryNodeGlobalInds = [] + boundaryNodeLocalInds = [] + boundaryNodeLocalProcs = [] + refAxes = [] + dvJacRows = [] + dvJacCols = [] + dvJacVals = [] + coordJacRows = [] + coordJacCols = [] + for ii in range(self.comm.size): + dvJacRows.append([]) + dvJacCols.append([]) + dvJacVals.append([]) + coordJacRows.append([]) + coordJacCols.append([]) + + # Get the boundary node IDs for each component + boundaryNodeIDs, boundaryNodeCoords = self._getComponentBoundaryNodes(compIDs) + + if self.rank == 0: + constraintInd = 0 + for compID in compIDs: + # Get the TACS element object associated with this compID to + # get the ref axis + elemObj = self.meshLoader.getElementObject(compID, 0) + transObj = elemObj.getTransform() + try: + refAxis = transObj.getRefAxis() + except AttributeError as e: + raise AttributeError( + f"The elements in component {self.meshLoader.compDescripts[compID]} do not have a reference axis. Please define one by using the 'ShellRefAxisTransform' class with your elements" + ) from e + + # For a more accurate length calculation, roject the ref axis + # onto the "average" plane of the baseline panel geometry by + # using an SVD to compute a normal vector + centroid = np.mean(boundaryNodeCoords[compID], axis=0, keepdims=True) + centredPoints = boundaryNodeCoords[compID] - centroid + _, _, VT = np.linalg.svd(centredPoints, full_matrices=False) + panelNormal = VT[-1] + refAxis -= np.dot(refAxis, panelNormal) * panelNormal + refAxis /= np.linalg.norm(refAxis) + refAxes.append(refAxis) + + # Now figure out where the DV for this component lives + globalDvNums = elemObj.getDesignVarNums(0) + dvGlobalInds.append(globalDvNums[dvIndex]) + dvProcs.append(self.DVMap[globalDvNums[dvIndex]]["proc"]) + dvLocalInds.append(self.DVMap[globalDvNums[dvIndex]]["localInd"]) + + # Do the same for the boundary nodes, this is a little more + # complicated because each node may be on a different proc + GlobalInds = [] + LocalInds = [] + LocalProcs = [] + for nodeID in boundaryNodeIDs[compID]: + GlobalInds.append(nodeID) + LocalInds.append(self.nodeMap[nodeID]["localInd"]) + LocalProcs.append(self.nodeMap[nodeID]["proc"]) + boundaryNodeGlobalInds.append(GlobalInds) + boundaryNodeLocalInds.append(LocalInds) + boundaryNodeLocalProcs.append(LocalProcs) + + # Figure out the jacobian sparsity for each proc + # The DV jacobian on the proc that owns this component's DV + # will have a -1 in the row corresponding to this constraint + # and the column corresponding to the local DV index + dvJacRows[dvProcs[-1]].append(constraintInd) + dvJacCols[dvProcs[-1]].append(dvLocalInds[-1]) + dvJacVals[dvProcs[-1]].append(-1.0) + + for ii in range(len(boundaryNodeIDs[compID])): + # the coordinate jacobian on the proc that owns this node + # will have 3 entries in the row corresponding to this + # constraint and the columns corresponding to the local + # node index on the proc + proc = boundaryNodeLocalProcs[-1][ii] + localNodeInd = boundaryNodeLocalInds[-1][ii] + coordJacRows[proc] += [constraintInd] * 3 + coordJacCols[proc] += [ + 3 * localNodeInd, + 3 * localNodeInd + 1, + 3 * localNodeInd + 2, + ] + + constraintInd += 1 + + # Add the constraint to the constraint list, we need to store: + # - The size of this constraint + # - The global index of each DV + # - The proc number that is in charge of each DV + # - The local index of each DV on the proc that is in charge of it + # - The global boundary node IDs for each component + # - The proc that owns each boundary node for each component + # - The local index of each boundary node on the proc that owns it + # - The reference axis direction for each component + # - The DV jacobian for each proc (because it's constant) + # - The coordinate jacobian sparsity pattern for each proc (because it's also constant) + self.constraintList[conName] = { + "nCon": len(compIDs), + "compIDs": compIDs, + "dvGlobalInds": dvGlobalInds, + "dvProcs": dvProcs, + "dvLocalInds": dvLocalInds, + "boundaryNodeGlobalInds": boundaryNodeGlobalInds, + "boundaryNodeLocalInds": boundaryNodeLocalInds, + "boundaryNodeLocalProcs": boundaryNodeLocalProcs, + "refAxes": refAxes, + } + else: + self.constraintList[conName] = {"nCon": len(compIDs)} + dvJacRows = None + dvJacCols = None + dvJacVals = None + coordJacRows = None + coordJacCols = None + + # These constraints are linear w.r.t the DVs so we can just precompute + # the DV jacobian for each proc + dvJacRows = self.comm.scatter(dvJacRows, root=0) + dvJacCols = self.comm.scatter(dvJacCols, root=0) + dvJacVals = self.comm.scatter(dvJacVals, root=0) + coordJacRows = self.comm.scatter(coordJacRows, root=0) + coordJacCols = self.comm.scatter(coordJacCols, root=0) + self.constraintList[conName]["dvJac"] = sp.sparse.csr_matrix( + (dvJacVals, (dvJacRows, dvJacCols)), + shape=(len(compIDs), self.numLocalDVs), + ) + + # The constraints aren't linear w.r.t the coordinates, but the + # sparsity pattern is constant so we can store that + self.constraintList[conName]["coordJacRows"] = coordJacRows + self.constraintList[conName]["coordJacCols"] = coordJacCols + + self.constraintsUpToDate[conName] = False + self.constraintsSensUpToDate[conName] = False + success = True + + return success + + def getConstraintBounds(self, bounds, evalCons=None): + """ + Get bounds for constraints. The constraints corresponding to the strings in + `evalCons` are evaluated and updated into the provided + dictionary. + + The panel length constraints are equality constraints so both the upper and lower bounds are zero + + Parameters + ---------- + bounds : dict + Dictionary into which the constraint bounds are saved. + Bounds will be saved as a tuple: (lower, upper) + evalCons : iterable object containing strings. + If not none, use these constraints to evaluate. + + Examples + -------- + >>> conBounds = {} + >>> tacsConstraint.getConstraintBounds(conBounds, 'LE_SPAR') + >>> conBounds + >>> # Result will look like (if TACSConstraint has name of 'c1'): + >>> # {'c1_LE_SPAR': (array([-1e20]), array([1e20]))} + """ + # Check if user specified which constraints to output + # Otherwise, output them all + evalCons = self._processEvalCons(evalCons) + + # Loop through each requested constraint set + for conName in evalCons: + key = f"{self.name}_{conName}" + nCon = self.constraintList[conName]["nCon"] + bounds[key] = (np.zeros(nCon), np.zeros(nCon)) + + def getConstraintSizes(self, sizes, evalCons=None): + """ + Get number for constraint equations in each set. + The constraints corresponding to the strings in `evalCons` + are evaluated and updated into the provided dictionary. + + Parameters + ---------- + sizes : dict + Dictionary into which the constraint sizes are saved. + evalCons : iterable object containing strings. + If not none, use these constraints to evaluate. + + Examples + -------- + >>> conSizes = {} + >>> tacsConstraint.getConstraintSizes(conSizes, 'LE_SPAR') + >>> funconSizescs + >>> # Result will look like (if TACSConstraint has name of 'c1'): + >>> # {'c1_LE_SPAR': 10} + """ + # Check if user specified which constraints to output + # Otherwise, output them all + evalCons = self._processEvalCons(evalCons) + + # Loop through each requested constraint set + for conName in evalCons: + key = f"{self.name}_{conName}" + sizes[key] = self.constraintList[conName]["nCon"] + + def evalConstraints(self, funcs, evalCons=None, ignoreMissing=False): + """ + Evaluate values for constraints. The constraints corresponding to the strings in + evalCons are evaluated and updated into the provided dictionary. + + The same constraint arrays are returned on every proc + + Parameters + ---------- + funcs : dict + Dictionary into which the constraints are saved. + evalCons : iterable object containing strings. + If not none, use these constraints to evaluate. + ignoreMissing : bool + Flag to supress checking for a valid constraint. Please use + this option with caution. + + Examples + -------- + >>> funcs = {} + >>> adjConstraint.evalConstraints(funcs, 'LE_SPAR') + >>> funcs + >>> # Result will look like (if PanelLengthConstraint has name of 'c1'): + >>> # {'c1_LE_SPAR': array([1.325, 2.1983645, 3.1415926, ...])} + """ + + # Check if user specified which constraints to output + # Otherwise, output them all + evalCons = self._processEvalCons(evalCons, ignoreMissing) + + # We will compute everything on the root proc and then broadcast the + # results, this is definitely not the most efficient way to do this + # so we may want to re-do it in future, but this works for now + + DVs = None + nodes = None + + # Loop through each requested constraint set + for conName in evalCons: + key = f"{self.name}_{conName}" + nCon = self.constraintList[conName]["nCon"] + if self.constraintsUpToDate[conName]: + funcs[key] = np.copy(self.funcs[key]) + else: + constraintValues = np.zeros(nCon, dtype=self.dtype) + if nodes is None: + # Get all of the DVs and nodes on the root proc + DVs = self.comm.gather(self.x.getArray(), root=0) + nodes = self.comm.gather(self.Xpts.getArray(), root=0) + if self.rank == 0: + for ii in range(self.comm.size): + nodes[ii] = nodes[ii].reshape(-1, 3) + if self.rank == 0: + for ii in range(nCon): + numPoints = len( + self.constraintList[conName]["boundaryNodeGlobalInds"][ii] + ) + boundaryPoints = np.zeros((numPoints, 3), dtype=self.dtype) + for jj in range(numPoints): + nodeProc = self.constraintList[conName][ + "boundaryNodeLocalProcs" + ][ii][jj] + localInd = self.constraintList[conName][ + "boundaryNodeLocalInds" + ][ii][jj] + boundaryPoints[jj] = nodes[nodeProc][localInd] + refAxis = self.constraintList[conName]["refAxes"][ii] + DVProc = self.constraintList[conName]["dvProcs"][ii] + DVLocalInd = self.constraintList[conName]["dvLocalInds"][ii] + constraintValues[ii] = ( + self.computePanelLength(boundaryPoints, refAxis) + - DVs[DVProc][DVLocalInd] + ) + funcs[key] = self.comm.bcast(constraintValues, root=0) + self.funcs[key] = np.copy(funcs[key]) + self.constraintsUpToDate[conName] = True + + def evalConstraintsSens(self, funcsSens, evalCons=None): + """This is the main routine for returning useful (sensitivity) + information from constraint. The derivatives of the constraints + corresponding to the strings in evalCons are evaluated and + updated into the provided dictionary. The derivitives with + respect to all design variables and node locations are computed. + + The sensitivities returned on each proc are a sparse m x n matrix + where m is the number of constraints and n is the number of design + variables or 3x the number of nodes on this proc. The matrix contains + the sensitivities of all constraints w.r.t only the design + variables/node coordinates on this proc. + + Parameters + ---------- + funcsSens : dict + Dictionary into which the derivatives are saved. + evalCons : iterable object containing strings + The constraints the user wants returned + + Examples + -------- + >>> funcsSens = {} + >>> adjConstraint.evalConstraintsSens(funcsSens, 'LE_SPAR') + >>> funcsSens + >>> # Result will look like (if AdjacencyConstraint has name of 'c1'): + >>> # {'c1_LE_SPAR':{'struct':<50x242 sparse matrix of type '' with 100 stored elements in Compressed Sparse Row format>}} + """ + + # Check if user specified which constraints to output + # Otherwise, output them all + evalCons = self._processEvalCons(evalCons) + + # We will compute everything on the root proc and then broadcast the results, + # this is definitely not the most efficient way to do this so we may want to + # re-do it in future, but this works for now + + nodes = None + + # Get number of nodes coords on this proc + nCoords = self.getNumCoordinates() + + # Loop through each requested constraint set + for conName in evalCons: + key = f"{self.name}_{conName}" + nCon = self.constraintList[conName]["nCon"] + funcsSens[key] = {} + funcsSens[key][self.varName] = self.constraintList[conName]["dvJac"] + if self.constraintsSensUpToDate[conName]: + funcsSens[key][self.coordName] = self.funcsSens[key].copy() + else: + # Get all of the nodes on the root proc + if nodes is None: + nodes = self.comm.gather(self.Xpts.getArray(), root=0) + if self.rank == 0: + for ii in range(self.comm.size): + nodes[ii] = nodes[ii].reshape(-1, 3) + funcsSens[key][self.coordName] = sp.sparse.csr_matrix( + (nCon, nCoords), dtype=self.dtype + ) + if self.rank == 0: + coordJacVals = [] + for ii in range(self.comm.size): + coordJacVals.append([]) + for ii in range(nCon): + numPoints = len( + self.constraintList[conName]["boundaryNodeGlobalInds"][ii] + ) + boundaryPoints = np.zeros((numPoints, 3), dtype=self.dtype) + + for jj in range(numPoints): + nodeProc = self.constraintList[conName][ + "boundaryNodeLocalProcs" + ][ii][jj] + localInd = self.constraintList[conName][ + "boundaryNodeLocalInds" + ][ii][jj] + boundaryPoints[jj] = nodes[nodeProc][localInd] + refAxis = self.constraintList[conName]["refAxes"][ii] + LSens = self.computePanelLengthSens(boundaryPoints, refAxis) + for jj in range(numPoints): + nodeProc = self.constraintList[conName][ + "boundaryNodeLocalProcs" + ][ii][jj] + coordJacVals[nodeProc] += LSens[jj].tolist() + else: + coordJacVals = None + coordJacVals = self.comm.scatter(coordJacVals, root=0) + coordJacRows = self.constraintList[conName]["coordJacRows"] + coordJacCols = self.constraintList[conName]["coordJacCols"] + self.funcsSens[key] = sp.sparse.csr_matrix( + (coordJacVals, (coordJacRows, coordJacCols)), + (nCon, nCoords), + dtype=self.dtype, + ) + funcsSens[key][self.coordName] = self.funcsSens[key].copy() + self.constraintsSensUpToDate[conName] = True + + def _getComponentBoundaryNodes(self, compIDs): + """For a given list of components, find the nodes on the boundaries of + each of the components. + + The results are broadcast to all procs + + Parameters + ---------- + compIDs: list[int] + List of compIDs to find boundaries of. + + Returns + -------- + dict[int, list[int]] + Dictionary where dict[compID] = sorted list of nodeIDs on the + boundary of the component + dict[int, np.array] + Dictionary where dict[compID] = array of node coordinates on the + boundary of the component + """ + + boundaryNodeIDs = {} + boundaryNodeCoords = {} + + if self.rank == 0: + for compID in compIDs: + allEdges = set() + dupEdges = set() + compConn = self.meshLoader.getConnectivityForComp( + compID, nastranOrdering=False + ) + # Go over all the elements in the component and add their edges to the sets of all and possibly duplicate edges + for elemConn in compConn: + nnodes = len(elemConn) + if nnodes >= 2: + for j in range(nnodes): + nodeID1 = elemConn[j] + nodeID2 = elemConn[(j + 1) % nnodes] + + if nodeID1 < nodeID2: + key = (nodeID1, nodeID2) + else: + key = (nodeID2, nodeID1) + + # Skip degenerate edges + if key[0] != key[1]: + # Either add to allEdges or dupEdges depending on whether we've seen this edge before + if key not in allEdges: + allEdges.add(key) + else: + dupEdges.add(key) + # Now get a list of all the edges that aren't duplicated, these are the boundary edges + boundaryEdges = list(allEdges - dupEdges) + + # Create a nodeToElem Pointer using a dictionary: + nodeToElem = {} + for iEdge in range(len(boundaryEdges)): + edge = boundaryEdges[iEdge] + for ii in range(2): + if edge[ii] in nodeToElem: + nodeToElem[edge[ii]].append(iEdge) + else: + nodeToElem[edge[ii]] = [iEdge] + + # Now check that each nodeToElem has a length of + # 2. This means we have a chance it is a + # closed curve + for key in nodeToElem: + if len(nodeToElem[key]) != 2: + raise ValueError( + "The topology of the geometry associated with " + "a constitutive object is not manifold " + "(There is a node with three or more edges " + "attached. This constitutive object cannot " + "use a panel-type constitutive object. " + f"CompIDs are: {repr(compIDs)}" + ) + + # Now we will "order" the edges if possible. This + # will also allow us to detect multiple loops + # which isn't allowed, or a non-manifold local + # geometry - ie. in this context a node connected + # to three edges. This is also not allowed. + + nodeChain = [boundaryEdges[0][0], boundaryEdges[0][1]] + cont = True + curElem = 0 + while cont: + # We arbitrarily pick the first 'element' + # (edge) containing the first two nodes of our + # chain. Next step is to find the next element + # and node in the chain: + nextElems = nodeToElem[nodeChain[-1]] + # Get the 'nextElem' that isn't the current + # one + if nextElems[0] == curElem: + nextElem = nextElems[1] + else: + nextElem = nextElems[0] + + # Now nextElem is the next in the chain. Get + # the nodes for this elem: + nextNodes = boundaryEdges[nextElem] + + # Append the node that isn't the last one + # (that is already in the chain) + if nextNodes[0] == nodeChain[-1]: + nodeChain.append(nextNodes[1]) + else: + nodeChain.append(nextNodes[0]) + + # Exit condition: + if nodeChain[-1] == nodeChain[0]: + # We've made it all the way around! + cont = False + + # Set current element + curElem = nextElem + + # Now check that we've *actually* used all of our + # nodes. Since we've determined it is manifold, + # this must mean we have multiple loops which + # *also* isn't allowed. + if len(nodeChain) - 1 != len(boundaryEdges): + raise ValueError( + "Detected more than one closed loop for " + "constitutive object. This is not allowed. " + "This constitutive object cannot use a " + "panel-type constitutive object. " + f"CompIDs are: {repr(compIDs)}" + ) + nodeChain = nodeChain[:-1] + nodeChainCoords = self.meshLoader.getBDFNodes( + nodeChain, nastranOrdering=False + ) + nodeIDs, coords = simplifyPoly(nodeChain, nodeChainCoords) + boundaryNodeIDs[compID] = nodeIDs + boundaryNodeCoords[compID] = coords + + return self.comm.bcast(boundaryNodeIDs, root=0), self.comm.bcast( + boundaryNodeCoords, root=0 + ) diff --git a/tacs/mphys/mphys_tacs.py b/tacs/mphys/mphys_tacs.py index 6d6b9e938..6c6b05037 100644 --- a/tacs/mphys/mphys_tacs.py +++ b/tacs/mphys/mphys_tacs.py @@ -943,6 +943,9 @@ def initialize(self): self.fea_assembler = None self.constr = None + self.old_dvs = None + self.old_xs = None + def setup(self): self.fea_assembler = self.options["fea_assembler"] self.constr = self.options["constraint_object"] @@ -978,8 +981,43 @@ def setup(self): ) def _update_internal(self, inputs): - self.constr.setDesignVars(inputs["tacs_dvs"]) - self.constr.setNodes(inputs["x_struct0"]) + dvsNeedUpdate, xsNeedUpdate = self._need_update(inputs) + if dvsNeedUpdate: + self.constr.setDesignVars(inputs["tacs_dvs"]) + if xsNeedUpdate: + self.constr.setNodes(inputs["x_struct0"]) + + def _need_update(self, inputs): + dvsNeedUpdate = False + xsNeedUpdate = False + + dvs = inputs["tacs_dvs"] + xs = inputs["x_struct0"] + + if self.old_dvs is None: + self.old_dvs = inputs["tacs_dvs"].copy() + dvsNeedUpdate = True + + elif len(dvs) > 0: + if max(np.abs(dvs - self.old_dvs)) > 0.0: # 1e-7: + self.old_dvs = inputs["tacs_dvs"].copy() + dvsNeedUpdate = True + + if self.old_xs is None: + self.old_xs = inputs["x_struct0"].copy() + xsNeedUpdate = True + + elif len(xs) > 0: + if max(np.abs(xs - self.old_xs)) > 0.0: # 1e-7: + self.old_xs = inputs["x_struct0"].copy() + xsNeedUpdate = True + + tmp1 = dvsNeedUpdate + tmp2 = xsNeedUpdate + # Perform all reduce to check if any other procs came back True + dvsNeedUpdate = self.comm.allreduce(tmp1) + xsNeedUpdate = self.comm.allreduce(tmp2) + return dvsNeedUpdate, xsNeedUpdate def compute(self, inputs, outputs): self._update_internal(inputs) diff --git a/tacs/pytacs.py b/tacs/pytacs.py index 0f8103125..b2d2078c7 100755 --- a/tacs/pytacs.py +++ b/tacs/pytacs.py @@ -1989,6 +1989,36 @@ def createDVConstraint(self, name, options=None): constr.setNodes(self.Xpts0) return constr + @postinitialize_method + def createPanelLengthConstraint(self, name, options=None): + """Create a new PanelLengthConstraint for enforcing that the panel + length DV values passed to components match the actual panel lengths. + + Parameters + ---------- + name : str + Name to assign constraint. + options : dict + Class-specific options to pass to DVConstraint instance (case-insensitive). + + Returns + ---------- + constraint : PanelLengthConstraint + PanelLengthConstraint object used for calculating constraints. + """ + constr = tacs.constraints.PanelLengthConstraint( + name, + self.assembler, + self.comm, + self.outputViewer, + self.meshLoader, + options, + ) + # Set with original design vars and coordinates, in case they have changed + constr.setDesignVars(self.x0) + constr.setNodes(self.Xpts0) + return constr + @postinitialize_method def createVolumeConstraint(self, name, options=None): """ diff --git a/tests/constitutive_tests/test_blade_sitffened_shell_constitutive.py b/tests/constitutive_tests/test_blade_sitffened_shell_constitutive.py new file mode 100644 index 000000000..918ecf110 --- /dev/null +++ b/tests/constitutive_tests/test_blade_sitffened_shell_constitutive.py @@ -0,0 +1,300 @@ +import unittest + +import numpy as np + +from tacs import TACS, constitutive, elements + +DEG2RAD = np.pi / 180.0 + + +class ConstitutiveTest(unittest.TestCase): + def setUp(self): + # fd/cs step size + if TACS.dtype is complex: + self.dh = 1e-200 + self.rtol = 1e-9 + else: + self.dh = 1e-8 + self.rtol = 1e-3 + self.dtype = TACS.dtype + + # The failure value returned by the model is an aggregate of multiple + # possible failure modes, we will run the failure tests multiple + # times to try and cover strain states that cause each failure mode + self.numFailureTests = 10 + + # Basically, only check relative tolerance + self.atol = self.rtol + self.print_level = 0 + + # Set element index + self.elem_index = 0 + + # Set the variable arrays + self.x = np.ones(3, dtype=self.dtype) + self.pt = np.zeros(3) + + self.panelLength = 2.0 + self.panelLengthNum = 0 + self.stiffenerPitch = 0.2 + self.stiffenerPitchNum = 1 + self.stiffenerHeight = 0.075 + self.stiffenerHeightNum = 2 + self.stiffenerThickness = 1e-2 + self.stiffenerThicknessNum = 3 + self.panelThickness = 1.5e-2 + self.panelThicknessNum = 4 + + self.numPanelPlies = 3 + self.panelPlyAngles = np.array([0.0, 45.0, 90.0], dtype=self.dtype) * DEG2RAD + self.panelPlyFracs = np.random.random(self.numPanelPlies).astype(self.dtype) + self.panelPlyFracs /= np.sum(self.panelPlyFracs) # Make sure ply Fracs sum to 1 + self.panelPlyFracNums = np.arange(5, 5 + self.numPanelPlies, dtype=np.intc) + + self.numStiffenerPlies = 2 + self.stiffenerPlyAngles = np.array([0.0, 60.0], dtype=self.dtype) * DEG2RAD + self.stiffenerPlyFracs = np.random.random(self.numStiffenerPlies).astype( + self.dtype + ) + self.stiffenerPlyFracs /= np.sum( + self.stiffenerPlyFracs + ) # Make sure ply Fracs sum to 1 + self.stiffenerPlyFracNums = np.arange( + 5 + self.numPanelPlies, 5 + self.numStiffenerPlies, dtype=np.intc + ) + + self.dvs = ( + [ + self.panelLength, + self.stiffenerPitch, + self.stiffenerHeight, + self.stiffenerThickness, + self.panelThickness, + ] + + list(self.panelPlyFracs) + + list(self.stiffenerPlyFracs) + ) + self.dvs = np.array(self.dvs, dtype=self.dtype) + + self.flangeFraction = 0.8 + self.kcorr = 5.0 / 6.0 + + # Create the isotropic layup + rho = 2700.0 + specific_heat = 921.096 + E = 70e3 + nu = 0.3 + ys = 270.0 + cte = 24.0e-6 + kappa = 230.0 + iso_prop = constitutive.MaterialProperties( + rho=rho, + specific_heat=specific_heat, + E=E, + nu=nu, + ys=ys, + cte=cte, + kappa=kappa, + ) + iso_ply = constitutive.OrthotropicPly(1e-3, iso_prop) + + # Create the orthotropic layup + rho = 1550.0 + specific_heat = 921.096 + E1 = 54e3 + E2 = 18e3 + nu12 = 0.25 + G12 = 9e3 + G13 = 9e3 + Xt = 2410.0 + Xc = 1040.0 + Yt = 73.0 + Yc = 173.0 + S12 = 71.0 + cte = 24.0e-6 + kappa = 230.0 + ortho_prop = constitutive.MaterialProperties( + rho=rho, + specific_heat=specific_heat, + E1=E1, + E2=E2, + nu12=nu12, + G12=G12, + G13=G13, + G23=G13, + Xt=Xt, + Xc=Xc, + Yt=Yt, + Yc=Yc, + S12=S12, + cte=cte, + kappa=kappa, + ) + ortho_ply = constitutive.OrthotropicPly(1e-3, ortho_prop) + + self.ply_list = [iso_ply, ortho_ply] + + # Seed random number generator in tacs for consistent test results + elements.SeedRandomGenerator(0) + + def get_con(self, ply): + con = constitutive.BladeStiffenedShellConstitutive( + ply, + ply, + self.kcorr, + self.panelLength, + self.panelLengthNum, + self.stiffenerPitch, + self.stiffenerPitchNum, + self.panelThickness, + self.panelThicknessNum, + self.numPanelPlies, + self.panelPlyAngles, + self.panelPlyFracs, + self.panelPlyFracNums, + self.stiffenerHeight, + self.stiffenerHeightNum, + self.stiffenerThickness, + self.stiffenerThicknessNum, + self.numStiffenerPlies, + self.stiffenerPlyAngles, + self.stiffenerPlyFracs, + self.stiffenerPlyFracNums, + self.flangeFraction, + ) + # Set the KS weight really low so that all failure modes make a + # significant contribution to the failure function derivatives + con.setKSWeight(0.1) + return con + + def test_constitutive_density(self): + # Test density dv sensitivity + for ply in self.ply_list: + with self.subTest(ply=ply): + con = self.get_con(ply) + fail = constitutive.TestConstitutiveDensity( + con, + self.elem_index, + self.pt, + self.x, + self.dvs, + self.dh, + self.print_level, + self.atol, + self.rtol, + ) + self.assertFalse(fail) + + # def test_constitutive_specific_heat(self): + # # Test specific heat dv sensitivity + # for ply in self.ply_list: + # with self.subTest(ply=ply): + # con = self.get_con(ply) + # fail = constitutive.TestConstitutiveSpecificHeat( + # con, + # self.elem_index, + # self.pt, + # self.x, + # self.dvs, + # self.dh, + # self.print_level, + # self.atol, + # self.rtol, + # ) + # self.assertFalse(fail) + + # def test_constitutive_heat_flux(self): + # # Test heat flux dv sensitivity + # for ply in self.ply_list: + # with self.subTest(ply=ply): + # con = self.get_con(ply) + # fail = constitutive.TestConstitutiveHeatFlux( + # con, + # self.elem_index, + # self.pt, + # self.x, + # self.dvs, + # self.dh, + # self.print_level, + # self.atol, + # self.rtol, + # ) + # self.assertFalse(fail) + + def test_constitutive_stress(self): + # Test stress dv sensitivity + for ply in self.ply_list: + with self.subTest(ply=ply): + con = self.get_con(ply) + fail = constitutive.TestConstitutiveStress( + con, + self.elem_index, + self.pt, + self.x, + self.dvs, + self.dh, + self.print_level, + self.atol, + self.rtol, + ) + self.assertFalse(fail) + + # def test_constitutive_thermal_strain(self): + # # Test thermal strain dv sensitivity + # for ply in self.ply_list: + # with self.subTest(ply=ply): + # con = self.get_con(ply) + # fail = constitutive.TestConstitutiveThermalStrain( + # con, + # self.elem_index, + # self.pt, + # self.x, + # self.dvs, + # self.dh, + # self.print_level, + # self.atol, + # self.rtol, + # ) + # self.assertFalse(fail) + + def test_constitutive_failure(self): + # Test failure dv sensitivity + for ply in self.ply_list: + with self.subTest(ply=ply): + con = self.get_con(ply) + fail = False + for _ in range(self.numFailureTests): + fail = fail or constitutive.TestConstitutiveFailure( + con, + self.elem_index, + self.pt, + self.x, + self.dvs, + self.dh, + self.print_level, + self.atol, + self.rtol, + ) + self.assertFalse(fail) + + def test_constitutive_failure_strain_sens(self): + for ply in self.ply_list: + with self.subTest(ply=ply): + con = self.get_con(ply) + fail = False + for _ in range(self.numFailureTests): + fail = fail or constitutive.TestConstitutiveFailureStrainSens( + con, + self.elem_index, + self.pt, + self.x, + self.dh, + self.print_level, + self.rtol, + self.atol, + ) + self.assertFalse(fail) + + +if __name__ == "__main__": + unittest.main() diff --git a/tests/element_tests/test_pcm_heat_conduction_2d.py b/tests/element_tests/test_pcm_heat_conduction_2d.py index d8a41f154..7410e9383 100644 --- a/tests/element_tests/test_pcm_heat_conduction_2d.py +++ b/tests/element_tests/test_pcm_heat_conduction_2d.py @@ -16,7 +16,7 @@ def setUp(self): self.rtol = 1e-2 self.atol = np.clip(1e-5 * self.rtol, 1e-8, 1e-14) - self.print_level = 2 + self.print_level = 0 # Set element index self.elem_index = 0 diff --git a/tests/integration_tests/test_shell_blade_stiffened_plate_quad.py b/tests/integration_tests/test_shell_blade_stiffened_plate_quad.py new file mode 100644 index 000000000..fda8da484 --- /dev/null +++ b/tests/integration_tests/test_shell_blade_stiffened_plate_quad.py @@ -0,0 +1,246 @@ +import os + +import numpy as np + +from pytacs_analysis_base_test import PyTACSTestCase +from tacs import pytacs, elements, constitutive, functions + +""" +This case is identical to the shell_plate_quad.py case, except that it uses the BladeStiffenedShell constitutive model +and involves a panel length computation. + +The nominal case is a 1m x 1m flat plate under three load cases: +a 10 kN point force at center, a 100kPa pressure applied to the surface, and a 100G gravity load. The +perimeter of the plate is fixed in all 6 degrees of freedom. The plate comprises +100 CQUAD4 elements and test KSFailure, StructuralMass, CenterOfMass, MomentOfInertia, +and Compliance functions and sensitivities. Finally, a modal analysis is performed +and the eigenvalues tested. +""" + +base_dir = os.path.dirname(os.path.abspath(__file__)) +bdf_file = os.path.join(base_dir, "./input_files/plate.bdf") + +# KS function weight +ksweight = 10.0 + +# Stiffener angle w.r.t. the x-axis +STIFFENER_ANGLE = np.deg2rad(30.0) +TRUE_PANEL_LENGTH = 1.0 / np.cos(STIFFENER_ANGLE) + + +class ProblemTest(PyTACSTestCase.PyTACSTest): + N_PROCS = 2 # this is how many MPI processes to use for this TestCase. + + FUNC_REFS = { + "point_load_Ixx": 1.4591536458333065, + "point_load_Ixy": 3.907985046680551e-14, + "point_load_Ixz": 0.0, + "point_load_Iyy": 1.459153645833294, + "point_load_Iyz": 0.0, + "point_load_Izz": 2.916666666666588, + "point_load_cgx": 0.500000000000004, + "point_load_cgy": 0.500000000000004, + "point_load_cgz": 0.0, + "point_load_compliance": 71.87161795633577, + "point_load_ks_vmfailure": 0.3304517634314118, + "point_load_mass": 17.5, + "pressure_Ixx": 1.4591536458333065, + "pressure_Ixy": 3.907985046680551e-14, + "pressure_Ixz": 0.0, + "pressure_Iyy": 1.459153645833294, + "pressure_Iyz": 0.0, + "pressure_Izz": 2.916666666666588, + "pressure_cgx": 0.500000000000004, + "pressure_cgy": 0.500000000000004, + "pressure_cgz": 0.0, + "pressure_compliance": 377.11604579572935, + "pressure_ks_vmfailure": 0.9085085771277308, + "pressure_mass": 17.5, + "gravity_Ixx": 1.4591536458333065, + "gravity_Ixy": 3.907985046680551e-14, + "gravity_Ixz": 0.0, + "gravity_Iyy": 1.459153645833294, + "gravity_Iyz": 0.0, + "gravity_Izz": 2.916666666666588, + "gravity_cgx": 0.500000000000004, + "gravity_cgy": 0.500000000000004, + "gravity_cgz": 0.0, + "gravity_compliance": 11.114479357783475, + "gravity_ks_vmfailure": 0.0908244150089233, + "gravity_mass": 17.5, + "modal_eigsm.0": 728895.1077101853, + "modal_eigsm.1": 1591857.6791554866, + "modal_eigsm.2": 3808105.1801748895, + "modal_eigsm.3": 5105458.113303573, + "panel_length_con_ALL": [0.0], + } + + def setup_tacs_problems(self, comm): + """ + Setup pytacs object for problems we will be testing. + """ + + # Overwrite default check values + if self.dtype == complex: + self.rtol = 1e-8 + self.atol = 1e-8 + self.dh = 1e-200 + else: + self.rtol = 1e-3 + self.atol = 1e-4 + self.dh = 1e-8 + + # Instantiate FEA Assembler + struct_options = {} + + fea_assembler = pytacs.pyTACS(bdf_file, comm, options=struct_options) + + def elem_call_back( + dv_num, comp_id, comp_descript, elem_descripts, global_dvs, **kwargs + ): + # Material properties + rho = 2500.0 # density kg/m^3 + E = 70e9 # Young's modulus (Pa) + nu = 0.3 # Poisson's ratio + ys = 464.0e6 # yield stress + + # Plate geometry + tPlate = 0.005 # 5 mm + tStiff = tPlate # Stiffener thickness 5 mm + hStiff = 5 * tStiff # Stiffener height + pStiff = 5 * hStiff # Stiffener pitch + lPanel = TRUE_PANEL_LENGTH # Panel length + + # Set up property model + prop = constitutive.MaterialProperties(rho=rho, E=E, nu=nu, ys=ys) + ply = constitutive.OrthotropicPly(1.0, prop) + + # Set up constitutive model + plyAngles = np.zeros(1) + plyFractions = stiffenerPlyFractions = np.ones(1) + + con = constitutive.BladeStiffenedShellConstitutive( + panelPly=ply, + stiffenerPly=ply, + kcorr=5.0 / 6.0, + panelLength=self.dtype(lPanel), + panelLengthNum=dv_num, + stiffenerPitch=self.dtype(pStiff), + stiffenerPitchNum=dv_num + 1, + panelThick=self.dtype(tPlate), + panelThickNum=dv_num + 2, + numPanelPlies=len(plyAngles), + panelPlyAngles=plyAngles.astype(self.dtype), + panelPlyFracs=plyFractions.astype(self.dtype), + panelPlyFracNums=np.array([dv_num + 3], dtype=np.intc), + stiffenerHeight=self.dtype(hStiff), + stiffenerHeightNum=dv_num + 4, + stiffenerThick=self.dtype(tStiff), + stiffenerThickNum=dv_num + 5, + numStiffenerPlies=1, + stiffenerPlyAngles=plyAngles.astype(self.dtype), + stiffenerPlyFracs=plyFractions.astype(self.dtype), + stiffenerPlyFracNums=np.array([dv_num + 6], dtype=np.intc), + ) + + # Set up reference axis along stiffener direction + refAxis = np.array([np.cos(STIFFENER_ANGLE), np.sin(STIFFENER_ANGLE), 0.0]) + transform = elements.ShellRefAxisTransform(refAxis) + + # Set up element + elem = elements.Quad4Shell(transform, con) + return elem + + # Set up constitutive objects and elements + fea_assembler.initialize(elem_call_back) + + tacs_probs = [] + + # Add point force to node 81 (center of plate) + sp = fea_assembler.createStaticProblem(name="point_load") + F = np.array([0.0, 0.0, 1e4, 0.0, 0.0, 0.0]) + sp.addLoadToNodes(81, F, nastranOrdering=True) + tacs_probs.append(sp) + + # Add pressure to entire plate + sp = fea_assembler.createStaticProblem(name="pressure") + P = 100e3 # Pa + compIDs = fea_assembler.selectCompIDs(include="PLATE") + sp.addPressureToComponents(compIDs, P) + tacs_probs.append(sp) + + # Add pressure to entire plate + sp = fea_assembler.createStaticProblem(name="gravity") + g = np.array([0.0, 0.0, -981.0], dtype=self.dtype) + sp.addInertialLoad(g) + tacs_probs.append(sp) + + # Add Functions + for problem in tacs_probs: + problem.addFunction("mass", functions.StructuralMass) + problem.addFunction("ks_vmfailure", functions.KSFailure, ksWeight=ksweight) + problem.addFunction("compliance", functions.Compliance) + problem.addFunction( + "cgx", functions.CenterOfMass, direction=[1.0, 0.0, 0.0] + ) + problem.addFunction( + "cgy", functions.CenterOfMass, direction=[0.0, 1.0, 0.0] + ) + problem.addFunction( + "cgz", functions.CenterOfMass, direction=[0.0, 0.0, 1.0] + ) + problem.addFunction( + "Ixx", + functions.MomentOfInertia, + direction1=[1.0, 0.0, 0.0], + direction2=[1.0, 0.0, 0.0], + aboutCM=True, + ) + problem.addFunction( + "Ixy", + functions.MomentOfInertia, + direction1=[1.0, 0.0, 0.0], + direction2=[0.0, 1.0, 0.0], + aboutCM=True, + ) + problem.addFunction( + "Ixz", + functions.MomentOfInertia, + direction1=[1.0, 0.0, 0.0], + direction2=[0.0, 0.0, 1.0], + aboutCM=True, + ) + problem.addFunction( + "Iyy", + functions.MomentOfInertia, + direction1=[0.0, 1.0, 0.0], + direction2=[0.0, 1.0, 0.0], + aboutCM=True, + ) + problem.addFunction( + "Iyz", + functions.MomentOfInertia, + direction1=[0.0, 0.0, 1.0], + direction2=[0.0, 1.0, 0.0], + aboutCM=True, + ) + problem.addFunction( + "Izz", + functions.MomentOfInertia, + direction1=[0.0, 0.0, 1.0], + direction2=[0.0, 0.0, 1.0], + aboutCM=True, + ) + + # Add modal problem + mp = fea_assembler.createModalProblem("modal", 7e4, 10) + mp.setOption("printLevel", 2) + tacs_probs.append(mp) + + # Create panel length constraint + allCompIDs = fea_assembler.selectCompIDs() + constraint = fea_assembler.createPanelLengthConstraint("panel_length_con") + constraint.addConstraint("ALL", compIDs=allCompIDs) + tacs_probs.append(constraint) + + return tacs_probs, fea_assembler diff --git a/tests/integration_tests/test_shell_plate_partitioned.py b/tests/integration_tests/test_shell_plate_partitioned.py index 299b8e8d8..e0f3a06da 100644 --- a/tests/integration_tests/test_shell_plate_partitioned.py +++ b/tests/integration_tests/test_shell_plate_partitioned.py @@ -6,7 +6,7 @@ from tacs import pytacs, elements, constitutive, functions """" -The nominal case is a 0.5m x 0.5m flat plate under three load cases: +The nominal case is a 0.5m x 0.5m flat plate under three load cases: a 1 MN point distributed force, a 10MPa pressure, and a 1 MPa traction. The perimeter of the plate is fixed in all 6 degrees of freedom. The plate comprises 100 CQUAD4 elements and test KSFailure, KSDisplacement, StructuralMass, and Compliance functions and sensitivities. @@ -93,7 +93,7 @@ def elem_call_back( prop = constitutive.MaterialProperties(rho=rho, E=E, nu=nu, ys=ys) # Set up constitutive model con = constitutive.IsoShellConstitutive(prop, t=tplate, tNum=dv_num) - transform = None + transform = elements.ShellRefAxisTransform(np.array([1.0, 0.5, 0.5])) # Set up element elem = elements.Quad4Shell(transform, con) scale = [100.0]