Performs physics-based model reduction using component mode synthesis (CMS) based on the Craig-Bampton method. Works with 3D and 2D structural FE models created with COMSOL Multiphysics. The formulations are based on "Sub-structure Coupling for Dynamic Analysis" by H.Jensen & C.Papadimitriou.
The code is written in MATLAB and communicates with COMSOL Multiphysics through LiveLink for MATLAB. I developed it for my diploma thesis "Advanced Model Reduction Techniques for Structural Dynamics Simulations" at the System Dynamics Lab (SDLab) of the Department of Mechanical Engineering, University of Thessaly. MATLAB must be started with a COMSOL server (using LiveLink). In the future, a user guide might be written.
Citing this work
- If you use this software in your work, please cite it using the metadata in the citation file.
- If you use the thesis in your work, please cite is as: F. Katsimalis, Advanced Model Reduction Techniques for Structural Dynamics Simulations (thesis). Univeristy of Thessaly, 2021.
User Guide: A user guide is underway and will be released once it is ready 😉
The non-parametrized reduced-order matrices are constant, independent of model parameters. Three variants of reduced-order models (ROMs) can be created based on treatment of the degrees of freedom (DOFs) at the interface between two or more components.
- NIR-ROM: ROM where reduction occurs only on internal DOFs of each component (No Interface Reduction)
- GIR-ROM: ROM where reduction occurs both on internal DOFs of each component and on the DOFs of the interface at the global level (Global Interface Reduction)
- LIR-ROM: ROM where reduction occurs both on internal DOFs of each component and on the DOFs of the interface at the local level (Local Interface Reduction)
The parametrized reduced-order matrices depend on model parameters. Model parametrization is used in structural dynamics simulations. Again, three variants of parametrized ROMs (pROMs) can be created based on treatment of interface DOFs.
- NIR-pROM: pROM where reduction occurs only on internal DOFs of each component (No Interface Reduction)
- GIR-pROM: pROM where reduction occurs both on internal DOFs of each component and on the DOFs of the interface at the global level (Global Interface Reduction)
- LIR-pROM: pROM where reduction occurs both on internal DOFs of each component and on the DOFs of the interface at the local level (Local Interface Reduction)
Some additional features that the user can set through the input file are:
- Consideration of residual normal modes (static correction)
- Meta-model for interpolation of interface modes (using minimum number of support points) without explicitly solving the interface eigenproblem
- Automatic definition of interfaces
- Optimization of number of kept modes to achieve a set accuracy
- Ability to run in parallel on systems with multi-core CPUs
To test the computational efficiency and accuracy of ROMs and pROMs created using this technique, a high-fidelity FE model of a highway bridge consisting of 944,613 DOFs was used.
Non-parametrized CMS was applied to the bridge model. The model is divided in 22 substructures and results in 928,200 internall DOFs (not shared between two or more components) and 16,413 interface DOFs (existing at the interface of two or more components).
Three ROMs were created each one with different treatment of interface modes. The complexity of ROMs in term of number of kept DOFs can be seen below.
| Model | Full FE Model | NIR-ROM | GIR-ROM | LIR-ROM |
|---|---|---|---|---|
| Internal DOF | 928,200 | 46 | 46 | 46 |
| Interface DOF | 16,413 | 16,413 | 36 | 291 |
| Total DOF | 944,613 | 16,459 | 82 | 337 |
Fractional modal frequency error - as a function of eigenmode number - between the predictions of the full-order model and the three ROMs
It can be seen that the maximum error for all ROMs is
Parametrized CMS was applied on the same bridge model. Each sub-structure is associated with one parameter (22 parameters) affecting its modulus of elasticity.
In this application, the pROMs were used to predict the first twenty modal frequencies of the bridge for different values of the 22 parameters affecting the modulus of elasticity of each sub-structure. To test the speed and accuracy of each pROM compared to the full model, 100 runs (predictions) were performed with parameters sampled from a 22-dim Gaussian distribution at every run.
Three pROMs were created with same number of internal and interface DOFs as the corresponding ROMs presented above. Each pROM calculates the interface modes at each step of the simulation using a different method.
- NIR-pROM: No interface reduction is performed, interface modes are explicitly calculated at each step of the simulation
- GIR-pROM/SX1: At each step of the simulation, interface modes are interpolated (not explicitly solved) using a proposed meta-model
- LIR-pROM/C: Interface modes are calculated once for the reference model and kept constant at each step of the simulation
Median fractional modal frequency error (from 100 runs) - as a function of eigenmode number - between the predictions of the full-order model and the three pROMs
It can be seen that the maximum error for all pROMs is
Fractional modal frequency error between the predictions of the full-order model and the three pROMs at each sample point for the first four modal frequencies
The mean computational times (from 100 runs) of a single simulation step for the full-order model and the three pROMs can be seen below.
| Model | Full FE Model | NIR-pROM | GIR-pROM/SX1 | LIR-pROM/C |
|---|---|---|---|---|
| Mean total iteration time [sec] | 116.5 | 32.6 | 6.9 | 0.02 |
| Speedup over the full FE model | 1x | 3.6x | 16.9x | 5825x |
It can be seen that the fastest performing model achieves a speedup of three orders of magnitude over the full-order model.
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International Public License.
