membrane_tutorial.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from dolfin import *\n",
    "# Curve plot along x = 0 comparing p and w\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from mshr import *\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "domain = Circle(Point(0, 0), 1)\n",
    "mesh = generate_mesh(domain, 64)\n",
    "V = FunctionSpace(mesh, 'P', 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define boundary condition\n",
    "w_D = Constant(0)\n",
    "\n",
    "def boundary(x, on_boundary):\n",
    "    return on_boundary\n",
    "\n",
    "bc = DirichletBC(V, w_D, boundary)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "beta = 8\n",
    "R0 = 0.6\n",
    "p = Expression('4*exp(-pow(beta, 2)*(pow(x[0], 2) + pow(x[1] - R0, 2)))',\n",
    "               degree=1, beta=beta, R0=R0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "p.beta = 12\n",
    "p.R0 = 0.3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "w = TrialFunction(V)\n",
    "v = TestFunction(V)\n",
    "a = dot(grad(w), grad(v))*dx\n",
    "L = p*v*dx\n",
    "\n",
    "w = Function(V)\n",
    "solve(a == L, w, bc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'interactive' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-7-b7f43d27851a>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mw\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtitle\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'Deflection'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mp\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtitle\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'Load'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 5\u001b[0;31m \u001b[0minteractive\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      6\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshow\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'interactive' is not defined"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot solution\n",
    "p = interpolate(p, V)\n",
    "plot(w, title='Deflection')\n",
    "plot(p, title='Load')\n",
    "interactive()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}