{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "#### 2D Linear Elasticity: Plate with a hole subjected to axial loading\n", "\n", "This example is heavily borrowed from the [online demo](https://comet-fenics.readthedocs.io/en/latest/demo/elasticity/orthotropic_elasticity.py.html) by J. Bleyer. " ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "from dolfin import *\n", "from mshr import *\n", "%matplotlib inline\n", "L, R = 1., 0.1\n", "N = 40 # mesh density\n", "\n", "domain = Rectangle(Point(0.,0.), Point(L, L)) - Circle(Point(0., 0.), R)\n", "mesh = generate_mesh(domain, N)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[,\n", " ]" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot(mesh)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will provide constitutive relation in terms of the Voigt notation (i.e., second order tensors will be written as vector of their components as discussed in the class Notes.) Let us take the case of __plane strain__. As per this case, we get that\n", "$${\\boldsymbol \\sigma} = {\\mathbf D}{\\boldsymbol \\epsilon},$$\n", "which could be expanded as\n", "$$\n", " \\begin{Bmatrix} \\sigma_{xx} \\\\ \\sigma_{yy} \\\\ \\sigma_{xy}\n", " \\end{Bmatrix} = {E \\over 1-\\nu^2}\\begin{bmatrix} 1 & \\nu& 0\\\\\n", " \\nu & 1 & 0 \\\\ 0 & 0 & {1-\\nu \\over 2} \\end{bmatrix}\\begin{Bmatrix}\n", " \\sigma_{xx} \\\\ \\sigma_{yy} \\\\ \\sigma_{xy}\n", " \\end{Bmatrix}\n", "$$" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "E = 200.e9\n", "nu = 0.3\n", "C = E/(1-nu*nu)*as_matrix([[1, nu, 0],[nu, 1, 0],[0, 0, (1-nu)/2]])" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "def eps(v):\n", " return sym(grad(v))\n", "def strain2voigt(e):\n", " \"\"\"e is a 2nd-order tensor, returns its Voigt vectorial representation\"\"\"\n", " return as_vector([e[0,0],e[1,1],2*e[0,1]])\n", "def voigt2stress(s):\n", " \"\"\"\n", " s is a stress-like vector (no 2 factor on last component)\n", " returns its tensorial representation\n", " \"\"\"\n", " return as_tensor([[s[0],s[2]],[s[2],s[1]]])\n", "def sigma(v):\n", " return voigt2stress(dot(C,strain2voigt(eps(v))))\n" ] }, { "cell_type": "code", "execution_count": 71, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Notation dx[meshfunction] is deprecated. Please use dx(subdomain_data=meshfunction) instead.\n" ] } ], "source": [ "class Top(SubDomain):\n", " def inside(self, x, on_boundary):\n", " return near(x[1],L) and on_boundary\n", "class Left(SubDomain):\n", " def inside(self, x, on_boundary):\n", " return near(x[0],0) and on_boundary\n", "class Bottom(SubDomain):\n", " def inside(self, x, on_boundary):\n", " return near(x[1],0) and on_boundary\n", "\n", "# exterior facets MeshFunction\n", "facets = MeshFunction(\"size_t\", mesh, 1)\n", "facets.set_all(0)\n", "Top().mark(facets, 1)\n", "Left().mark(facets, 2)\n", "Bottom().mark(facets, 3)\n", "ds = Measure('ds')[facets]" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "# Define function space\n", "V = VectorFunctionSpace(mesh, 'Lagrange', 2)\n", "\n", "# Define variational problem\n", "du = TrialFunction(V)\n", "u_ = TestFunction(V)\n", "u = Function(V, name='Displacement')\n", "a = inner(sigma(du), eps(u_))*dx\n", "\n", "# uniform traction on top boundary\n", "T = Constant((0, 1e-3))\n", "l = dot(T, u_)*ds(1)" ] }, { "cell_type": "code", "execution_count": 73, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# symmetry boundary conditions\n", "bc = [DirichletBC(V.sub(0), Constant(0.), facets, 2),\n", " DirichletBC(V.sub(1), Constant(0.), facets, 3)]\n", "\n", "solve(a == l, u, bc)\n", "\n", "import matplotlib.pyplot as plt\n", "p = plot(sigma(u)[1,1]/T[1], mode='color')\n", "plt.colorbar(p)\n", "plt.title(r\"$\\sigma_{yy}$\",fontsize=26)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "A = sigma(u)[1,1]" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Calling FFC just-in-time (JIT) compiler, this may take some time.\n", "Calling FFC just-in-time (JIT) compiler, this may take some time.\n", "Calling FFC just-in-time (JIT) compiler, this may take some time.\n", "Calling FFC just-in-time (JIT) compiler, this may take some time.\n" ] }, { "data": { "text/plain": [ "(Coefficient(FunctionSpace(Mesh(VectorElement(FiniteElement('Lagrange', triangle, 1), dim=2), 7), FiniteElement('Lagrange', triangle, 1)), 45),\n", " Coefficient(FunctionSpace(Mesh(VectorElement(FiniteElement('Lagrange', triangle, 1), dim=2), 7), FiniteElement('Lagrange', triangle, 1)), 49),\n", " Coefficient(FunctionSpace(Mesh(VectorElement(FiniteElement('Lagrange', triangle, 1), dim=2), 7), FiniteElement('Lagrange', triangle, 1)), 53),\n", " Coefficient(FunctionSpace(Mesh(VectorElement(FiniteElement('Lagrange', triangle, 1), dim=2), 7), FiniteElement('Lagrange', triangle, 1)), 57))" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "T = TensorFunctionSpace(mesh, 'CG', 1)\n", "t = project(grad(u), T)\n", "t.split()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.6.7" } }, "nbformat": 4, "nbformat_minor": 2 }