{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# 2D linear plane strain elasticity\n", "\n", "***\n", "***" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "![caption](fig/guinea_pig.png \"FEniCS course mascot\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## General formulation of the problem\n", "\n", "---\n", "Consider a rectangular domain $\\Omega$ with a circular hole of radius $R$ at its center (see the following figure). The body is fixed at the bottom boundary $\\Gamma_\\mathrm{D}$ and a constant linear loading $\\mathbf{g}$ is applied to the upper edge of the plate $\\Gamma_\\mathrm{N}$. Moreover, the body is under volumetric loading $\\mathbf{b}$. We are interested in the shape deformation of the circle and the concentration of stress around its circumference." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "hide_input": true, "nbsphinx": "hidden" }, "outputs": [], "source": [ "%load_ext tikzmagic" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%%tikz -l patterns -s 900,480\n", "\\input{formulation.tikz};" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Governing equations\n", "This problem is governed by the same boundary value formulation as the first one, let us repeat it:\n", "\\begin{equation}\n", "\\end{equation}\n", "\\begin{align}\n", " &&\n", " -\\mathrm{div}\\boldsymbol{\\sigma}\n", " &=\n", " \\mathbf{b} && \\text{in}\\ \\Omega, \\\\\n", " &&\n", " \\boldsymbol{\\sigma} \\cdot \\mathbf{n}\n", " &=\n", " \\mathbf{g} && \\text{on}\\ \\Gamma_\\mathrm{N}, \\\\\n", " &&\n", " \\mathbf{u}\n", " &=\n", " \\bar{\\mathbf{u}} && \\text{on}\\ \\Gamma_\\mathrm{D},\n", "\\end{align}\n", "where $\\mathbf{b}$ denotes the volumetric loading,\n", "$\\mathbf{g}$ is the surface loading\n", "($\\Gamma_\\mathrm{N}$ beeing the upper part of the boundary where the Neumann boundary condition is prescribed),\n", "and the Dirichlet boundary is applied on the bottom part of the boundary $\\Gamma_\\mathrm{D}$.\n", "The Cauchy stress tensor $\\boldsymbol{\\sigma}$ is given by\n", "\\begin{align*}\n", " \\boldsymbol{\\sigma} =\\lambda\\mathrm{tr}(\\boldsymbol{\\varepsilon})\\mathbf{I} + 2\\mu\\boldsymbol{\\varepsilon}\n", "\\end{align*}\n", "where the strain tensor $\\boldsymbol{\\varepsilon}$ is the symmetric part of the gradient of deformation\n", "$\\nabla\\mathbf{u}$, i.e.\n", "\\begin{equation}\n", " \\boldsymbol{\\varepsilon}=\\frac{1}{2}\\left(\\nabla\\mathbf{u}+ \\left( \\nabla\\mathbf{u} \\right)^{\\top} \\right)\\,,\n", "\\end{equation}\n", "and $\\lambda$ with $\\mu$ are the Lame's parametres that can be expressed in terms of the Young's modulus $E$ and Poisson's ratio $\\nu$\n", "\\begin{equation}\n", " \\lambda = \\frac{E \\nu}{(1 + \\nu) (1 - 2 \\nu)},\n", " \\qquad\n", " \\mu = \\frac{E}{2(1 + \\nu)}\\,.\n", "\\end{equation}\n", "\n", "\n", "\n", "Multiplying the bulk equation by a test function $\\delta\\mathbf{u}$, integrating over the spatial domain $\\Omega$, and integrating by parts yields the weak formulation of our problem: That is, find $\\mathbf{u}$ such that $\\mathbf{u}-\\bar{\\mathbf{u}} \\in \\mathbf{V}$ and\n", "\\begin{equation}\n", " \\int_{\\Omega} \\boldsymbol{\\sigma} : \\delta \\boldsymbol{\\varepsilon} \\, \\mathrm{d}V = \\int_{\\Omega} \\mathbf{b}\\cdot\\delta\\mathbf{u} \\, \\mathrm{d}V + \\int_{\\Gamma_N}\\mathbf{g}\\cdot\\delta\\mathbf{u} \\, \\mathrm{d}S, \\qquad \\forall \\delta\\mathbf{u} \\in \\mathbf{V}\\,,\n", "\\end{equation}\n", "where $\\mathbf{V} = \\{ \\mathbf{v} \\in H^1(\\Omega; \\mathbb{R}^2)| \\mathbf{v} = 0\\ \\text{on}\\ \\Gamma_\\mathrm{D}\\}$ is the function space for both the translated solution $\\mathbf{u}-\\bar{\\mathbf{u}}$ and the test function $\\delta\\mathbf{u}$ and $\\delta\\boldsymbol{\\varepsilon}$ is the symmetric part of the gradient $\\nabla \\delta\\mathbf{u}$ and\n", "\\begin{align}\n", "\\mathbf{u} = \\bar{\\mathbf{u}} & &\\text{on}\\ \\Gamma_\\mathrm{D},\n", "\\\\\n", "\\delta\\mathbf{u} = \\mathbf{0} & &\\text{on}\\ \\Gamma_\\mathrm{D}.\n", "\\end{align}\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ ">**Remark:** The volumetric load is ussualy models effects of a constant gravity field $\\tilde{\\mathbf{b}}$, i.e.\n", "\\begin{equation*}\n", " \\mathbf{b}(\\mathbf{x}) = \\rho(\\mathbf{x}) \\tilde{\\mathbf{b}}\n", "\\end{equation*}\n", "where $\\rho$ is the material's density.\n", "For cork we have\n", "\\begin{equation*}\n", " \\rho = 200 \\text{ kg}\\,\\text{m}^{-3}.\n", "\\end{equation*}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ ">**Remark:** The 2D in-plane stress formulation (accounting for an eventual thickening or narrowing of the material in the 3rd dimension) is analogical to the 3D formulation, with a minor change of the constitutive equation, namely\n", "\\begin{equation}\n", " \\boldsymbol{\\sigma} =\\lambda^*\\mathrm{tr}(\\boldsymbol{\\varepsilon})\\mathbf{I} + 2\\mu\\boldsymbol{\\varepsilon},\n", "\\end{equation}\n", "where\n", "\\begin{equation}\n", " \\lambda^* = \\frac{2\\lambda\\mu}{\\lambda + 2\\mu}.\n", "\\end{equation}\n", "It should be emphasized that this model does not consider buckling of the material." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Implementation\n", "\n", "---\n", "Let us first import the necessary libraries and mark the bottom boundary. For our convenience, we define the stress function $\\boldsymbol{\\sigma}$." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "import fenics as fe\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "\n", "# --------------------\n", "# Functions and classes\n", "# --------------------\n", "# Bottom boundary\n", "def bottom(x, on_boundary):\n", " return (on_boundary and fe.near(x[1], 0.0))\n", "\n", "# Strain function\n", "def epsilon(u):\n", " return fe.sym(fe.grad(u))\n", "\n", "# Stress function\n", "def sigma(u):\n", " return lambda_*fe.div(u)*fe.Identity(2) + 2*mu*epsilon(u)\n", "# lambda is a reserved python keyword, naming convention recommends using a single trailing underscore for such cases" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The function `bottom` defines a set of points that constitute the bottom boundary. Here, `x` represents a vector of spatial coordinates, i.e. `x[0]` is the $x$ coordinate, and `x[1]` is the $y$ coordinate. Function `sigma` defines the stress tensors as a function of the displacement field $\\mathbf{u}$. The UFL language offers implementations of the standart differential and tensor operators, including the divergence `div`, symmetric part of the gradient `sym`, and the identity tensor `Identity`. Here is a short table of other, frequently used operators:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "| FEniCS operators | Description |\n", "| -- | -- |\n", "| `grad(u)` | Gradient of function `u` |\n", "| `div(u)` | Divergence of function `u` |\n", "| `dot(u, v)` | Dot product between `u` and `v` |\n", "| `inner(u, v)` | Inner product between `u` and `v` |\n", "| `Identity(d)` | Identity tensor with dimension `d` |\n", "| `sym(A)` | Symmetric part of `A` |\n", "| `dev(A)` | Deviatoric part of `A` |\n", "| `A.T` | Transposition of the tensor `A`|\n", "\n", "For more, see the [documentation](https://fenicsproject.org/docs/ufl/1.6.0/ufl.html#ufl-package) of UFL (Unified Form Language, the language for expressing the weak forms)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Problem parameters\n", "Note that the vector loading $\\mathbf{b}$ and $\\mathbf{g}$ must be set as a tuple." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "# --------------------\n", "# Parameters\n", "# --------------------\n", "\n", "# Density\n", "rho = fe.Constant(200.0)\n", "\n", "# Young's modulus and Poisson's ratio\n", "E = 0.02e9\n", "nu = 0.0\n", "\n", "# Lame's constants\n", "lambda_ = E*nu/(1+nu)/(1-2*nu)\n", "mu = E/2/(1+nu)\n", "\n", "l_x, l_y = 5.0, 5.0 # Domain dimensions\n", "n_x, n_y = 20, 20 # Number of elements\n", "\n", "# Load\n", "g_z = -2.9575e5\n", "b_z = -10.0\n", "g = fe.Constant((0.0, g_z))\n", "b = fe.Constant((0.0, b_z))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Moreover, we add the plane stress correction." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "model = \"plane_strain\"\n", "\n", "if model == \"plane_stress\":\n", " lambda_ = 2*mu*lambda_/(lambda_+2*mu)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Geometry of the problem\n", "The variable `mesh` points to the `RectangleMesh` object that contains the geometry of a rectangular mesh. We initialize the object specifying the lower left vertex and the upper right vertex (both in the form of the FEniCS object `Point`) followed by two integers denoting the discretization in the $x$ and $y$ direction respectively." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# --------------------\n", "# Geometry\n", "# --------------------\n", "mesh = fe.RectangleMesh(fe.Point(0.0, 0.0), fe.Point(l_x, l_y), n_x, n_y)\n", "\n", "fe.plot(mesh)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "By default, the mesh is discretized with the triangles oriented to the \"right\". The orientation can be changed by adding the string `\"left\"` as the last (optional) argument." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fe.plot(fe.RectangleMesh(fe.Point(0.0, 0.0), fe.Point(l_x, l_y), n_x, n_y, \"left\"))\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Other types of mesh include `\"crossed\"`, which makes each of the `n_x*n_y` squares crossed, and `\"left/right\"`, which changes the orientation of the diagonal from one element to another." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fe.plot(fe.RectangleMesh(fe.Point(0.0, 0.0), fe.Point(l_x, l_y), n_x, n_y, \"crossed\"))\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fe.plot(fe.RectangleMesh(fe.Point(0.0, 0.0), fe.Point(l_x, l_y), n_x, n_y, \"left/right\"))\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Quadrilateral finite elements are also supported by FEniCS; a unit square mesh with quadrilateral discretization can be initialized by the `create()` method of the `UnitSquareMesh` object. We call it with the flag `CellType.Type.quadrilateral`." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "mesh_quad = fe.UnitSquareMesh.create(n_x, n_y, fe.CellType.Type.quadrilateral)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Nevertheless, quadrilateral elements are not fully implemented in FEniCS, e.g., `plot()` is not applicable to these meshes. \n", " \n", "Other than elementary mesh geometries need to be imported into FEniCS. One possibility is to transfer the mesh from an external `.xml` file into the `Mesh` object." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "mesh = fe.Mesh(\"external_mesh.xml\")\n", "fe.plot(mesh)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The external `.xml` file can be generated for example using the [Gmsh](http://gmsh.info/) software. See [this](http://mypages.iit.edu/~asriva13/?page_id=586) short tutorial on generating meshes with Gmsh and importing it into FEniCS, or the full [documentation](http://gmsh.info/doc/texinfo/gmsh.html) if necessary." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Function spaces definition\n", "In this example, the trial and test functions are vector valued, thus we work with a cartesian product of the space $V$ ($V\\times V$ in 2D and $V\\times V\\times V$ in 3D). In FEniCS, the `VectorFunctionSpace` object implements such space." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "# --------------------\n", "# Function spaces\n", "# --------------------\n", "V = fe.VectorFunctionSpace(mesh, \"CG\", 1)\n", "u_tr = fe.TrialFunction(V)\n", "u_test = fe.TestFunction(V)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We use the linear Lagrange elements again. Other types of elements, or approximation spaces, are summarized in the following table (more exhaustive list can be found [here](https://fenicsproject.org/olddocs/dolfin/1.3.0/python/programmers-reference/functions/functionspace/FunctionSpace.html))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "| Keyword | Description |\n", "| -- | -- |\n", "| `\"CG\"` | Lagrange / Continous Galerkin |\n", "| `\"DG\"` | Discountinous Galerkin |\n", "| `\"HER\"` | Hermite elements - only partly supported |\n", "| `\"B\"` | Bubble functions |" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Vector function defined in this space must be defined using a tuple as" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Boundary conditions\n", "\n", "#### Dirichlet boundary conditions\n", "We repeat the initialization of the `DirichletBC` object representing the Dirichlet boundary conditions from the previous problem." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "# --------------------\n", "# Boundary conditions\n", "# --------------------\n", "bc = fe.DirichletBC(V, fe.Constant((0.0, 0.0)), bottom)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Alternatively, we can restrict displacements in one direction only. In such case, the first argument of `DirichletBC` is a subspace `V.sub(1)` of the vector function space `V`. For example the following piece of code prescribes zero displacement in the $y$-direction" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "bc = fe.DirichletBC(V.sub(1), 0.0, bottom)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Neumann boundary conditions\n", "The top boundary can be created by the `SubDomain` object that is able to mark a subset of the domain specified by a given function. The function can be defined as a python class or as the compact `lambda` function." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "top = fe.AutoSubDomain(lambda x: fe.near(x[1], l_y))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We mark the top boundary using the `MeshFunction` object, which is a function evaluated on mesh entities defined by the topological dimension (third argument of the `MeshFunction` initialization). The topological dimension 1 returns function on facets out two dimensional problem." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "# Definition of Neumann boundary condition domain\n", "boundaries = fe.MeshFunction(\"size_t\", mesh, mesh.topology().dim() - 1)\n", "boundaries.set_all(0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, we can label the sub-domain `top` by integer 1." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "top.mark(boundaries, 1)\n", "ds = fe.ds(subdomain_data=boundaries)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Weak formulation\n", "\n", "The weak form is implemented using pre-defined FEniCS operators as follows" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "# --------------------\n", "# Weak form\n", "# --------------------\n", "a = fe.inner(sigma(u_tr), epsilon(u_test))*fe.dx\n", "l = rho*fe.dot(b, u_test)*fe.dx + fe.inner(g, u_test)*ds(1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The objects `dx` and `ds` represent the integration domain. The following table gives the three basic implemented integration domains.\n", "\n", "| FEniCS object | Description |\n", "| -- | -- |\n", "| `dx` | Volume integration |\n", "| `ds` | Outer boundary integration |\n", "| `dS`| Internal boundary integration |\n", "\n", "Moreover, integration domain accepts the optional argument which defines only part of the domain. For example domain `ds(1)` represents part of the outer boundary labelled with 1." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To solve the problem, it is possible to use `fe.solve(a==l, V, bc)` again. However, we introduce another solution that is useful when we need to access the system matrices directly. For this purpose FEniCS provides a function `assembly_system` with three arguments: the left-hand side of the problem, the right-hand side, and the Dirichlet boundary conditions. This function returns assembled matrix `A` of the system and a vector `L` of the right-hand side of the linear system. Assembling is based on the selected type of function space. The variational continuous system is converted into an algebraic system $\\mathbf{A}\\mathbf{x}=\\mathbf{L}$. The regularity of $\\mathbf{A}$ is affected e.g. by the mesh degeneracy, an improper set of boundary conditions, or by the insuffuciency of the numerical integration." ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "# --------------------\n", "# Solver\n", "# --------------------\n", "u = fe.Function(V)\n", "A, L = fe.assemble_system(a, l, bc)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "FEniCS provides an overloaded function `solve` for solving linear systems that returns the vector of displacements $\\mathbf{u}$. Therefore we must use `u.vector()`, which returns the `Vector` object, as the second argument." ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "problem = fe.LinearVariationalProblem(a,l,u,bc)\n", "solver = fe.LinearVariationalSolver(problem)\n", "\n", "fe.solve(A, u.vector(), L)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Post-processing\n", "\n", "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Node values can be accessed by `.vector()` function. It returns an iterable `PETScVector` object which enables us to manipulate with nodal values. Since the displacement is a vector field, it cannot be plotted directly. We must specify scalar subspace for plotting of the results." ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fe.plot(u.sub(0))\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A second option for visualization of the result is to call an optional argument mode with value `\"displacement\"` which plots the displaced domain" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fe.plot(u, mode=\"displacement\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Stress can be plotted similarly but since it is a second-order tensor we must specify a scalar subspace by two indices. For example stress $\\sigma_{yy}$ is obtained by `sigma(u)[1,1]`" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "stress = sigma(u)\n", "fe.plot(stress[1, 1])\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This procedure is sufficient for plotting the components of $\\boldsymbol{\\sigma}$ or for reusing $\\boldsymbol{\\sigma}$ in another weak form. However, if we need to access stress nodal values, we must first project it onto a suitable space. The displacement field \"lives\" in `CG1`, so the corresponding space for stress is the `DG0` space. Moreover, since the stress is a second-order tensor we must define it as the `TensorFunctionSpace` object." ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "V0 = fe.TensorFunctionSpace(mesh, \"DG\", 0)\n", "stress_1 = fe.project(stress, V0)\n", "fe.plot(stress_1[1, 1])\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", " Projection of a function $u\\in V$ onto a space $W$ means solving the following variational problem:\n", " \\begin{equation}\n", " \\text{Find}\\,g\\in W\\,\\text{s.t.}\\,\\int_\\Omega uv\\ \\mathrm{d}V = \\int_\\Omega gv\\ \\mathrm{d}V,\\ \\forall v\\in W.\n", " \\end{equation}\n", "
\n", "\n", "Sometimes, it can be useful tool to convert a function into a non-corresponding space. However, the stress is obtained from the displacement by differentiation of the basis functions and thus the projection can be unnecessarily expensive. More effective way is to make the projection element-wise. Since we want to project the stress on the `DG0` space, where no continuity at nodes is required, we can perform this local projection without loss of generality. It can be done by the following subroutine:" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def local_project(fce, space):\n", " lp_trial, lp_test = fe.TrialFunction(space), fe.TestFunction(space)\n", " lp_a = fe.inner(lp_trial, lp_test)*fe.dx\n", " lp_L = fe.inner(fce, lp_test)*fe.dx\n", " local_solver = fe.LocalSolver(lp_a, lp_L)\n", " local_solver.factorize()\n", " lp_f = fe.Function(space)\n", " local_solver.solve_local_rhs(lp_f)\n", " return lp_f\n", "stress_2 = local_project(stress, V0)\n", "fe.plot(stress_1[1, 1])\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Complete code\n", "\n", "---" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "scrolled": true }, "outputs": [], "source": [ "import fenics as fe\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "\n", "# --------------------\n", "# Functions and classes\n", "# --------------------\n", "def bottom(x, on_boundary):\n", " return (on_boundary and fe.near(x[1], 0.0))\n", "\n", "# Strain function\n", "def epsilon(u):\n", " return fe.sym(fe.grad(u))\n", "\n", "# Stress function\n", "def sigma(u):\n", " return lambda_*fe.div(u)*fe.Identity(2) + 2*mu*epsilon(u)\n", "\n", "\n", "# --------------------\n", "# Parameters\n", "# --------------------\n", "\n", "# Density\n", "rho = fe.Constant(200.0)\n", "\n", "# Young's modulus and Poisson's ratio\n", "E = 0.02e9\n", "nu = 0.0\n", "\n", "# Lame's constants\n", "lambda_ = E*nu/(1+nu)/(1-2*nu)\n", "mu = E/2/(1+nu)\n", "\n", "l_x, l_y = 5.0, 5.0 # Domain dimensions\n", "n_x, n_y = 20, 20 # Number of elements\n", "\n", "# Load\n", "g_z = -2.9575e5\n", "b_z = -10.0\n", "g = fe.Constant((0.0, g_z))\n", "b = fe.Constant((0.0, b_z))\n", "\n", "# Model type\n", "model = \"plane_strain\"\n", "if model == \"plane_stress\":\n", " lambda_ = 2*mu*lambda_/(lambda_+2*mu)\n", "\n", "# --------------------\n", "# Geometry\n", "# --------------------\n", "mesh = fe.Mesh(\"external_mesh.xml\")\n", "\n", "# Definition of Neumann condition domain\n", "boundaries = fe.MeshFunction(\"size_t\", mesh, mesh.topology().dim() - 1)\n", "boundaries.set_all(0)\n", "\n", "top = fe.AutoSubDomain(lambda x: fe.near(x[1], l_y))\n", "\n", "top.mark(boundaries, 1)\n", "ds = fe.ds(subdomain_data=boundaries)\n", "\n", "# --------------------\n", "# Function spaces\n", "# --------------------\n", "V = fe.VectorFunctionSpace(mesh, \"CG\", 1)\n", "u_tr = fe.TrialFunction(V)\n", "u_test = fe.TestFunction(V)\n", "\n", "# --------------------\n", "# Boundary conditions\n", "# --------------------\n", "bc = fe.DirichletBC(V, fe.Constant((0.0, 0.0)), bottom)\n", "\n", "# --------------------\n", "# Weak form\n", "# --------------------\n", "a = fe.inner(sigma(u_tr), epsilon(u_test))*fe.dx\n", "l = rho*fe.dot(b, u_test)*fe.dx + fe.inner(g, u_test)*ds(1)\n", "\n", "# --------------------\n", "# Solver\n", "# --------------------\n", "u = fe.Function(V)\n", "A_ass, L_ass = fe.assemble_system(a, l, bc)\n", "\n", "fe.solve(A_ass, u.vector(), L_ass)\n", "\n", "print(np.amax(u.vector()[:]))\n", "\n", "# --------------------\n", "# Post-process\n", "# --------------------\n", "fe.plot(u, mode=\"displacement\")\n", "plt.show()" ] } ], "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": "3.6.8" } }, "nbformat": 4, "nbformat_minor": 2 }