beam_buckling-checkpoint.ipynb 50.4 KB
 Jeremy BLEYER committed Jul 05, 2018 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Eulerian buckling of a beam\n", "\n", "In this numerical tour, we will compute the critical buckling load of a straight beam under normal compression, the classical Euler buckling problem. Usually, buckling is an important mode of failure for slender beams so that a standard Euler-Bernoulli beam model is sufficient. However, since FEniCS does not support Hermite elements ensuring $C^1$-formulation for the transverse deflection, implementing such models is not straightforward and requires using advanced DG formulations for instance, see the fenics-shell [implemntation of the Love-Kirchhoff plate model](http://fenics-shells.readthedocs.io/en/latest/demo/kirchhoff-love-clamped/demo_kirchhoff-love-clamped.py.html) or the [FEniCS documented demo on the biharmonic equation](http://fenics.readthedocs.io/projects/dolfin/en/2017.2.0/demos/biharmonic/python/demo_biharmonic.py.html).\n", "\n", "As a result, we will simply formulate the buckling problem using a Timoshenko beam model.\n", "\n", "## Timoshenko beam model formulation\n", "\n", "We first formulate the stiffness bilinear form of the Timoshenko model given by:\n", "\\n", "k((w,\\theta),(\\widehat{w},\\widehat{\\theta}))= \\int_0^L EI \\dfrac{d\\theta}{dx}\\dfrac{d\\widehat{\\theta}}{dx} dx + \\int_0^L \\kappa \\mu S \\left(\\dfrac{dw}{dx}-\\theta\\right)\\left(\\dfrac{d\\widehat{w}}{dx}-\\widehat{\\theta}\\right) dx\n", "\\n", "where $I=bh^3/12$ is the bending inertia for a rectangular beam of width $b$ and height $h$, $S=bh$ the cross-section area, $E$ the material Young modulus and $\\mu$ the shear modulus and $\\kappa=5/6$ the shear correction factor. We will use a $P^2/P^1$ interpolation for the mixed field $(w,\\theta)$. " ] }, { "cell_type": "raw",  Jeremy BLEYER committed Jul 06, 2018 24 25 26  "metadata": { "raw_mimetype": "text/restructuredtext" },  Jeremy BLEYER committed Jul 05, 2018 27 28 29 30 31 32  "source": [ "For issues related to shear-locking and reduced integration formulation, we refer to the :ref:ReissnerMindlinQuads tour." ] }, { "cell_type": "code",  Jeremy BLEYER committed Feb 15, 2019 33  "execution_count": 1,  Jeremy BLEYER committed Jul 05, 2018 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65  "metadata": {}, "outputs": [], "source": [ "from dolfin import *\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "%matplotlib notebook\n", "\n", "L = 10.\n", "thick = Constant(0.03)\n", "width = Constant(0.01)\n", "E = Constant(70e3)\n", "nu = Constant(0.)\n", "\n", "EI = E*width*thick**3/12\n", "GS = E/2/(1+nu)*thick*width\n", "kappa = Constant(5./6.)\n", "\n", "\n", "N = 100\n", "mesh = IntervalMesh(N, 0, L) \n", "\n", "U = FiniteElement(\"CG\", mesh.ufl_cell(), 2)\n", "T = FiniteElement(\"CG\", mesh.ufl_cell(), 1)\n", "V = FunctionSpace(mesh, U*T)\n", "\n", "u_ = TestFunction(V)\n", "du = TrialFunction(V)\n", "(w_, theta_) = split(u_)\n", "(dw, dtheta) = split(du)\n", "\n", "\n",  Jeremy BLEYER committed Jul 13, 2018 66 67  "k_form = EI*inner(grad(theta_), grad(dtheta))*dx + \\\n", " kappa*GS*dot(grad(w_)[0]-theta_, grad(dw)[0]-dtheta)*dx\n",  Jeremy BLEYER committed Jul 05, 2018 68 69 70 71 72  "l_form = Constant(1.)*u_[0]*dx" ] }, { "cell_type": "raw",  Jeremy BLEYER committed Jul 06, 2018 73 74 75  "metadata": { "raw_mimetype": "text/restructuredtext" },  Jeremy BLEYER committed Jul 05, 2018 76  "source": [  Jeremy BLEYER committed Jul 13, 2018 77  "As in the :ref:ModalAnalysis tour, a dummy linear form :code:l_form is used to call the :code:assemble_system function which retains the symmetric structure of the associated matrix when imposing boundary conditions. Here, we will consider clamped conditions on the left side :math:x=0 and simple supports on the right side :math:x=L."  Jeremy BLEYER committed Jul 05, 2018 78 79 80 81  ] }, { "cell_type": "code",  Jeremy BLEYER committed Feb 15, 2019 82  "execution_count": 2,  Jeremy BLEYER committed Jul 05, 2018 83  "metadata": {},  Jeremy BLEYER committed Dec 16, 2018 84  "outputs": [  Jeremy BLEYER committed Feb 15, 2019 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115  { "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" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/usr/lib/python3/dist-packages/ffc/uflacs/analysis/dependencies.py:61: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use arr[tuple(seq)] instead of arr[seq]. In the future this will be interpreted as an array index, arr[np.array(seq)], which will result either in an error or a different result.\n", " active[targets] = 1\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Calling FFC just-in-time (JIT) compiler, this may take some time.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/usr/lib/python3/dist-packages/ffc/uflacs/analysis/dependencies.py:61: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use arr[tuple(seq)] instead of arr[seq]. In the future this will be interpreted as an array index, arr[np.array(seq)], which will result either in an error or a different result.\n", " active[targets] = 1\n" ] },  Jeremy BLEYER committed Dec 16, 2018 116 117 118  { "data": { "text/plain": [  Jeremy BLEYER committed Feb 15, 2019 119 120  "(,\n", " )"  Jeremy BLEYER committed Dec 16, 2018 121 122  ] },  Jeremy BLEYER committed Feb 15, 2019 123  "execution_count": 2,  Jeremy BLEYER committed Dec 16, 2018 124 125 126 127  "metadata": {}, "output_type": "execute_result" } ],  Jeremy BLEYER committed Jul 05, 2018 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163  "source": [ "def both_ends(x, on_boundary):\n", " return on_boundary\n", "def left_end(x, on_boundary):\n", " return near(x[0], 0) and on_boundary\n", "\n", "bc = [DirichletBC(V.sub(0), Constant(0.), both_ends),\n", " DirichletBC(V.sub(1), Constant(0.), left_end)]\n", "\n", "K = PETScMatrix()\n", "assemble_system(k_form, l_form, bc, A_tensor=K)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Construction of the geometric stiffness matrix\n", "\n", "The buckling analysis amounts to solving an eigenvalue problem of the form:\n", "\n", "\\n", "(\\mathbf{K}+\\lambda\\mathbf{K_G})\\mathbf{U} = 0\n", "\\n", "\n", "in which the geometric stiffness matrix $\\mathbf{K_G}$ depends (linearly) on a prestressed state, the amplitude of which is represented by $\\lambda$. The eigenvalue/eigenvector $(\\lambda,\\mathbf{U})$ solving the previous generalized eigenproblem respectively correspond to the critical buckling load and its associated buckling mode. For a beam in which the prestressed state correspond to a purely compression state of intensity $N_0>0$, the geometric stiffness bilinear form is given by:\n", "\n", "\\n", "k_G((w,\\theta),(\\widehat{w},\\widehat{\\theta}))= -\\int_0^L N_0 \\dfrac{dw}{dx}\\dfrac{d\\widehat{w}}{dx} dx\n", "\\n", "\n", "which is assembled below into the KG PETScMatrix (up to the negative sign)." ] }, { "cell_type": "code",  Jeremy BLEYER committed Feb 15, 2019 164  "execution_count": 3,  Jeremy BLEYER committed Jul 05, 2018 165  "metadata": {},  Jeremy BLEYER committed Feb 15, 2019 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182  "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Calling FFC just-in-time (JIT) compiler, this may take some time.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/usr/lib/python3/dist-packages/ffc/uflacs/analysis/dependencies.py:61: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use arr[tuple(seq)] instead of arr[seq]. In the future this will be interpreted as an array index, arr[np.array(seq)], which will result either in an error or a different result.\n", " active[targets] = 1\n" ] } ],  Jeremy BLEYER committed Jul 05, 2018 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204  "source": [ "N0 = Constant(1e-3)\n", "kg_form = N0*dot(grad(w_), grad(dw))*dx\n", "KG = PETScMatrix()\n", "assemble(kg_form, tensor=KG)\n", "for bci in bc:\n", " bci.zero(KG)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that we made use of the zero method of DirichletBC making the rows of the matrix associated with the boundary condition zero. If we used instead the apply method, the rows would have been replaced with a row of zeros with a 1 on the diagonal (as for the stiffness matrix K). As a result, we would have obtained an eigenvalue equal to 1 for each row with a boundary condition which can make more troublesome the computation of eigenvalues if they happen to be close to 1. Replacing with a full row of zeros in KG results in infinite eigenvalues for each boundary condition which is more suitable when looking for the lowest eigenvalues of the buckling problem.\n", "\n", "## Setting and solving the eigenvalue problem\n", "\n", "Up to the negative sign cancelling from the previous definition of KG, we now formulate the generalized eigenvalue problem $\\mathbf{KU}=-\\lambda\\mathbf{K_G U}$ using the SLEPcEigenSolver. The only difference from what has already been discussed in the dynamic modal analysis numerical tour is that buckling eigenvalue problem may be more difficult to solve than modal analysis in certain cases, it is therefore beneficial to prescribe a value of the spectral shift close to the critical buckling load." ] }, { "cell_type": "code",  Jeremy BLEYER committed Feb 15, 2019 205  "execution_count": 5,  Jeremy BLEYER committed Jul 05, 2018 206 207 208 209 210 211  "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [  Jeremy BLEYER committed Feb 15, 2019 212 213 214 215 216  "Computing 3 first eigenvalues...\n", "Critical buckling loads:\n", "Exact: 0.31800 FE: 0.31805 Rel. gap 0.01%%\n", "Exact: 0.93995 FE: 0.94033 Rel. gap 0.04%%\n", "Exact: 1.87267 FE: 1.87415 Rel. gap 0.08%%\n"  Jeremy BLEYER committed Jul 05, 2018 217 218 219  ] }, {  Jeremy BLEYER committed Feb 15, 2019 220 221 222 223 224 225  "name": "stderr", "output_type": "stream", "text": [ "/home/bleyerj/.local/lib/python3.6/site-packages/matplotlib/font_manager.py:1241: UserWarning: findfont: Font family ['serif'] not found. Falling back to DejaVu Sans.\n", " (prop.get_family(), self.defaultFamily[fontext]))\n" ]  Jeremy BLEYER committed Jul 05, 2018 226 227 228  }, { "data": {  Jeremy BLEYER committed Feb 15, 2019 229  "image/png": 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\n",  Jeremy BLEYER committed Jul 05, 2018 230  "text/plain": [  Jeremy BLEYER committed Feb 15, 2019 231  "