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JuliaFEM.jl/notebooks/2015-06-25-elasticity-solver-example.ipynb
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Jukka Aho 7ba60c8dc7 unfinished notebooks
2015-06-25 23:11:57 +03:00

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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Elasticity solver examples\n",
"\n",
"Author(s): Jukka Aho <jukka.aho@kapsi.fi>"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"\n",
"WARNING: deprecated syntax \"{a=>b, ...}\" at /Users/jukka/.julia/v0.4/JuliaFEM/src/abaqus_reader.jl:29.\n",
"Use \"Dict{Any,Any}(a=>b, ...)\" instead.\n"
]
},
{
"data": {
"text/plain": [
"Logger(root,DEBUG,Pipe(open, 0 bytes waiting),root)"
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# These are internal module functions and not intended to use like this.\n",
"using JuliaFEM.elasticity_solver\n",
"using JuliaFEM.xdmf\n",
"using JuliaFEM.abaqus_reader\n",
"using Logging\n",
"Logging.configure(level=DEBUG)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 2d beam with linear elements"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Converged\n"
]
},
{
"data": {
"text/plain": [
"2x4 Array{Float64,2}:\n",
" 0.0 -0.399145 -0.0722858 0.0\n",
" 0.0 -2.17799 -2.22224 0.0"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function one_elem_fixture()\n",
" X = [0.0 0.0; 10.0 0.0; 10.0 1.0; 0.0 1.0]'\n",
" elmap = [1; 2; 3; 4]\n",
" nodalloads = [0 0; 0 0; 0 -2; 0 0]'\n",
" dirichletbc = [0 0; NaN NaN; NaN NaN; 0 0]'\n",
"\n",
" E = 90\n",
" nu = 0.25\n",
" mu = E/(2*(1+nu))\n",
" la = E*nu/((1+nu)*(1-2*nu))\n",
" la = 2*la*mu/(la + 2*mu)\n",
"\n",
" la = la*ones(1, 4)\n",
" mu = mu*ones(1, 4)\n",
" u = zeros(2, 4)\n",
" du = zeros(2, 4)\n",
"\n",
" N(xi) = [\n",
" (1-xi[1])*(1-xi[2])/4\n",
" (1+xi[1])*(1-xi[2])/4\n",
" (1+xi[1])*(1+xi[2])/4\n",
" (1-xi[1])*(1+xi[2])/4\n",
" ]\n",
"\n",
" dNdξ(ξ) = [-(1-ξ[2])/4.0 -(1-ξ[1])/4.0\n",
" (1-ξ[2])/4.0 -(1+ξ[1])/4.0\n",
" (1+ξ[2])/4.0 (1+ξ[1])/4.0\n",
" -(1+ξ[2])/4.0 (1-ξ[1])/4.0]\n",
"\n",
" ipoints = 1/sqrt(3)*[-1 -1; 1 -1; 1 1; -1 1]\n",
" iweights = [1 1 1 1]\n",
"\n",
" return (X, u, du, elmap, nodalloads, dirichletbc,\n",
" la, mu, N, dNdξ, ipoints, iweights)\n",
"end\n",
"\n",
"(X, u, du, elmap, nodalloads, dirichletbc,\n",
" la, mu, N, dNdξ, ipoints, iweights) = one_elem_fixture()\n",
" \n",
"for i=1:10\n",
" JuliaFEM.elasticity_solver.solve_elasticity_increment!(X, u, du, elmap, nodalloads, dirichletbc,\n",
" la, mu, N, dNdξ, ipoints, iweights)\n",
" u += du\n",
" if norm(du) < 1.0e-9\n",
" println(\"Converged\")\n",
" break\n",
" end\n",
"end\n",
"\n",
"u"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"u3d = [u; 0 0 0 0] # extend to 3d vector field\n",
"X3d = [X; 0 0 0 0]\n",
"elmap2 = [0x5; elmap]'';"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"<?xml version=\"1.0\" encoding=\"utf-8\"?>\n",
"<Xdmf xmlns:xi=\"http://www.w3.org/2001/XInclude\" Version=\"2.1\">\n",
" <Domain>\n",
" <Grid CollectionType=\"Temporal\" GridType=\"Collection\" Name=\"Collection\">\n",
" <Geometry Type=\"None\"/>\n",
" <Topology Dimensions=\"0\" Type=\"NoTopology\"/>\n",
" <Grid Name=\"Grid\">\n",
" <Time Value=\"0\"/>\n",
" <Geometry Type=\"XYZ\">\n",
" <DataItem DataType=\"Float\" Dimensions=\"12\" Format=\"XML\" Precision=\"4\">0.0 0.0 0.0 10.0 0.0 0.0 10.0 1.0 0.0 0.0 1.0 0.0</DataItem>\n",
" </Geometry>\n",
" <Topology Dimensions=\"1\" Type=\"Mixed\">\n",
" <DataItem DataType=\"Int\" Dimensions=\"5\" Format=\"XML\" Precision=\"4\">5 0 1 2 3</DataItem>\n",
" </Topology>\n",
" <Attribute Center=\"Node\" Name=\"Displacement\" Type=\"Vector\">\n",
" <DataItem DataType=\"Float\" Dimensions=\"12\" Format=\"XML\" Precision=\"4\">0.0 0.0 0.0 -0.3991450609547433 -2.17798923170735 0.0 -0.07228582695592455 -2.222244754401764 0.0 0.0 0.0 0.0</DataItem>\n",
" </Attribute>\n",
" </Grid>\n",
" </Grid>\n",
" </Domain>\n",
"</Xdmf>\n",
"\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"WARNING: int(x) is deprecated, use Int(x) instead.\n"
]
},
{
"data": {
"text/plain": [
"1015"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
},
{
"name": "stderr",
"output_type": "stream",
"text": [
" in depwarn at /Applications/Julia-0.4.0-dev-539c818c4e.app/Contents/Resources/julia/lib/julia/sys.dylib\n",
" in int at deprecated.jl:49\n",
" in save_file at /Users/jukka/.julia/v0.4/LightXML/src/document.jl:108\n",
" in xdmf_save_model at /Users/jukka/.julia/v0.4/JuliaFEM/src/xdmf.jl:106\n",
" in include_string at loading.jl:99\n",
" in execute_request_0x535c5df2 at /Users/jukka/.julia/v0.4/IJulia/src/execute_request.jl:157\n",
" in eventloop at /Users/jukka/.julia/v0.4/IJulia/src/IJulia.jl:123\n",
" in anonymous at task.jl:365\n",
"while loading In[4], in expression starting on line 7\n"
]
}
],
"source": [
"xdoc, model = JuliaFEM.xdmf.xdmf_new_model()\n",
"temporal_collection = JuliaFEM.xdmf.xdmf_new_temporal_collection(model)\n",
"grid = JuliaFEM.xdmf.xdmf_new_grid(temporal_collection; time=0)\n",
"JuliaFEM.xdmf.xdmf_new_mesh(grid, X3d, elmap2)\n",
"JuliaFEM.xdmf.xdmf_new_field(grid, \"Displacement\", \"nodes\", u3d)\n",
"print(xdoc)\n",
"JuliaFEM.xdmf.xdmf_save_model(xdoc, \"/tmp/foo.xmf\")"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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"
],
"text/plain": [
"PyObject <IPython.core.display.Image object>"
]
},
"execution_count": 25,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"using PyCall\n",
"@pyimport IPython.display as d\n",
"d.Image(\"/tmp/displacement.png\")"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true
},
"source": [
"## 3d beam with quadratic elements"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"25-Jun 20:00:29:INFO:root:Registered handlers: Any[\"ELEMENT\",\"NODE\",\"NSET\"]\n",
"WARNING: beginswith is deprecated, use startswith instead.\n",
" in depwarn at /Applications/Julia-0.4.0-dev-539c818c4e.app/Contents/Resources/julia/lib/julia/sys.dylib\n",
" in beginswith at deprecated.jl:30\n",
" in parse_abaqus at /Users/jukka/.julia/v0.4/JuliaFEM/src/abaqus_reader.jl:110\n",
" in include_string at loading.jl:99\n",
" in execute_request_0x535c5df2 at /Users/jukka/.julia/v0.4/IJulia/src/execute_request.jl:157\n",
" in eventloop at /Users/jukka/.julia/v0.4/IJulia/src/IJulia.jl:123\n",
" in anonymous at task.jl:365\n",
"while loading In[5], in expression starting on line 2\n",
"WARNING: beginswith is deprecated, use startswith instead.\n",
" in depwarn at /Applications/Julia-0.4.0-dev-539c818c4e.app/Contents/Resources/julia/lib/julia/sys.dylib\n",
" in beginswith at deprecated.jl:30\n",
" in parse_abaqus at /Users/jukka/.julia/v0.4/JuliaFEM/src/abaqus_reader.jl:110\n",
" in include_string at loading.jl:99\n",
" in execute_request_0x535c5df2 at /Users/jukka/.julia/v0.4/IJulia/src/execute_request.jl:157\n",
" in eventloop at /Users/jukka/.julia/v0.4/IJulia/src/IJulia.jl:123\n",
" in anonymous at task.jl:365\n",
"while loading In[5], in expression starting on line 2\n",
"25-Jun 20:00:30:DEBUG:root:Found NODE section\n",
"25-Jun 20:00:30:DEBUG:root:Found ELEMENT section\n",
"WARNING: integer(s::AbstractString) is deprecated, use parse(Int,s) instead.\n",
" in depwarn at /Applications/Julia-0.4.0-dev-539c818c4e.app/Contents/Resources/julia/lib/julia/sys.dylib\n",
" in integer at deprecated.jl:49\n",
" in map at abstractarray.jl:1251\n",
" in parse_element_section at /Users/jukka/.julia/v0.4/JuliaFEM/src/abaqus_reader.jl:56\n",
" in process_section at /Users/jukka/.julia/v0.4/JuliaFEM/src/abaqus_reader.jl:105\n",
" in parse_abaqus at /Users/jukka/.julia/v0.4/JuliaFEM/src/abaqus_reader.jl:114\n",
" in include_string at loading.jl:99\n",
" in execute_request_0x535c5df2 at /Users/jukka/.julia/v0.4/IJulia/src/execute_request.jl:157\n",
" in eventloop at /Users/jukka/.julia/v0.4/IJulia/src/IJulia.jl:123\n",
" in anonymous at task.jl:365\n",
"while loading In[5], in expression starting on line 2\n",
"25-Jun 20:00:31:DEBUG:root:120 elements found\n",
"25-Jun 20:00:31:INFO:root:Creating ELSET Body1\n",
"25-Jun 20:00:31:DEBUG:root:Found NSET section\n",
"25-Jun 20:00:31:DEBUG:root:Creating node set SUPPORT\n",
"25-Jun 20:00:31:DEBUG:root:Found NSET section\n",
"25-Jun 20:00:31:DEBUG:root:Creating node set LOAD\n",
"25-Jun 20:00:31:DEBUG:root:Found NSET section\n",
"25-Jun 20:00:31:DEBUG:root:Creating node set TOP\n"
]
},
{
"data": {
"text/plain": [
"Dict{Any,Any} with 4 entries:\n",
" \"nodes\" => Dict{Any,Any}(288=>[97.5,7.5,10.0],11=>[92.5,2.5,5.0],134=>[45.…\n",
" \"elements\" => Dict{Any,Any}(68=>[71,144,149,198,51,150,57,43,50,214],2=>[204,…\n",
" \"elsets\" => Dict{Any,Any}(\"Body1\"=>[1,2,3,4,5,6,7,8,9,10 … 111,112,113,11…\n",
" \"nsets\" => Dict{Any,Any}(\"LOAD\"=>[82,84,87,179,197,246,249,256,257],\"SUPPO…"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"fid = open(\"../geometry/3d_beam/palkki.inp\")\n",
"model = JuliaFEM.abaqus_reader.parse_abaqus(fid)\n",
"close(fid)\n",
"model"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"10x120 Array{Int64,2}:\n",
" 47 56 91 87 72 72 176 290 … 260 165 101 18 271 72 24\n",
" 173 236 176 45 97 253 173 22 236 181 261 201 211 146 166\n",
" 76 97 139 49 253 158 76 252 202 87 19 71 18 289 196\n",
" 202 111 242 290 289 289 47 49 254 290 254 255 277 29 133\n",
" 156 10 120 53 74 169 144 127 114 95 75 2 100 67 135\n",
" 88 214 266 291 270 118 88 70 … 14 185 104 235 257 180 198\n",
" 16 89 179 40 169 209 44 17 103 68 215 12 212 200 65\n",
" 134 278 199 4 200 200 34 177 147 163 145 121 170 167 92\n",
" 32 187 221 243 210 37 156 240 195 7 117 80 9 48 52\n",
" 132 15 265 177 37 233 16 268 79 4 263 168 208 57 150"
]
},
"execution_count": 30,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"nnodes = length(model[\"nodes\"])\n",
"nelements = length(model[\"elements\"])\n",
"dim = 3\n",
"E = 90\n",
"nu = 0.25\n",
"mu = E/(2*(1+nu))\n",
"la = E*nu/((1+nu)*(1-2*nu))\n",
"\n",
"X = zeros(dim, nnodes)\n",
"u = zeros(dim, nnodes)\n",
"du = zeros(dim, nnodes)\n",
"elmap = zeros(Int, 10, nelements)\n",
"nodalloads = zeros(3, nnodes)\n",
"dirichletbc = NaN*ones(3, nnodes)\n",
"la = la*ones(1, nnodes)\n",
"mu = mu*ones(1, nnodes)\n",
"\n",
"# calculate permutation which maps node ids to matrix indices\n",
"perm = Dict()\n",
"for (j, k) in enumerate(keys(model[\"nodes\"]))\n",
" perm[k] = j\n",
"end\n",
"\n",
"for j=1:nnodes\n",
" X[:,j] = model[\"nodes\"][perm[j]]\n",
"end\n",
"\n",
"for (j, k) in enumerate(keys(model[\"elements\"]))\n",
" node_ids = model[\"elements\"][k]\n",
" for l=1:10\n",
" elmap[l, j] = perm[node_ids[l]]\n",
" end\n",
"end\n",
"\n",
"elmap"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"3x298 Array{Float64,2}:\n",
" NaN NaN NaN NaN NaN NaN NaN NaN … NaN NaN NaN NaN NaN NaN NaN\n",
" NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN\n",
" NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN"
]
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Handle dirichlet boundaries on SUPPORT\n",
"for j in model[\"nsets\"][\"SUPPORT\"]\n",
" dirichletbc[perm[j]] = 0.0\n",
"end\n",
"dirichletbc"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Shape functions and integration points"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"dNtet (generic function with 1 method)"
]
},
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Ntet(xi) = [ -xi[1] - xi[2] - xi[3] + 1\n",
" xi[1]\n",
" xi[2]\n",
" xi[3]\n",
" 4*xi[1]*(-xi[1] - xi[2] - xi[3] + 1)\n",
" 4*xi[1]*xi[2]\n",
" 4*xi[2]*(-xi[1] - xi[2] - xi[3] + 1)\n",
" 4*xi[3]*(-xi[1] - xi[2] - xi[3] + 1)\n",
" 4*xi[1]*xi[3]\n",
" 4*xi[2]*xi[3]]\n",
"\n",
"dNtet(xi) = [\n",
" -1 -1 -1\n",
" 1 0 0\n",
" 0 1 0\n",
" 0 0 1\n",
"-8*xi[1] - 4*xi[2] - 4*xi[3] + 4 -4*xi[1] -4*xi[1]\n",
" 4*xi[2] 4*xi[1] 0\n",
" -4*xi[2] -4*xi[1] - 8*xi[2] - 4*xi[3] + 4 -4*xi[2]\n",
" -4*xi[3] -4*xi[3] -4*xi[1] - 4*xi[2] - 8*xi[3] + 4\n",
" 4*xi[3] 0 4*xi[1]\n",
" 0 4*xi[3] 4*xi[2]]"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"10x3 Array{Int64,2}:\n",
" -1 -1 -1\n",
" 1 0 0\n",
" 0 1 0\n",
" 0 0 1\n",
" -4 0 0\n",
" 4 0 0\n",
" -4 -8 -4\n",
" -4 -4 -8\n",
" 4 0 0\n",
" 0 4 4"
]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"dNtet([0, 1, 1])"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"1x4 Array{Float64,2}:\n",
" 0.0416667 0.0416667 0.0416667 0.0416667"
]
},
"execution_count": 25,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# from code aster documentation\n",
"a = 1/20*(5-sqrt(5))\n",
"b = 1/20*(5+3*sqrt(5))\n",
"ipoints = [a a a; a a b; a b a; b a a]\n",
"iweights = 1/24*[1 1 1 1]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Add point force to LOAD nodeset"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"9-element Array{Int64,1}:\n",
" 82\n",
" 84\n",
" 87\n",
" 179\n",
" 197\n",
" 246\n",
" 249\n",
" 256\n",
" 257"
]
},
"execution_count": 33,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"model[\"nsets\"][\"LOAD\"]"
]
},
{
"cell_type": "code",
"execution_count": 40,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[95.0,10.0,5.0]\n"
]
}
],
"source": [
"nodalloads[3, perm[82]] = -0.0001\n",
"println(model[\"nodes\"][83])"
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"3x298 Array{Float64,2}:\n",
" -76167.8 -73.0493 … 5.19615e7 -43075.8 \n",
" -7.72988e5 6.45188e5 8.51808e7 559158.0 \n",
" 1.26765e6 -74404.1 -2.43735e7 6.01587e5"
]
},
"execution_count": 39,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"u = zeros(dim, nnodes)\n",
"du = zeros(dim, nnodes)\n",
"\n",
"for i=1:10\n",
" JuliaFEM.elasticity_solver.solve_elasticity_increment!(X, u, du, elmap, nodalloads, dirichletbc,\n",
" la, mu, Ntet, dNtet, ipoints, iweights)\n",
" u += du\n",
" if norm(du) < 1.0e-9\n",
" println(\"Converged\")\n",
" break\n",
" end\n",
"end\n",
"u"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Not converging."
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Julia 0.4.0-dev",
"language": "julia",
"name": "julia-0.4"
},
"language_info": {
"name": "julia",
"version": "0.4.0"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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