mirror of
https://github.com/JuliaFEM/JuliaFEM.jl.git
synced 2026-09-19 01:48:47 +00:00
Updated shape functions. Let's calculate them.
This commit is contained in:
Jukka Aho
@@ -50,6 +50,27 @@
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"execution_count": 1,
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"metadata": {},
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"output_type": "execute_result"
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},
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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" in depwarn at /Applications/Julia-0.4.0-dev-539c818c4e.app/Contents/Resources/julia/lib/julia/sys.dylib\n",
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" in int32 at deprecated.jl:49\n",
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" in recv at /Users/jukka/.julia/v0.4/ZMQ/src/ZMQ.jl:617\n",
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" in recv_ipython at /Users/jukka/.julia/v0.4/IJulia/src/msg.jl:63\n",
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" in eventloop at /Users/jukka/.julia/v0.4/IJulia/src/IJulia.jl:120\n",
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" in anonymous at task.jl:365\n",
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"while loading /Users/jukka/.julia/v0.4/IJulia/src/kernel.jl, in expression starting on line 35\n",
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"WARNING: int32(x) is deprecated, use Int32(x) instead.\n",
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" in depwarn at /Applications/Julia-0.4.0-dev-539c818c4e.app/Contents/Resources/julia/lib/julia/sys.dylib\n",
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" in int32 at deprecated.jl:49\n",
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" in recv at /Users/jukka/.julia/v0.4/ZMQ/src/ZMQ.jl:617\n",
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" in recv_ipython at /Users/jukka/.julia/v0.4/IJulia/src/msg.jl:63\n",
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" in eventloop at /Users/jukka/.julia/v0.4/IJulia/src/IJulia.jl:120\n",
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" in anonymous at task.jl:365\n",
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"while loading /Users/jukka/.julia/v0.4/IJulia/src/kernel.jl, in expression starting on line 35\n"
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]
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}
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],
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"source": [
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@@ -73,7 +94,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 18,
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"execution_count": 2,
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"metadata": {
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"collapsed": false
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},
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@@ -84,7 +105,7 @@
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"calc_local_matrices! (generic function with 1 method)"
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]
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},
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"execution_count": 18,
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"execution_count": 2,
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"metadata": {},
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"output_type": "execute_result"
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}
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@@ -218,7 +239,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 16,
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"execution_count": 3,
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"metadata": {
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"collapsed": true
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},
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@@ -229,7 +250,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 19,
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"execution_count": 4,
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"metadata": {
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"collapsed": false,
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"scrolled": false
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@@ -246,17 +267,17 @@
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"11-Aug 21:42:03:DEBUG:root:Converged in 6 iterations.\n",
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"11-Aug 21:42:03:DEBUG:root:solution vector: \n",
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"13-Aug 00:37:26:DEBUG:root:Converged in 6 iterations.\n",
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"13-Aug 00:37:26:DEBUG:root:solution vector: \n",
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" [0.0 -0.3991450609547433 -0.07228582695592461 0.0\n",
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" 0.0 -2.1779892317073504 -2.222244754401764 0.0]\n",
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"11-Aug 21:42:03:DEBUG:root:norm of u: 3.1292483947150047\n",
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"11-Aug 21:42:03:DEBUG:root:Converged in 6 iterations.\n",
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"11-Aug 21:42:03:DEBUG:root:solution vector: \n",
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"13-Aug 00:37:26:DEBUG:root:norm of u: 3.1292483947150047\n",
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"13-Aug 00:37:27:DEBUG:root:Converged in 6 iterations.\n",
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"13-Aug 00:37:27:DEBUG:root:solution vector: \n",
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" [0.0 0.7433248532717796 1.048521014723486 0.0\n",
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" 0.0 -2.085766534304891 -1.9606633242166027 0.0]\n",
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"11-Aug 21:42:03:DEBUG:root:norm of u: 3.1292483947150056\n",
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"11-Aug 21:42:03:DEBUG:root:Iteration 1\n"
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"13-Aug 00:37:27:DEBUG:root:norm of u: 3.1292483947150056\n",
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"13-Aug 00:37:27:DEBUG:root:Iteration 1\n"
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]
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},
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{
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@@ -270,15 +291,38 @@
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"11-Aug 21:42:04:DEBUG:root:Norm of du: 0.5992228342549063\n",
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"11-Aug 21:42:04:DEBUG:root:Element displacement: [0.0 -0.02264423092574128 0.022536491965822688 0.0\n",
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"13-Aug 00:37:27:DEBUG:root:Norm of du: 0.5992228342549063\n",
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"13-Aug 00:37:27:DEBUG:root:Element displacement: [0.0 -0.02264423092574128 0.022536491965822688 0.0\n",
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" 0.0 -0.12688379170176511 -0.12679760053383046 0.0]\n",
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"11-Aug 21:42:04:DEBUG:root:Element displacement: [-0.02264423092574128 -0.029998807330416523 0.030242156525002267 0.022536491965822688\n",
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"13-Aug 00:37:27:DEBUG:root:Element displacement: [-0.02264423092574128 -0.029998807330416523 0.030242156525002267 0.022536491965822688\n",
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" -0.12688379170176511 -0.4041002710283739 -0.40446733271991214 -0.12679760053383046]\n",
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"11-Aug 21:42:04:DEBUG:root:solution vector: \n",
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"13-Aug 00:37:27:DEBUG:root:solution vector: \n",
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" [-0.02264423092574128 -0.029998807330416523 0.022536491965822688 0.030242156525002267 0.0 0.0\n",
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" -0.12688379170176511 -0.4041002710283739 -0.12679760053383046 -0.40446733271991214 0.0 0.0]\n",
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"11-Aug 21:42:04:DEBUG:root:norm of u: 0.5992228342549063\n"
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"13-Aug 00:37:27:DEBUG:root:norm of u: 0.5992228342549063\n"
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]
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},
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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":\n",
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" 132.8 0.0 23.6 -3.0 -113.6 … 23.6 3.0 -33.2 15.0\n",
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" 0.0 324.8 3.0 77.6 0.0 -3.0 77.6 15.0 -81.2\n",
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" 23.6 3.0 66.4 -15.0 -33.2 0.0 0.0 0.0 0.0\n",
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" -3.0 77.6 -15.0 162.4 15.0 0.0 0.0 0.0 0.0\n",
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" -113.6 0.0 -33.2 15.0 132.8 -33.2 -15.0 23.6 -3.0\n",
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" 0.0 -317.6 15.0 -81.2 0.0 … -15.0 -81.2 3.0 77.6\n",
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" -33.2 -15.0 -56.8 3.0 23.6 0.0 0.0 0.0 0.0\n",
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" -15.0 -81.2 -3.0 -158.8 3.0 0.0 0.0 0.0 0.0\n",
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" 23.6 -3.0 0.0 0.0 -33.2 66.4 15.0 -56.8 3.0\n",
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" 3.0 77.6 0.0 0.0 -15.0 15.0 162.4 -3.0 -158.8\n",
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" -33.2 15.0 0.0 0.0 23.6 … -56.8 -3.0 66.4 -15.0\n",
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" 15.0 -81.2 0.0 0.0 -3.0 3.0 -158.8 -15.0 162.4\n",
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"K norm = 708.0378644377365\n",
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"du = [-0.02264423092574128 -0.029998807330416523 0.022536491965822688 0.030242156525002267 0.0 0.0\n",
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" -0.12688379170176511 -0.4041002710283739 -0.12679760053383046 -0.40446733271991214 0.0 0.0]\n",
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"Out of 3 total facts:"
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]
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},
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{
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@@ -287,34 +331,9 @@
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"delayed_handler (generic function with 4 methods)"
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]
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},
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"execution_count": 19,
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"execution_count": 4,
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"metadata": {},
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"output_type": "execute_result"
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},
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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":\n",
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" 132.8 0.0 23.6 -3.0 -113.6 0.0 -33.2 -15.0 23.6 3.0 -33.2 15.0\n",
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" 0.0 324.8 3.0 77.6 0.0 -317.6 -15.0 -81.2 -3.0 77.6 15.0 -81.2\n",
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" 23.6 3.0 66.4 -15.0 -33.2 15.0 -56.8 -3.0 0.0 0.0 0.0 0.0\n",
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" -3.0 77.6 -15.0 162.4 15.0 -81.2 3.0 -158.8 0.0 0.0 0.0 0.0\n",
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" -113.6 0.0 -33.2 15.0 132.8 0.0 23.6 3.0 -33.2 -15.0 23.6 -3.0\n",
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" 0.0 -317.6 15.0 -81.2 0.0 324.8 -3.0 77.6 -15.0 -81.2 3.0 77.6\n",
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" -33.2 -15.0 -56.8 3.0 23.6 -3.0 66.4 15.0 0.0 0.0 0.0 0.0\n",
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" -15.0 -81.2 -3.0 -158.8 3.0 77.6 15.0 162.4 0.0 0.0 0.0 0.0\n",
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" 23.6 -3.0 0.0 0.0 -33.2 -15.0 0.0 0.0 66.4 15.0 -56.8 3.0\n",
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" 3.0 77.6 0.0 0.0 -15.0 -81.2 0.0 0.0 15.0 162.4 -3.0 -158.8\n",
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" -33.2 15.0 0.0 0.0 23.6 3.0 0.0 0.0 -56.8 -3.0 66.4 -15.0\n",
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" 15.0 -81.2 0.0 0.0 -3.0 77.6 0.0 0.0 3.0 -158.8 -15.0 162.4\n",
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"K norm = 708.0378644377365\n",
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"du = [-0.02264423092574128 -0.029998807330416523 0.022536491965822688 0.030242156525002267 0.0 0.0\n",
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" -0.12688379170176511 -0.4041002710283739 -0.12679760053383046 -0.40446733271991214 0.0 0.0]\n",
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"Out of 3 total facts:\n",
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" Verified: 2\n",
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" Pending: 1\n"
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]
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}
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],
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"source": [
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@@ -473,7 +492,17 @@
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"\n",
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" Verified: 2\n",
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" Pending: 1\n"
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]
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}
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],
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"source": [
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"type Assembly\n",
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" # LHS\n",
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@@ -533,28 +562,30 @@
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" -(1+xi[2])/4.0 (1-xi[1])/4.0]\n",
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" return basis, dbasis\n",
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" elseif (nnodes == 10) & (ndim == 3)\n",
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" basis(xi) = [(xi[1] + xi[2] + xi[3] - 1)*(2*xi[1] + 2*xi[2] + 2*xi[3] - 1)\n",
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" -xi[1]*(-2*xi[1] + 1)\n",
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" -xi[2]*(-2*xi[2] + 1)\n",
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" -xi[3]*(-2*xi[3] + 1)\n",
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" 4*xi[1]*(-xi[1] - xi[2] - xi[3] + 1)\n",
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" 4*xi[1]*xi[2]\n",
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" 4*xi[2]*(-xi[1] - xi[2] - xi[3] + 1)\n",
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" 4*xi[1]*xi[3]\n",
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" 4*xi[2]*xi[3]\n",
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" 4*xi[3]*(-xi[1] - xi[2] - xi[3] + 1)]\n",
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"\n",
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" basis(xi) = [\n",
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" (xi[1] + xi[2] + xi[3] - 1)*(2*xi[1] + 2*xi[2] + 2*xi[3] - 1)\n",
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" xi[1]*(2*xi[1] - 1)\n",
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" xi[2]*(2*xi[2] - 1)\n",
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" xi[3]*(2*xi[3] - 1)\n",
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" -4*xi[1]*(xi[1] + xi[2] + xi[3] - 1)\n",
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" 4*xi[1]*xi[2]\n",
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" -4*xi[2]*(xi[1] + xi[2] + xi[3] - 1)\n",
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" -4*xi[3]*(xi[1] + xi[2] + xi[3] - 1)\n",
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" 4*xi[1]*xi[3]\n",
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" 4*xi[2]*xi[3]\n",
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" ]\n",
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" dbasis(xi) = [\n",
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" 4*xi[1] + 4*xi[2] + 4*xi[3] - 3 4*xi[1] + 4*xi[2] + 4*xi[3] - 3 4*xi[1] + 4*xi[2] + 4*xi[3] - 3\n",
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" 4*xi[1] - 1 0 0\n",
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" 0 4*xi[2] - 1 0\n",
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" 0 0 4*xi[3] - 1\n",
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" -8*xi[1] - 4*xi[2] - 4*xi[3] + 4 -4*xi[1] -4*xi[1]\n",
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" 4*xi[2] 4*xi[1] 0\n",
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" -4*xi[2] -4*xi[1] - 8*xi[2] - 4*xi[3] + 4 -4*xi[2]\n",
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" 4*xi[3] 0 4*xi[1]\n",
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" 0 4*xi[3] 4*xi[2]\n",
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" -4*xi[3] -4*xi[3] -4*xi[1] - 4*xi[2] - 8*xi[3] + 4]\n",
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" 4*xi[1] + 4*xi[2] + 4*xi[3] - 3 4*xi[1] + 4*xi[2] + 4*xi[3] - 3 4*xi[1] + 4*xi[2] + 4*xi[3] - 3\n",
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" 4*xi[1] - 1 0 0\n",
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" 0 4*xi[2] - 1 0\n",
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" 0 0 4*xi[3] - 1\n",
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" -4*(2*xi[1] + xi[2] + xi[3] - 1) -4*xi[1] -4*xi[1]\n",
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" 4*xi[2] 4*xi[1] 0\n",
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" -4*xi[2] -4*(xi[1] + 2*xi[2] + xi[3] - 1) -4*xi[2]\n",
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" -4*xi[3] -4*xi[3] -4*(xi[1] + xi[2] + 2*xi[3] - 1)\n",
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" 4*xi[3] 0 4*xi[1]\n",
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" 0 4*xi[3] 4*xi[2]\n",
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" ]\n",
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" return basis, dbasis\n",
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" end\n",
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" throw(\"Unknown function space, ndim=$ndim, nnodes=$nnodes\")\n",
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@@ -668,28 +699,28 @@
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"11-Aug 21:39:42:DEBUG:root:Adding nodes to array\n",
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"11-Aug 21:39:42:DEBUG:root:Creating elements\n",
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"11-Aug 21:39:42:DEBUG:root:Starting iteration 1\n",
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"11-Aug 21:39:42:DEBUG:root:Assembling\n",
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"11-Aug 21:39:42:DEBUG:root:Solution norm = 3.090022136728999\n",
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"11-Aug 21:39:42:DEBUG:root:Starting iteration 2\n",
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"11-Aug 21:39:42:DEBUG:root:Assembling\n",
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"11-Aug 21:39:43:DEBUG:root:Solution norm = 0.32121316021535135\n",
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"11-Aug 21:39:43:DEBUG:root:Starting iteration 3\n",
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"11-Aug 21:39:43:DEBUG:root:Assembling\n",
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"11-Aug 21:39:43:DEBUG:root:Solution norm = 0.040431781939994194\n",
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"11-Aug 21:39:43:DEBUG:root:Starting iteration 4\n",
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"11-Aug 21:39:43:DEBUG:root:Assembling\n",
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"11-Aug 21:39:43:DEBUG:root:Solution norm = 0.0009291101052124042\n",
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"11-Aug 21:39:43:DEBUG:root:Starting iteration 5\n",
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"11-Aug 21:39:43:DEBUG:root:Assembling\n",
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"11-Aug 21:39:43:DEBUG:root:Solution norm = 1.5638899022213175e-7\n",
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"11-Aug 21:39:43:DEBUG:root:Starting iteration 6\n",
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"11-Aug 21:39:43:DEBUG:root:Assembling\n",
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"11-Aug 21:39:43:DEBUG:root:Solution norm = 1.0118539067290854e-14\n",
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"11-Aug 21:39:43:DEBUG:root:Converged in 6 iterations.\n",
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"11-Aug 21:39:43:DEBUG:root:Displacement of element = \n",
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"13-Aug 00:37:30:DEBUG:root:Adding nodes to array\n",
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"13-Aug 00:37:30:DEBUG:root:Creating elements\n",
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"13-Aug 00:37:30:DEBUG:root:Starting iteration 1\n",
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"13-Aug 00:37:30:DEBUG:root:Assembling\n",
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"13-Aug 00:37:30:DEBUG:root:Solution norm = 3.090022136728999\n",
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"13-Aug 00:37:30:DEBUG:root:Starting iteration 2\n",
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"13-Aug 00:37:30:DEBUG:root:Assembling\n",
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"13-Aug 00:37:30:DEBUG:root:Solution norm = 0.32121316021535135\n",
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"13-Aug 00:37:30:DEBUG:root:Starting iteration 3\n",
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"13-Aug 00:37:30:DEBUG:root:Assembling\n",
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"13-Aug 00:37:30:DEBUG:root:Solution norm = 0.040431781939994194\n",
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"13-Aug 00:37:30:DEBUG:root:Starting iteration 4\n",
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"13-Aug 00:37:30:DEBUG:root:Assembling\n",
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"13-Aug 00:37:30:DEBUG:root:Solution norm = 0.0009291101052124042\n",
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"13-Aug 00:37:30:DEBUG:root:Starting iteration 5\n",
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"13-Aug 00:37:30:DEBUG:root:Assembling\n",
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"13-Aug 00:37:30:DEBUG:root:Solution norm = 1.5638899022213175e-7\n",
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"13-Aug 00:37:30:DEBUG:root:Starting iteration 6\n",
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"13-Aug 00:37:30:DEBUG:root:Assembling\n",
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"13-Aug 00:37:30:DEBUG:root:Solution norm = 1.0118539067290854e-14\n",
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"13-Aug 00:37:30:DEBUG:root:Converged in 6 iterations.\n",
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"13-Aug 00:37:30:DEBUG:root:Displacement of element = \n",
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"[-0.39914506095474334 -0.0722858269559246 0.0 0.0\n",
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" -2.1779892317073504 -2.2222447544017645 0.0 0.0]\n"
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]
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@@ -813,48 +844,48 @@
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"name": "stderr",
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"output_type": "stream",
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"text": [
|
||||
"11-Aug 21:39:49:DEBUG:root:Creating elements\n",
|
||||
"11-Aug 21:39:49:INFO:root:create_ldof2gdofmap: dofs per node: 2\n",
|
||||
"11-Aug 21:39:49:DEBUG:root:Dict(4=>[7,8],2=>[3,4],3=>[5,6],5=>[9,10],6=>[11,12],1=>[1,2])\n",
|
||||
"11-Aug 21:39:50:INFO:root:solve!: dofs per node: 2\n",
|
||||
"11-Aug 21:39:50:DEBUG:root:Problem size = 12\n",
|
||||
"11-Aug 21:39:50:DEBUG:root:Starting iteration 1\n",
|
||||
"11-Aug 21:39:50:DEBUG:root:Assembling\n",
|
||||
"11-Aug 21:39:50:DEBUG:root:Adding Dirichlet boundary conditions using Lagrange multipliers\n",
|
||||
"11-Aug 21:39:50:DEBUG:root:Added 5 Lagrange multipliers to model\n",
|
||||
"11-Aug 21:39:50:DEBUG:root:Adding Neumann boundary conditions\n",
|
||||
"11-Aug 21:39:50:DEBUG:root:Solving system of equations. Total size = 16\n",
|
||||
"11-Aug 21:39:51:DEBUG:root:Solution norm du = 0.6015838690633517\n",
|
||||
"11-Aug 21:39:51:DEBUG:root:Starting iteration 2\n",
|
||||
"11-Aug 21:39:51:DEBUG:root:Assembling\n",
|
||||
"11-Aug 21:39:51:DEBUG:root:Adding Dirichlet boundary conditions using Lagrange multipliers\n",
|
||||
"11-Aug 21:39:51:DEBUG:root:Added 5 Lagrange multipliers to model\n",
|
||||
"11-Aug 21:39:51:DEBUG:root:Adding Neumann boundary conditions\n",
|
||||
"11-Aug 21:39:51:DEBUG:root:Solving system of equations. Total size = 16\n",
|
||||
"11-Aug 21:39:51:DEBUG:root:Solution norm du = 0.013420417380980414\n",
|
||||
"11-Aug 21:39:51:DEBUG:root:Starting iteration 3\n",
|
||||
"11-Aug 21:39:51:DEBUG:root:Assembling\n",
|
||||
"11-Aug 21:39:51:DEBUG:root:Adding Dirichlet boundary conditions using Lagrange multipliers\n",
|
||||
"11-Aug 21:39:51:DEBUG:root:Added 5 Lagrange multipliers to model\n",
|
||||
"11-Aug 21:39:51:DEBUG:root:Adding Neumann boundary conditions\n",
|
||||
"11-Aug 21:39:51:DEBUG:root:Solving system of equations. Total size = 16\n",
|
||||
"11-Aug 21:39:51:DEBUG:root:Solution norm du = 0.00032202957936854873\n",
|
||||
"11-Aug 21:39:51:DEBUG:root:Starting iteration 4\n",
|
||||
"11-Aug 21:39:51:DEBUG:root:Assembling\n",
|
||||
"11-Aug 21:39:51:DEBUG:root:Adding Dirichlet boundary conditions using Lagrange multipliers\n",
|
||||
"11-Aug 21:39:51:DEBUG:root:Added 5 Lagrange multipliers to model\n",
|
||||
"11-Aug 21:39:51:DEBUG:root:Adding Neumann boundary conditions\n",
|
||||
"11-Aug 21:39:51:DEBUG:root:Solving system of equations. Total size = 16\n",
|
||||
"11-Aug 21:39:51:DEBUG:root:Solution norm du = 9.906677094801476e-8\n",
|
||||
"11-Aug 21:39:51:DEBUG:root:Starting iteration 5\n",
|
||||
"11-Aug 21:39:51:DEBUG:root:Assembling\n",
|
||||
"11-Aug 21:39:51:DEBUG:root:Adding Dirichlet boundary conditions using Lagrange multipliers\n",
|
||||
"11-Aug 21:39:51:DEBUG:root:Added 5 Lagrange multipliers to model\n",
|
||||
"11-Aug 21:39:51:DEBUG:root:Adding Neumann boundary conditions\n",
|
||||
"11-Aug 21:39:51:DEBUG:root:Solving system of equations. Total size = 16\n",
|
||||
"11-Aug 21:39:51:DEBUG:root:Solution norm du = 5.027624635820698e-15\n",
|
||||
"11-Aug 21:39:51:DEBUG:root:Converged in 5 iterations.\n",
|
||||
"11-Aug 21:39:51:DEBUG:root:Displacement of element = \n",
|
||||
"13-Aug 00:37:31:DEBUG:root:Creating elements\n",
|
||||
"13-Aug 00:37:31:INFO:root:create_ldof2gdofmap: dofs per node: 2\n",
|
||||
"13-Aug 00:37:31:DEBUG:root:Dict(4=>[7,8],2=>[3,4],3=>[5,6],5=>[9,10],6=>[11,12],1=>[1,2])\n",
|
||||
"13-Aug 00:37:32:INFO:root:solve!: dofs per node: 2\n",
|
||||
"13-Aug 00:37:32:DEBUG:root:Problem size = 12\n",
|
||||
"13-Aug 00:37:32:DEBUG:root:Starting iteration 1\n",
|
||||
"13-Aug 00:37:32:DEBUG:root:Assembling\n",
|
||||
"13-Aug 00:37:32:DEBUG:root:Adding Dirichlet boundary conditions using Lagrange multipliers\n",
|
||||
"13-Aug 00:37:32:DEBUG:root:Added 5 Lagrange multipliers to model\n",
|
||||
"13-Aug 00:37:32:DEBUG:root:Adding Neumann boundary conditions\n",
|
||||
"13-Aug 00:37:32:DEBUG:root:Solving system of equations. Total size = 16\n",
|
||||
"13-Aug 00:37:32:DEBUG:root:Solution norm du = 0.6015838690633517\n",
|
||||
"13-Aug 00:37:32:DEBUG:root:Starting iteration 2\n",
|
||||
"13-Aug 00:37:32:DEBUG:root:Assembling\n",
|
||||
"13-Aug 00:37:32:DEBUG:root:Adding Dirichlet boundary conditions using Lagrange multipliers\n",
|
||||
"13-Aug 00:37:32:DEBUG:root:Added 5 Lagrange multipliers to model\n",
|
||||
"13-Aug 00:37:32:DEBUG:root:Adding Neumann boundary conditions\n",
|
||||
"13-Aug 00:37:32:DEBUG:root:Solving system of equations. Total size = 16\n",
|
||||
"13-Aug 00:37:32:DEBUG:root:Solution norm du = 0.013420417380980414\n",
|
||||
"13-Aug 00:37:33:DEBUG:root:Starting iteration 3\n",
|
||||
"13-Aug 00:37:33:DEBUG:root:Assembling\n",
|
||||
"13-Aug 00:37:33:DEBUG:root:Adding Dirichlet boundary conditions using Lagrange multipliers\n",
|
||||
"13-Aug 00:37:33:DEBUG:root:Added 5 Lagrange multipliers to model\n",
|
||||
"13-Aug 00:37:33:DEBUG:root:Adding Neumann boundary conditions\n",
|
||||
"13-Aug 00:37:33:DEBUG:root:Solving system of equations. Total size = 16\n",
|
||||
"13-Aug 00:37:33:DEBUG:root:Solution norm du = 0.00032202957936854873\n",
|
||||
"13-Aug 00:37:33:DEBUG:root:Starting iteration 4\n",
|
||||
"13-Aug 00:37:33:DEBUG:root:Assembling\n",
|
||||
"13-Aug 00:37:33:DEBUG:root:Adding Dirichlet boundary conditions using Lagrange multipliers\n",
|
||||
"13-Aug 00:37:33:DEBUG:root:Added 5 Lagrange multipliers to model\n",
|
||||
"13-Aug 00:37:33:DEBUG:root:Adding Neumann boundary conditions\n",
|
||||
"13-Aug 00:37:33:DEBUG:root:Solving system of equations. Total size = 16\n",
|
||||
"13-Aug 00:37:33:DEBUG:root:Solution norm du = 9.906677094801476e-8\n",
|
||||
"13-Aug 00:37:33:DEBUG:root:Starting iteration 5\n",
|
||||
"13-Aug 00:37:33:DEBUG:root:Assembling\n",
|
||||
"13-Aug 00:37:33:DEBUG:root:Adding Dirichlet boundary conditions using Lagrange multipliers\n",
|
||||
"13-Aug 00:37:33:DEBUG:root:Added 5 Lagrange multipliers to model\n",
|
||||
"13-Aug 00:37:33:DEBUG:root:Adding Neumann boundary conditions\n",
|
||||
"13-Aug 00:37:33:DEBUG:root:Solving system of equations. Total size = 16\n",
|
||||
"13-Aug 00:37:33:DEBUG:root:Solution norm du = 5.027624635820698e-15\n",
|
||||
"13-Aug 00:37:33:DEBUG:root:Converged in 5 iterations.\n",
|
||||
"13-Aug 00:37:33:DEBUG:root:Displacement of element = \n",
|
||||
"[-0.02442313597467864 -0.039356000063335075 0.021097993207232584 0.020877031423993653\n",
|
||||
" -0.12673626841485705 -0.40433021969759375 -0.40656320177872923 -0.1275776940913048]\n"
|
||||
]
|
||||
@@ -1105,7 +1136,7 @@
|
||||
"\n",
|
||||
"WARNING: deprecated syntax \"{a=>b, ...}\" at /Users/jukka/.julia/v0.4/JuliaFEM/src/abaqus_reader.jl:32.\n",
|
||||
"Use \"Dict{Any,Any}(a=>b, ...)\" instead.\n",
|
||||
"11-Aug 21:40:01:INFO:root:Registered handlers: Any[\"ELEMENT\",\"NODE\",\"NSET\"]\n",
|
||||
"13-Aug 00:37:37: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",
|
||||
@@ -1124,8 +1155,8 @@
|
||||
" in eventloop at /Users/jukka/.julia/v0.4/IJulia/src/IJulia.jl:123\n",
|
||||
" in anonymous at task.jl:365\n",
|
||||
"while loading In[13], in expression starting on line 3\n",
|
||||
"11-Aug 21:40:01:DEBUG:root:Found NODE section\n",
|
||||
"11-Aug 21:40:01:DEBUG:root:Found ELEMENT section\n",
|
||||
"13-Aug 00:37:38:DEBUG:root:Found NODE section\n",
|
||||
"13-Aug 00:37:38: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",
|
||||
@@ -1138,14 +1169,14 @@
|
||||
" in eventloop at /Users/jukka/.julia/v0.4/IJulia/src/IJulia.jl:123\n",
|
||||
" in anonymous at task.jl:365\n",
|
||||
"while loading In[13], in expression starting on line 3\n",
|
||||
"11-Aug 21:40:03:DEBUG:root:120 elements found\n",
|
||||
"11-Aug 21:40:03:INFO:root:Creating ELSET Body1\n",
|
||||
"11-Aug 21:40:03:DEBUG:root:Found NSET section\n",
|
||||
"11-Aug 21:40:03:DEBUG:root:Creating node set SUPPORT\n",
|
||||
"11-Aug 21:40:03:DEBUG:root:Found NSET section\n",
|
||||
"11-Aug 21:40:03:DEBUG:root:Creating node set LOAD\n",
|
||||
"11-Aug 21:40:03:DEBUG:root:Found NSET section\n",
|
||||
"11-Aug 21:40:03:DEBUG:root:Creating node set TOP\n"
|
||||
"13-Aug 00:37:39:DEBUG:root:120 elements found\n",
|
||||
"13-Aug 00:37:40:INFO:root:Creating ELSET Body1\n",
|
||||
"13-Aug 00:37:40:DEBUG:root:Found NSET section\n",
|
||||
"13-Aug 00:37:40:DEBUG:root:Creating node set SUPPORT\n",
|
||||
"13-Aug 00:37:40:DEBUG:root:Found NSET section\n",
|
||||
"13-Aug 00:37:40:DEBUG:root:Creating node set LOAD\n",
|
||||
"13-Aug 00:37:40:DEBUG:root:Found NSET section\n",
|
||||
"13-Aug 00:37:40:DEBUG:root:Creating node set TOP\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -1173,7 +1204,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 34,
|
||||
"execution_count": 14,
|
||||
"metadata": {
|
||||
"collapsed": false,
|
||||
"scrolled": false
|
||||
@@ -1183,47 +1214,47 @@
|
||||
"name": "stderr",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"11-Aug 22:15:29:DEBUG:root:Creating elements\n",
|
||||
"11-Aug 22:15:29:INFO:root:create_ldof2gdofmap: dofs per node: 3\n",
|
||||
"11-Aug 22:15:29:INFO:root:solve!: dofs per node: 3\n",
|
||||
"11-Aug 22:15:29:DEBUG:root:Problem size = 894\n",
|
||||
"11-Aug 22:15:29:DEBUG:root:Starting iteration 1\n",
|
||||
"11-Aug 22:15:29:DEBUG:root:Assembling\n",
|
||||
"11-Aug 22:15:30:DEBUG:root:Adding Dirichlet boundary conditions using Lagrange multipliers\n",
|
||||
"11-Aug 22:15:30:DEBUG:root:Added 28 Lagrange multipliers to model\n",
|
||||
"11-Aug 22:15:30:DEBUG:root:Adding Neumann boundary conditions\n",
|
||||
"11-Aug 22:15:30:DEBUG:root:Solving system of equations. Total size = 921\n",
|
||||
"11-Aug 22:15:30:DEBUG:root:Solution norm du = 72.87727091053921\n",
|
||||
"11-Aug 22:15:30:DEBUG:root:Starting iteration 2\n",
|
||||
"11-Aug 22:15:31:DEBUG:root:Assembling\n",
|
||||
"11-Aug 22:15:32:DEBUG:root:Adding Dirichlet boundary conditions using Lagrange multipliers\n",
|
||||
"11-Aug 22:15:32:DEBUG:root:Added 28 Lagrange multipliers to model\n",
|
||||
"11-Aug 22:15:32:DEBUG:root:Adding Neumann boundary conditions\n",
|
||||
"11-Aug 22:15:32:DEBUG:root:Solving system of equations. Total size = 921\n",
|
||||
"11-Aug 22:15:32:DEBUG:root:Solution norm du = 2.737285770100854\n",
|
||||
"11-Aug 22:15:32:DEBUG:root:Starting iteration 3\n",
|
||||
"11-Aug 22:15:32:DEBUG:root:Assembling\n",
|
||||
"11-Aug 22:15:33:DEBUG:root:Adding Dirichlet boundary conditions using Lagrange multipliers\n",
|
||||
"11-Aug 22:15:34:DEBUG:root:Added 28 Lagrange multipliers to model\n",
|
||||
"11-Aug 22:15:34:DEBUG:root:Adding Neumann boundary conditions\n",
|
||||
"11-Aug 22:15:34:DEBUG:root:Solving system of equations. Total size = 921\n",
|
||||
"11-Aug 22:15:34:DEBUG:root:Solution norm du = 0.07997112801214978\n",
|
||||
"11-Aug 22:15:34:DEBUG:root:Starting iteration 4\n",
|
||||
"11-Aug 22:15:34:DEBUG:root:Assembling\n",
|
||||
"11-Aug 22:15:35:DEBUG:root:Adding Dirichlet boundary conditions using Lagrange multipliers\n",
|
||||
"11-Aug 22:15:35:DEBUG:root:Added 28 Lagrange multipliers to model\n",
|
||||
"11-Aug 22:15:35:DEBUG:root:Adding Neumann boundary conditions\n",
|
||||
"11-Aug 22:15:35:DEBUG:root:Solving system of equations. Total size = 921\n",
|
||||
"11-Aug 22:15:35:DEBUG:root:Solution norm du = 6.406557430235748e-5\n",
|
||||
"11-Aug 22:15:35:DEBUG:root:Starting iteration 5\n",
|
||||
"11-Aug 22:15:35:DEBUG:root:Assembling\n",
|
||||
"11-Aug 22:15:37:DEBUG:root:Adding Dirichlet boundary conditions using Lagrange multipliers\n",
|
||||
"11-Aug 22:15:37:DEBUG:root:Added 28 Lagrange multipliers to model\n",
|
||||
"11-Aug 22:15:37:DEBUG:root:Adding Neumann boundary conditions\n",
|
||||
"11-Aug 22:15:37:DEBUG:root:Solving system of equations. Total size = 921\n",
|
||||
"11-Aug 22:15:37:DEBUG:root:Solution norm du = 6.870072007793185e-11\n",
|
||||
"11-Aug 22:15:37:DEBUG:root:Converged in 5 iterations.\n",
|
||||
"11-Aug 22:15:37:INFO:root:Maximum absolute displacement in y direction: 6.9925206227884695\n"
|
||||
"13-Aug 00:37:41:DEBUG:root:Creating elements\n",
|
||||
"13-Aug 00:37:41:INFO:root:create_ldof2gdofmap: dofs per node: 3\n",
|
||||
"13-Aug 00:37:41:INFO:root:solve!: dofs per node: 3\n",
|
||||
"13-Aug 00:37:41:DEBUG:root:Problem size = 894\n",
|
||||
"13-Aug 00:37:41:DEBUG:root:Starting iteration 1\n",
|
||||
"13-Aug 00:37:41:DEBUG:root:Assembling\n",
|
||||
"13-Aug 00:37:43:DEBUG:root:Adding Dirichlet boundary conditions using Lagrange multipliers\n",
|
||||
"13-Aug 00:37:43:DEBUG:root:Added 28 Lagrange multipliers to model\n",
|
||||
"13-Aug 00:37:43:DEBUG:root:Adding Neumann boundary conditions\n",
|
||||
"13-Aug 00:37:43:DEBUG:root:Solving system of equations. Total size = 921\n",
|
||||
"13-Aug 00:37:43:DEBUG:root:Solution norm du = 54.19642700242575\n",
|
||||
"13-Aug 00:37:43:DEBUG:root:Starting iteration 2\n",
|
||||
"13-Aug 00:37:43:DEBUG:root:Assembling\n",
|
||||
"13-Aug 00:37:45:DEBUG:root:Adding Dirichlet boundary conditions using Lagrange multipliers\n",
|
||||
"13-Aug 00:37:45:DEBUG:root:Added 28 Lagrange multipliers to model\n",
|
||||
"13-Aug 00:37:45:DEBUG:root:Adding Neumann boundary conditions\n",
|
||||
"13-Aug 00:37:45:DEBUG:root:Solving system of equations. Total size = 921\n",
|
||||
"13-Aug 00:37:45:DEBUG:root:Solution norm du = 1.68729144400063\n",
|
||||
"13-Aug 00:37:45:DEBUG:root:Starting iteration 3\n",
|
||||
"13-Aug 00:37:45:DEBUG:root:Assembling\n",
|
||||
"13-Aug 00:37:47:DEBUG:root:Adding Dirichlet boundary conditions using Lagrange multipliers\n",
|
||||
"13-Aug 00:37:47:DEBUG:root:Added 28 Lagrange multipliers to model\n",
|
||||
"13-Aug 00:37:47:DEBUG:root:Adding Neumann boundary conditions\n",
|
||||
"13-Aug 00:37:47:DEBUG:root:Solving system of equations. Total size = 921\n",
|
||||
"13-Aug 00:37:47:DEBUG:root:Solution norm du = 0.04175080278208098\n",
|
||||
"13-Aug 00:37:47:DEBUG:root:Starting iteration 4\n",
|
||||
"13-Aug 00:37:47:DEBUG:root:Assembling\n",
|
||||
"13-Aug 00:37:48:DEBUG:root:Adding Dirichlet boundary conditions using Lagrange multipliers\n",
|
||||
"13-Aug 00:37:48:DEBUG:root:Added 28 Lagrange multipliers to model\n",
|
||||
"13-Aug 00:37:48:DEBUG:root:Adding Neumann boundary conditions\n",
|
||||
"13-Aug 00:37:48:DEBUG:root:Solving system of equations. Total size = 921\n",
|
||||
"13-Aug 00:37:49:DEBUG:root:Solution norm du = 2.4176157836844963e-5\n",
|
||||
"13-Aug 00:37:49:DEBUG:root:Starting iteration 5\n",
|
||||
"13-Aug 00:37:49:DEBUG:root:Assembling\n",
|
||||
"13-Aug 00:37:50:DEBUG:root:Adding Dirichlet boundary conditions using Lagrange multipliers\n",
|
||||
"13-Aug 00:37:50:DEBUG:root:Added 28 Lagrange multipliers to model\n",
|
||||
"13-Aug 00:37:50:DEBUG:root:Adding Neumann boundary conditions\n",
|
||||
"13-Aug 00:37:50:DEBUG:root:Solving system of equations. Total size = 921\n",
|
||||
"13-Aug 00:37:50:DEBUG:root:Solution norm du = 1.4448231751500831e-11\n",
|
||||
"13-Aug 00:37:50:DEBUG:root:Converged in 5 iterations.\n",
|
||||
"13-Aug 00:37:50:INFO:root:Maximum absolute displacement in y direction: 5.245400568184194\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
@@ -1294,7 +1325,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 49,
|
||||
"execution_count": 15,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
@@ -1307,7 +1338,7 @@
|
||||
"</Grid>\n"
|
||||
]
|
||||
},
|
||||
"execution_count": 49,
|
||||
"execution_count": 15,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
@@ -1327,7 +1358,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 50,
|
||||
"execution_count": 16,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
@@ -1336,8 +1367,8 @@
|
||||
"name": "stderr",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"11-Aug 22:38:28:INFO:root:Number of nodes in model: 298\n",
|
||||
"11-Aug 22:38:28:INFO:root:Number of elements in model: 120\n"
|
||||
"13-Aug 00:37:51:INFO:root:Number of nodes in model: 298\n",
|
||||
"13-Aug 00:37:51:INFO:root:Number of elements in model: 120\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
@@ -1365,7 +1396,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 51,
|
||||
"execution_count": 17,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
@@ -1376,7 +1407,7 @@
|
||||
"true"
|
||||
]
|
||||
},
|
||||
"execution_count": 51,
|
||||
"execution_count": 17,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
@@ -1429,7 +1460,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 52,
|
||||
"execution_count": 18,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
@@ -1440,7 +1471,7 @@
|
||||
"10435"
|
||||
]
|
||||
},
|
||||
"execution_count": 52,
|
||||
"execution_count": 18,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
@@ -1458,7 +1489,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 53,
|
||||
"execution_count": 19,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
@@ -1467,35 +1498,35 @@
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"Dict{Any,Any} with 298 entries:\n",
|
||||
" 288 => [-0.21784897897079505,-6.64256844921929,0.18339325827190953]\n",
|
||||
" 11 => [-0.17342410820059667,-6.343125806991628,0.17544367431766225]\n",
|
||||
" 158 => [-0.0007723334905839533,-0.2321904799732306,-0.03883691791045858]\n",
|
||||
" 215 => [-0.03299227384130259,-4.2236276356937505,-0.0017757488281830807]\n",
|
||||
" 134 => [-0.06336705102703495,-3.3332586850719337,0.06555932581531249]\n",
|
||||
" 160 => [0.03205303832663507,-0.536361456950779,-0.07291283371223893]\n",
|
||||
" 29 => [-0.01620524134284992,-0.19455583841608232,-0.03838421619811468]\n",
|
||||
" 131 => [0.04015396763870081,-3.5101776818531523,0.10045744211179368]\n",
|
||||
" 249 => [-0.2491004521409732,-6.570813533283954,0.06837890174506163]\n",
|
||||
" 207 => [0.03974407267311282,-3.48588780058722,0.007971846403163977]\n",
|
||||
" 173 => [-0.04472757590353555,-4.582185697159958,-0.04434348606400347]\n",
|
||||
" 289 => [-0.16494613158592017,-6.360857515886982,0.33435404817411213]\n",
|
||||
" 74 => [-0.03449870789750817,-3.947284664599636,0.0692691027146262]\n",
|
||||
" 201 => [-0.00128347996939122,-3.8527236749372054,0.054216444201382656]\n",
|
||||
" 176 => [-0.004729440266412542,-3.132546258410676,0.0036604388995965386]\n",
|
||||
" 57 => [-0.021453552968802154,-4.134921994863808,0.04888988010136468]\n",
|
||||
" 31 => [-0.005045439296021616,-0.3424143474221696,-0.0365148544462663]\n",
|
||||
" 285 => [-0.19371941654927557,-6.446502168659889,0.18022053743770028]\n",
|
||||
" 70 => [0.006277500845425116,-3.802694347992476,0.06251589929767469]\n",
|
||||
" 33 => [-0.02778798411401373,-0.5091869603980016,0.03538255963543149]\n",
|
||||
" 252 => [-0.11915625386204923,-1.2182594899567352,-0.025975085489623087]\n",
|
||||
" 114 => [-0.14643901527350212,-0.4628626545501056,-0.0057156433415159625]\n",
|
||||
" 165 => [-0.07462160313837857,-4.426674712264929,-0.04391022455570823]\n",
|
||||
" 96 => [0.0541064545893336,-5.057801826440659,-0.01669155772495867]\n",
|
||||
" 133 => [0.01615115174975327,-3.140610327091724,0.028951801068022566]\n",
|
||||
" 288 => [-0.11672879201601734,-4.945796660856531,0.34641446977739976]\n",
|
||||
" 11 => [-0.10351195894967631,-4.756564623966246,0.3419475317395125]\n",
|
||||
" 158 => [-0.004781967238459207,-0.15800625216143013,-0.03641750463465448]\n",
|
||||
" 215 => [-0.009679264390442352,-3.1283115653077243,0.1060066992444004]\n",
|
||||
" 134 => [-0.012153531002752209,-2.568061461984137,0.1358780416251414]\n",
|
||||
" 160 => [0.045841800099574996,-0.3952996715282528,-0.04337647899598485]\n",
|
||||
" 29 => [-0.019610173840903154,-0.13106872577808154,-0.04187494739380516]\n",
|
||||
" 131 => [0.04911611452200464,-2.5861023637514955,0.15290704689462717]\n",
|
||||
" 249 => [-0.18589774363886435,-4.932931637644884,0.27789363131184]\n",
|
||||
" 207 => [0.05588675730587902,-2.563471323701039,0.0669746466494972]\n",
|
||||
" 173 => [-0.017826777186855432,-3.4323824666471117,0.08923268461041232]\n",
|
||||
" 289 => [-0.08168560138254058,-4.782381469728047,0.4566974667444831]\n",
|
||||
" 74 => [-0.013759506382279562,-2.9054222587693794,0.1389413161160111]\n",
|
||||
" 201 => [0.006183182231407451,-2.8511450493652664,0.14659955727801022]\n",
|
||||
" 176 => [0.04229935999959756,-2.349387641785469,0.09405299762367403]\n",
|
||||
" 57 => [-0.0022029054234204426,-3.062804411311773,0.14846103116563106]\n",
|
||||
" 31 => [0.005313697788644969,-0.25237461591643895,-0.030307540603490793]\n",
|
||||
" 285 => [-0.10859185872935265,-4.832314881155342,0.35832378735042353]\n",
|
||||
" 70 => [0.042811232565748765,-2.7950866978216338,0.1421452814276251]\n",
|
||||
" 33 => [-0.016450709743293015,-0.379272230318473,0.027549328283933208]\n",
|
||||
" 252 => [-0.14470395638682446,-0.9284887677850233,0.043594035381458736]\n",
|
||||
" 114 => [-0.14842327883584733,-0.3532980011491899,-0.018641651848308006]\n",
|
||||
" 165 => [-0.04346921888336824,-3.2745129973662452,0.07316785266950793]\n",
|
||||
" 96 => [0.1501458469524447,-3.8471140528652787,0.1489845291162686]\n",
|
||||
" 133 => [0.09045793517058681,-2.3950191788705957,0.12799724500423504]\n",
|
||||
" ⋮ => ⋮"
|
||||
]
|
||||
},
|
||||
"execution_count": 53,
|
||||
"execution_count": 19,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
@@ -1512,7 +1543,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 54,
|
||||
"execution_count": 20,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
@@ -1521,12 +1552,12 @@
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"3x298 Array{Float64,2}:\n",
|
||||
" -0.202475 -0.17437 0.0131267 -0.0340868 -0.0252162 0.0521758 … -0.054781 -0.169903 0.186936 0.102666 -0.0970747 -0.164397 0.0\n",
|
||||
" -1.34204 -1.66404 -3.20587 -3.27673 -3.68732 -3.36789 -4.33822 -1.03943 -2.27466 -1.67467 -2.91213 -2.52353 0.0\n",
|
||||
" 0.0211856 0.0324162 0.00213878 0.0377156 0.0683502 0.030081 -0.00684333 -0.035509 0.304867 0.26033 0.113802 0.152433 0.0"
|
||||
" -0.174259 -0.175081 0.0359566 0.0279021 0.00925611 0.0379208 … -0.0248959 -0.116472 0.191156 0.193018 -0.0153311 -0.123282 0.0\n",
|
||||
" -0.978534 -1.32327 -2.42646 -2.50175 -2.72095 -2.59357 -3.20696 -0.707364 -1.76025 -1.33439 -2.22191 -1.93398 0.0\n",
|
||||
" 0.0535874 0.111758 0.125464 0.115461 0.145374 0.1251 0.0902774 0.00418633 0.368958 0.387435 0.185441 0.230546 0.0"
|
||||
]
|
||||
},
|
||||
"execution_count": 54,
|
||||
"execution_count": 20,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
@@ -1541,7 +1572,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 55,
|
||||
"execution_count": 21,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
@@ -1552,7 +1583,7 @@
|
||||
"true"
|
||||
]
|
||||
},
|
||||
"execution_count": 55,
|
||||
"execution_count": 21,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
@@ -1563,7 +1594,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 56,
|
||||
"execution_count": 22,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
@@ -1571,10 +1602,10 @@
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"28330"
|
||||
"28215"
|
||||
]
|
||||
},
|
||||
"execution_count": 56,
|
||||
"execution_count": 22,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
|
||||
@@ -1,5 +1,16 @@
|
||||
{
|
||||
"cells": [
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"# Shape function and integration points\n",
|
||||
"\n",
|
||||
"Author(s): Jukka Aho\n",
|
||||
"\n",
|
||||
"**Abstract**: Shape functions and element descriptions used in JuliaFEM."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 1,
|
||||
@@ -8,18 +19,325 @@
|
||||
},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"from sympy import *"
|
||||
"from sympy import *\n",
|
||||
"#init_printing()"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 2,
|
||||
"metadata": {
|
||||
"collapsed": true
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"xi = DeferredVector(\"xi\")"
|
||||
"xi = DeferredVector(r\"xi\")"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## 1D shape function"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"### Linear 2-node segment (Lagrange family)\n",
|
||||
"\n",
|
||||
"| | $\\xi_1$ |\n",
|
||||
"| ----- | -------:|\n",
|
||||
"| $N_1$ | -1 |\n",
|
||||
"| $N_2$ | 1 |\n",
|
||||
"\n",
|
||||
"\\begin{equation}\n",
|
||||
" \\left(\\mathbf{P}\\boldsymbol{\\alpha}\\right)\\left(\\xi_1\\right) = \\alpha_{1}+\\alpha_{2}\\xi_{1}\n",
|
||||
"\\end{equation}"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 3,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"(Matrix([\n",
|
||||
" [-xi[1]/2 + 1/2],\n",
|
||||
" [ xi[1]/2 + 1/2]]), Matrix([\n",
|
||||
" [-1/2],\n",
|
||||
" [ 1/2]]))"
|
||||
]
|
||||
},
|
||||
"execution_count": 3,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"A = Matrix([[1, -1], [1, 1]])\n",
|
||||
"P = Matrix([1, xi[1]]).T\n",
|
||||
"N = (P*A.inv()).T\n",
|
||||
"dN = Matrix([N.diff(xi[1]).T]).T\n",
|
||||
"N, dN"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"### Quadratic 3-node segment (Lagrange family)\n",
|
||||
"\n",
|
||||
"| | $\\xi_1$ |\n",
|
||||
"| ----- | -------:|\n",
|
||||
"| $N_1$ | -1 |\n",
|
||||
"| $N_2$ | 1 |\n",
|
||||
"| $N_3$ | 0 |\n",
|
||||
"\n",
|
||||
"\\begin{equation}\n",
|
||||
" \\left(\\mathbf{P}\\boldsymbol{\\alpha}\\right)\\left(\\xi_1\\right) = \\alpha_1 + \\alpha_2\\xi_1 + \\alpha_3\\xi_1^2\n",
|
||||
"\\end{equation}"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 4,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"(Matrix([\n",
|
||||
" [xi[1]**2/2 - xi[1]/2],\n",
|
||||
" [xi[1]**2/2 + xi[1]/2],\n",
|
||||
" [ -xi[1]**2 + 1]]), Matrix([\n",
|
||||
" [xi[1] - 1/2],\n",
|
||||
" [xi[1] + 1/2],\n",
|
||||
" [ -2*xi[1]]]))"
|
||||
]
|
||||
},
|
||||
"execution_count": 4,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"A = Matrix([[1, -1, (-1)**2],\n",
|
||||
" [1, 1, 1**2],\n",
|
||||
" [1, 0, 0**2]])\n",
|
||||
"P = Matrix([1, xi[1], xi[1]**2]).T\n",
|
||||
"N = (P*A.inv()).T\n",
|
||||
"dN = Matrix([N.diff(xi[1]).T]).T\n",
|
||||
"N, dN"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"### P-elements"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## 2D shape functions"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"### Linear triangle\n",
|
||||
"\n",
|
||||
"| | $\\xi_1$ | $\\xi_2$ |\n",
|
||||
"| ----- | -------:| -------:|\n",
|
||||
"| $N_1$ | 0 | 0 |\n",
|
||||
"| $N_2$ | 1 | 0 |\n",
|
||||
"| $N_3$ | 0 | 1 |"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 5,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"(Matrix([\n",
|
||||
" [-xi[1] - xi[2] + 1],\n",
|
||||
" [ xi[1]],\n",
|
||||
" [ xi[2]]]), Matrix([\n",
|
||||
" [-1, -1],\n",
|
||||
" [ 1, 0],\n",
|
||||
" [ 0, 1]]))"
|
||||
]
|
||||
},
|
||||
"execution_count": 5,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"A = Matrix([[1, 0, 0], [1, 1, 0], [1, 0, 1]])\n",
|
||||
"P = Matrix([1, xi[1], xi[2]]).T\n",
|
||||
"N = (P*A.inv()).T\n",
|
||||
"dN = Matrix([N.diff(xi[1]).T, N.diff(xi[2]).T]).T\n",
|
||||
"N, dN"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"### Quadratic triangle\n",
|
||||
"\n",
|
||||
"| | $\\xi_1$ | $\\xi_2$ |\n",
|
||||
"| ----- | -------:| -------:|\n",
|
||||
"| $N_1$ | 0 | 0 |\n",
|
||||
"| $N_2$ | 1 | 0 |\n",
|
||||
"| $N_3$ | 0 | 1 |\n",
|
||||
"| $N_4$ | 1/2 | 0 |\n",
|
||||
"| $N_5$ | 1/2 | 1/2 |\n",
|
||||
"| $N_6$ | 0 | 1/2 |"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 6,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"Matrix([\n",
|
||||
"[1, 0, 0, 0, 0, 0],\n",
|
||||
"[1, 1, 0, 1, 0, 0],\n",
|
||||
"[1, 0, 1, 0, 1, 0],\n",
|
||||
"[1, 1/2, 0, 1/4, 0, 0],\n",
|
||||
"[1, 1/2, 1/2, 1/4, 1/4, 1/4],\n",
|
||||
"[1, 0, 1/2, 0, 1/4, 0]])"
|
||||
]
|
||||
},
|
||||
"execution_count": 6,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"P = Matrix([1, xi[1], xi[2], xi[1]**2, xi[2]**2, xi[1]*xi[2]]).T\n",
|
||||
"A = Matrix([\n",
|
||||
" P.subs({xi[1]: 0, xi[2]: 0}),\n",
|
||||
" P.subs({xi[1]: 1, xi[2]: 0}),\n",
|
||||
" P.subs({xi[1]: 0, xi[2]: 1}),\n",
|
||||
" P.subs({xi[1]: Rational(1,2), xi[2]: 0}),\n",
|
||||
" P.subs({xi[1]: Rational(1,2), xi[2]: Rational(1,2)}),\n",
|
||||
" P.subs({xi[1]: 0, xi[2]: Rational(1,2)}),\n",
|
||||
" ])\n",
|
||||
"A"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 7,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"(Matrix([\n",
|
||||
" [2*xi[1]**2 + 4*xi[1]*xi[2] - 3*xi[1] + 2*xi[2]**2 - 3*xi[2] + 1],\n",
|
||||
" [ 2*xi[1]**2 - xi[1]],\n",
|
||||
" [ 2*xi[2]**2 - xi[2]],\n",
|
||||
" [ -4*xi[1]**2 - 4*xi[1]*xi[2] + 4*xi[1]],\n",
|
||||
" [ 4*xi[1]*xi[2]],\n",
|
||||
" [ -4*xi[1]*xi[2] - 4*xi[2]**2 + 4*xi[2]]]), Matrix([\n",
|
||||
" [ 4*xi[1] + 4*xi[2] - 3, 4*xi[1] + 4*xi[2] - 3],\n",
|
||||
" [ 4*xi[1] - 1, 0],\n",
|
||||
" [ 0, 4*xi[2] - 1],\n",
|
||||
" [-8*xi[1] - 4*xi[2] + 4, -4*xi[1]],\n",
|
||||
" [ 4*xi[2], 4*xi[1]],\n",
|
||||
" [ -4*xi[2], -4*xi[1] - 8*xi[2] + 4]]))"
|
||||
]
|
||||
},
|
||||
"execution_count": 7,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"N = (P*A.inv()).T\n",
|
||||
"dN = Matrix([N.diff(xi[1]).T, N.diff(xi[2]).T]).T\n",
|
||||
"N, dN"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## 3D shape functions"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"### Linear tetrahedra, **tet4**\n",
|
||||
"\n",
|
||||
"| | $\\xi_1$ | $\\xi_2$ | $\\xi_2$ |\n",
|
||||
"| ----- | -------:| -------:| -------:|\n",
|
||||
"| $N_1$ | 0 | 0 | 0 |\n",
|
||||
"| $N_2$ | 1 | 0 | 0 |\n",
|
||||
"| $N_3$ | 0 | 1 | 0 |\n",
|
||||
"| $N_4$ | 0 | 0 | 1 |"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 8,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"Matrix([\n",
|
||||
"[1, 0, 0, 0],\n",
|
||||
"[1, 1, 0, 0],\n",
|
||||
"[1, 0, 1, 0],\n",
|
||||
"[1, 0, 0, 1]])"
|
||||
]
|
||||
},
|
||||
"execution_count": 8,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"P = Matrix([1, xi[1], xi[2], xi[3]]).T\n",
|
||||
"A = Matrix([\n",
|
||||
" P.subs({xi[1]: 0, xi[2]: 0, xi[3]: 0}),\n",
|
||||
" P.subs({xi[1]: 1, xi[2]: 0, xi[3]: 0}),\n",
|
||||
" P.subs({xi[1]: 0, xi[2]: 1, xi[3]: 0}),\n",
|
||||
" P.subs({xi[1]: 0, xi[2]: 0, xi[3]: 1}),\n",
|
||||
" ])\n",
|
||||
"A"
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -32,17 +350,15 @@
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"Matrix([\n",
|
||||
"[ -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]]])"
|
||||
"(Matrix([\n",
|
||||
" [-xi[1] - xi[2] - xi[3] + 1],\n",
|
||||
" [ xi[1]],\n",
|
||||
" [ xi[2]],\n",
|
||||
" [ xi[3]]]), Matrix([\n",
|
||||
" [-1, -1, -1],\n",
|
||||
" [ 1, 0, 0],\n",
|
||||
" [ 0, 1, 0],\n",
|
||||
" [ 0, 0, 1]]))"
|
||||
]
|
||||
},
|
||||
"execution_count": 9,
|
||||
@@ -51,23 +367,29 @@
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"def c3d10():\n",
|
||||
" N1 = 1 - xi[1] - xi[2] - xi[3]\n",
|
||||
" N2 = xi[1]\n",
|
||||
" N3 = xi[2]\n",
|
||||
" N4 = xi[3]\n",
|
||||
" N5 = 4*xi[1]*(1-xi[1]-xi[2]-xi[3])\n",
|
||||
" N6 = 4*xi[1]*xi[2]\n",
|
||||
" N7 = 4*xi[2]*(1-xi[1]-xi[2]-xi[3])\n",
|
||||
" N8 = 4*xi[3]*(1-xi[1]-xi[2]-xi[3])\n",
|
||||
" N9 = 4*xi[1]*xi[3]\n",
|
||||
" N10 = 4*xi[2]*xi[3]\n",
|
||||
" N = Matrix([N1, N2, N3, N4, N5, N6, N7, N8, N9, N10])\n",
|
||||
" dN = Matrix([N.diff(xi[1]).T, N.diff(xi[2]).T, N.diff(xi[3]).T]).T\n",
|
||||
" return N, dN\n",
|
||||
"N = (P*A.inv()).T\n",
|
||||
"dN = Matrix([N.diff(xi[1]).T, N.diff(xi[2]).T, N.diff(xi[3]).T]).T\n",
|
||||
"N, dN"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"### Quadratic Lagrange tetrahedral element, 10 nodes, **tet10**\n",
|
||||
"\n",
|
||||
"N, dN = c3d10()\n",
|
||||
"N"
|
||||
"| | $\\xi_1$ | $\\xi_2$ | $\\xi_2$ |\n",
|
||||
"| ----- | -------:| -------:| -------:|\n",
|
||||
"| $N_1$ | 0 | 0 | 0 |\n",
|
||||
"| $N_2$ | 1 | 0 | 0 |\n",
|
||||
"| $N_3$ | 0 | 1 | 0 |\n",
|
||||
"| $N_4$ | 0 | 0 | 1 |\n",
|
||||
"| $N_5$ | 1/2 | 0 | 0 |\n",
|
||||
"| $N_6$ | 1/2 | 1/2 | 0 |\n",
|
||||
"| $N_7$ | 0 | 1/2 | 0 |\n",
|
||||
"| $N_8$ | 0 | 0 | 1/2 |\n",
|
||||
"| $N_9$ | 1/2 | 0 | 1/2 |\n",
|
||||
"| $N_{10}$ | 0 | 1/2 | 1/2 |"
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -81,16 +403,16 @@
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"Matrix([\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]]])"
|
||||
"[1, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
|
||||
"[1, 1, 0, 0, 1, 0, 0, 0, 0, 0],\n",
|
||||
"[1, 0, 1, 0, 0, 0, 1, 0, 0, 0],\n",
|
||||
"[1, 0, 0, 1, 0, 0, 0, 0, 1, 0],\n",
|
||||
"[1, 1/2, 0, 0, 1/4, 0, 0, 0, 0, 0],\n",
|
||||
"[1, 1/2, 1/2, 0, 1/4, 1/4, 1/4, 0, 0, 0],\n",
|
||||
"[1, 0, 1/2, 0, 0, 0, 1/4, 0, 0, 0],\n",
|
||||
"[1, 0, 0, 1/2, 0, 0, 0, 0, 1/4, 0],\n",
|
||||
"[1, 1/2, 0, 1/2, 1/4, 0, 0, 0, 1/4, 1/4],\n",
|
||||
"[1, 0, 1/2, 1/2, 0, 0, 1/4, 1/4, 1/4, 0]])"
|
||||
]
|
||||
},
|
||||
"execution_count": 10,
|
||||
@@ -99,17 +421,89 @@
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"dN"
|
||||
"P = Matrix([1, xi[1], xi[2], xi[3], xi[1]**2, xi[1]*xi[2], xi[2]**2, xi[2]*xi[3], xi[3]**2, xi[1]*xi[3]]).T\n",
|
||||
"A = Matrix([\n",
|
||||
" P.subs({xi[1]: 0, xi[2]: 0, xi[3]: 0}),\n",
|
||||
" P.subs({xi[1]: 1, xi[2]: 0, xi[3]: 0}),\n",
|
||||
" P.subs({xi[1]: 0, xi[2]: 1, xi[3]: 0}),\n",
|
||||
" P.subs({xi[1]: 0, xi[2]: 0, xi[3]: 1}),\n",
|
||||
"\n",
|
||||
" P.subs({xi[1]: Rational(1,2), xi[2]: 0, xi[3]: 0}),\n",
|
||||
" P.subs({xi[1]: Rational(1,2), xi[2]: Rational(1,2), xi[3]: 0}),\n",
|
||||
" P.subs({xi[1]: 0, xi[2]: Rational(1,2), xi[3]: 0}),\n",
|
||||
"\n",
|
||||
" P.subs({xi[1]: 0, xi[2]: 0, xi[3]: Rational(1,2)}),\n",
|
||||
" P.subs({xi[1]: Rational(1,2), xi[2]: 0, xi[3]: Rational(1,2)}),\n",
|
||||
" P.subs({xi[1]: 0, xi[2]: Rational(1,2), xi[3]: Rational(1,2)}),\n",
|
||||
" ])\n",
|
||||
"A"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"execution_count": 11,
|
||||
"metadata": {
|
||||
"collapsed": true
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [],
|
||||
"source": []
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"Matrix([\n",
|
||||
"[(xi[1] + xi[2] + xi[3] - 1)*(2*xi[1] + 2*xi[2] + 2*xi[3] - 1)],\n",
|
||||
"[ xi[1]*(2*xi[1] - 1)],\n",
|
||||
"[ xi[2]*(2*xi[2] - 1)],\n",
|
||||
"[ xi[3]*(2*xi[3] - 1)],\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]]])"
|
||||
]
|
||||
},
|
||||
"execution_count": 11,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"N = (P*A.inv()).T\n",
|
||||
"dN = Matrix([N.diff(xi[1]).T, N.diff(xi[2]).T, N.diff(xi[3]).T]).T\n",
|
||||
"factor(N)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 12,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"Matrix([\n",
|
||||
"[ 4*xi[1] + 4*xi[2] + 4*xi[3] - 3, 4*xi[1] + 4*xi[2] + 4*xi[3] - 3, 4*xi[1] + 4*xi[2] + 4*xi[3] - 3],\n",
|
||||
"[ 4*xi[1] - 1, 0, 0],\n",
|
||||
"[ 0, 4*xi[2] - 1, 0],\n",
|
||||
"[ 0, 0, 4*xi[3] - 1],\n",
|
||||
"[-4*(2*xi[1] + xi[2] + xi[3] - 1), -4*xi[1], -4*xi[1]],\n",
|
||||
"[ 4*xi[2], 4*xi[1], 0],\n",
|
||||
"[ -4*xi[2], -4*(xi[1] + 2*xi[2] + xi[3] - 1), -4*xi[2]],\n",
|
||||
"[ -4*xi[3], -4*xi[3], -4*(xi[1] + xi[2] + 2*xi[3] - 1)],\n",
|
||||
"[ 4*xi[3], 0, 4*xi[1]],\n",
|
||||
"[ 0, 4*xi[3], 4*xi[2]]])"
|
||||
]
|
||||
},
|
||||
"execution_count": 12,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"factor(dN)"
|
||||
]
|
||||
}
|
||||
],
|
||||
"metadata": {
|
||||
@@ -128,7 +522,7 @@
|
||||
"name": "python",
|
||||
"nbconvert_exporter": "python",
|
||||
"pygments_lexer": "ipython2",
|
||||
"version": "2.7.9"
|
||||
"version": "2.7.10"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
|
||||
Reference in New Issue
Block a user