mirror of
https://github.com/JuliaFEM/JuliaFEM.jl.git
synced 2026-08-06 04:21:33 +00:00
Jukka Aho
2161 lines
102 KiB
Plaintext
2161 lines
102 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Solving elasticity problems using JuliaFEM\n",
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"\n",
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"Author(s): Jukka Aho\n",
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"\n",
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"**Abstract**: A workflow to solve typical elasticity problem. This document also tries to give some quidelines how to develop JuliaFEM."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"*Design principle 1*: we introduce new ideas using Notebooks."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"*Design principle 2*: we use ``Logging``. Forget ``println``."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"Logger(root,DEBUG,Pipe(open, 0 bytes waiting),root)"
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]
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},
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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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"source": [
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"using Logging\n",
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"Logging.configure(level=DEBUG)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"*Design principle 3*: we write docstrings using [numpy style](https://github.com/numpy/numpy/blob/master/doc/HOWTO_DOCUMENT.rst.txt).\n",
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"\n",
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"*Design principle 4*: we don't use greek characters in code which is implemented to JuliaFEM. In notebooks they are ok.\n",
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"\n",
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"*Design principle 5*: we use 4 space indentation like in Python.\n",
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"\n",
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"First we write some elementary functions to calculate stiffness matrix. Our development direction is \"bottom-up\" to interface."
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]
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},
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{
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"cell_type": "code",
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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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"outputs": [
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{
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"data": {
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"text/plain": [
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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": 2,
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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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"source": [
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"\"\"\"\n",
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"Calculate local tangent stiffness matrix and residual force vector\n",
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"R = T - F for elasticity problem.\n",
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"\n",
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"Parameters\n",
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"----------\n",
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"X : Element coordinates\n",
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"u : Displacement field\n",
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"R : Residual force vector\n",
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"K : Tangent stiffness matrix\n",
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"basis : Basis functions\n",
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"dbasis : Derivative of basis functions\n",
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"lambda : Material parameter\n",
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"mu : Material parameter\n",
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"ipoints : integration points\n",
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"iweights : integration weights\n",
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"\n",
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"Returns\n",
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"-------\n",
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"None\n",
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"\n",
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"Notes\n",
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"-----\n",
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"If material parameters are given in list, they are interpolated to gauss\n",
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"points using shape functions.\n",
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"\n",
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"Examples\n",
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"--------\n",
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"\n",
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"\"\"\"\n",
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"function calc_local_matrices!(X, u, R, K, basis, dbasis, lambda_, mu_, ipoints, iweights)\n",
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" dim, nnodes = size(X)\n",
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" I = eye(dim)\n",
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" R[:,:] = 0.0\n",
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" K[:,:] = 0.0\n",
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"\n",
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" dF = zeros(dim, dim)\n",
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"\n",
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" for m = 1:length(iweights)\n",
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" w = iweights[m]\n",
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" xi = ipoints[m, :]\n",
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" # calculate material parameters\n",
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" lambda = typeof(lambda_) == Float64 ? lambda_ : dot(lambda_, basis(xi))\n",
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" mu = typeof(mu_) == Float64 ? mu_ : dot(mu_, basis(xi))\n",
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" Jt = X*dbasis(xi)\n",
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" detJ = det(Jt)\n",
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" dbasisdX = dbasis(xi)*inv(Jt)\n",
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"\n",
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" gradu = u*dbasisdX\n",
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" F = I + gradu # Deformation gradient\n",
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" E = 1/2*(gradu' + gradu + gradu'*gradu) # Green-Lagrange strain tensor\n",
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" S = lambda*trace(E)*I + 2*mu*E # PK2 stress tensor\n",
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" P = F*S # PK1 stress tensor\n",
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"\n",
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" R[:,:] += w*P*dbasisdX'*detJ\n",
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"\n",
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" for p = 1:nnodes\n",
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" for i = 1:dim\n",
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" dF[:,:] = 0.0\n",
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" dF[i,:] = dbasisdX[p,:]\n",
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" dE = 1/2*(F'*dF + dF'*F)\n",
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" dS = lambda*trace(dE)*I + 2*mu*dE\n",
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" dP = dF*S + F*dS\n",
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" for q = 1:nnodes\n",
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" for j = 1:dim\n",
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" K[dim*(p-1)+i,dim*(q-1)+j] += w*(dP[j,:]*dbasisdX[q,:]')[1]*detJ\n",
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" end\n",
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" end\n",
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" end\n",
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" end\n",
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"\n",
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" end\n",
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"end"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"*Design principle 6*: we test our code. We use FactCheck for testing."
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]
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},
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{
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"cell_type": "code",
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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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"outputs": [],
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"source": [
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"using FactCheck"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {
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"collapsed": false
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},
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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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"test solve one element model\n"
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]
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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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"29-Jul 23:12:24:DEBUG:root:Converged in 6 iterations.\n",
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"29-Jul 23:12:24:DEBUG:root:solution vector: \n",
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" [0.0 -0.39914506095474317 -0.07228582695592449 0.0\n",
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" 0.0 -2.1779892317073504 -2.222244754401764 0.0]\n",
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"29-Jul 23:12:24:DEBUG:root:norm of u: 3.1292483947150043\n",
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"29-Jul 23:12:25:DEBUG:root:Converged in 6 iterations.\n",
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"29-Jul 23:12:25:DEBUG:root:solution vector: \n",
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" [0.0 0.7433248532717793 1.0485210147234858 0.0\n",
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" 0.0 -2.085766534304891 -1.9606633242166027 0.0]\n",
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"29-Jul 23:12:25:DEBUG:root:norm of u: 3.129248394715006\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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"2 facts verified.\n"
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]
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},
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{
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"data": {
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"text/plain": [
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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": 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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"source": [
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"facts(\"test solve one element model\") do\n",
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" X = [0.0 0.0; 10.0 0.0; 10.0 1.0; 0.0 1.0]'\n",
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" F = [0 0; 0 0; 0 -2; 0 0]'\n",
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"\n",
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" # Material properties\n",
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" E = 90\n",
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" nu = 0.25\n",
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" mu = E/(2*(1+nu))\n",
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" la = E*nu/((1+nu)*(1-2*nu))\n",
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" la = 2*la*mu/(la + 2*mu)\n",
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"\n",
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" u = zeros(2, 4)\n",
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" du = zeros(2, 4)\n",
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" R = zeros(2, 4)\n",
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" K = zeros(8, 8)\n",
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"\n",
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" basis(xi) = [\n",
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" (1-xi[1])*(1-xi[2])/4\n",
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" (1+xi[1])*(1-xi[2])/4\n",
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" (1+xi[1])*(1+xi[2])/4\n",
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" (1-xi[1])*(1+xi[2])/4]\n",
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"\n",
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" dbasis(xi) = [-(1-xi[2])/4.0 -(1-xi[1])/4.0\n",
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" (1-xi[2])/4.0 -(1+xi[1])/4.0\n",
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" (1+xi[2])/4.0 (1+xi[1])/4.0\n",
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" -(1+xi[2])/4.0 (1-xi[1])/4.0]\n",
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"\n",
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" ipoints = 1/sqrt(3)*[-1 -1; 1 -1; 1 1; -1 1]\n",
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" iweights = [1, 1, 1, 1]\n",
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" free_dofs = [3, 4, 5, 6]\n",
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"\n",
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" for i=1:10\n",
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" calc_local_matrices!(X, u, R, K, basis, dbasis, la, mu, ipoints, iweights)\n",
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" du[free_dofs] = K[free_dofs, free_dofs] \\ -(R - F)[free_dofs]\n",
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" u += du\n",
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" if norm(du) < 1.0e-9\n",
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" Logging.debug(\"Converged in $i iterations.\")\n",
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" break\n",
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" end\n",
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" end\n",
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"\n",
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" # Tested against Elmer solution\n",
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" Logging.debug(\"solution vector: \\n $u\")\n",
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" @fact u[2, 3] => roughly(-2.222244754401764)\n",
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" norm1 = norm(u)\n",
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" Logging.debug(\"norm of u: $(norm(u))\")\n",
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"\n",
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" # We rotate model a bit and make sure that L2 norm is same\n",
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" phi = 30/180*pi\n",
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" rmat = [\n",
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" cos(phi) -sin(phi)\n",
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" sin(phi) cos(phi)]\n",
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" X = rmat*X\n",
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" F = rmat*F\n",
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" u = zeros(2, 4)\n",
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" for i=1:10\n",
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" calc_local_matrices!(X, u, R, K, basis, dbasis, la, mu, ipoints, iweights)\n",
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" du[free_dofs] = K[free_dofs, free_dofs] \\ -(R - F)[free_dofs]\n",
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" u += du\n",
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" if norm(du) < 1.0e-9\n",
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" Logging.debug(\"Converged in $i iterations.\")\n",
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" break\n",
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" end\n",
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" end\n",
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" Logging.debug(\"solution vector: \\n $u\")\n",
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" Logging.debug(\"norm of u: $(norm(u))\")\n",
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" @fact norm(u) => roughly(norm1) \n",
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||
"end"
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||
]
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||
},
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||
{
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||
"cell_type": "markdown",
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||
"metadata": {},
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"source": [
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"One element solutions are not particularly interesting so next step is to create function that assembles global matrix from local matrices. Some data types:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"type Node\n",
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" id :: Int\n",
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" elements :: Array{Int64, 1}\n",
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"end"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"type Element\n",
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" id :: Int\n",
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" nodes :: Array{Int64, 1}\n",
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" coordinates :: Array{Float64, 2}\n",
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" attributes :: Dict{ASCIIString, Any}\n",
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"end"
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]
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},
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{
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"cell_type": "code",
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||
"execution_count": 7,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"type Assembly\n",
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" # LHS\n",
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" I :: Array{Int64, 1}\n",
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" J :: Array{Int64, 1}\n",
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" A :: Array{Float64, 1}\n",
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" # RHS\n",
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" i :: Array{Int64, 1}\n",
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" b :: Array{Float64, 1}\n",
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" # global dofs for each element\n",
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" gdofs :: Dict{Int64, Array{Int64, 1}}\n",
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"end"
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]
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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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||
"metadata": {
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||
"collapsed": false
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||
},
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||
"outputs": [
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||
{
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||
"data": {
|
||
"text/plain": [
|
||
"get_shape_functions (generic function with 1 method)"
|
||
]
|
||
},
|
||
"execution_count": 19,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
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}
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],
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"source": [
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"\"\"\"\n",
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"Return shape functions and their derivatives for a element.\n",
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"\n",
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"Parameters\n",
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"----------\n",
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"element::Element\n",
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"\n",
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"Returns\n",
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"-------\n",
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"tuple (basis, dbasis)\n",
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"\"\"\"\n",
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"function get_shape_functions(el::Element)\n",
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" ndim, nnodes = size(el.coordinates)\n",
|
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" if (nnodes == 4) & (ndim == 2)\n",
|
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" basis(xi) = [\n",
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" (1-xi[1])*(1-xi[2])/4\n",
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" (1+xi[1])*(1-xi[2])/4\n",
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" (1+xi[1])*(1+xi[2])/4\n",
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" (1-xi[1])*(1+xi[2])/4]\n",
|
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" dbasis(xi) = [-(1-xi[2])/4.0 -(1-xi[1])/4.0\n",
|
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" (1-xi[2])/4.0 -(1+xi[1])/4.0\n",
|
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" (1+xi[2])/4.0 (1+xi[1])/4.0\n",
|
||
" -(1+xi[2])/4.0 (1-xi[1])/4.0]\n",
|
||
" return basis, dbasis\n",
|
||
" end\n",
|
||
" throw(\"Unknown function space\")\n",
|
||
"end"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 20,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"get_integration_scheme (generic function with 2 methods)"
|
||
]
|
||
},
|
||
"execution_count": 20,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"\"\"\"\n",
|
||
"\"\"\"\n",
|
||
"function get_integration_scheme(el::Element, order=2)\n",
|
||
" ndim, nnodes = size(el.coordinates)\n",
|
||
" if (nnodes == 4) & (order == 2)\n",
|
||
" ipoints = 1/sqrt(3)*[-1 -1; 1 -1; 1 1; -1 1]\n",
|
||
" iweights = [1, 1, 1, 1]\n",
|
||
" return ipoints, iweights\n",
|
||
" end\n",
|
||
"end"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 48,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"assemble_element! (generic function with 2 methods)"
|
||
]
|
||
},
|
||
"execution_count": 48,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"function assemble_element!(ass::Assembly, el::Element, io=2)\n",
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||
"\n",
|
||
" # Material properties\n",
|
||
" E = el.attributes[\"Young\"]\n",
|
||
" nu = el.attributes[\"Poisson\"]\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",
|
||
" dofs = prod(size(el.coordinates))\n",
|
||
" X = el.coordinates\n",
|
||
" u = el.attributes[\"displacement\"]\n",
|
||
" R = el.attributes[\"displacement nodal force\"]\n",
|
||
" K = el.attributes[\"displacement tangent stiffness\"]\n",
|
||
"\n",
|
||
" gdofs = ass.gdofs[el.id]\n",
|
||
" basis, dbasis = get_shape_functions(el)\n",
|
||
" ipoints, iweights = get_integration_scheme(el, io)\n",
|
||
" calc_local_matrices!(X, u, R, K, basis, dbasis, la, mu, ipoints, iweights)\n",
|
||
"\n",
|
||
" for i=1:dofs\n",
|
||
" for j=1:dofs\n",
|
||
" push!(ass.I, gdofs[i])\n",
|
||
" push!(ass.J, gdofs[j])\n",
|
||
" push!(ass.A, K[i,j])\n",
|
||
" end\n",
|
||
" push!(ass.i, gdofs[i])\n",
|
||
" push!(ass.b, R[i])\n",
|
||
" end\n",
|
||
"end"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Time to test again. From last test we know that correct solution is\n",
|
||
"\n",
|
||
" [0.0 -0.39914506095474317 -0.07228582695592449 0.0\n",
|
||
" 0.0 -2.1779892317073504 -2.222244754401764 0.0]\n",
|
||
"\n",
|
||
"This time we assemble global stiffness matrix in different order, 2 3 4 1"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 49,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"one element assembly\n"
|
||
]
|
||
},
|
||
{
|
||
"name": "stderr",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"30-Jul 00:08:18:DEBUG:root:Creating nodes\n",
|
||
"30-Jul 00:08:18:DEBUG:root:Creating elements\n",
|
||
"30-Jul 00:08:18:DEBUG:root:Starting iteration 1\n",
|
||
"30-Jul 00:08:18:DEBUG:root:Assembling\n",
|
||
"30-Jul 00:08:18:DEBUG:root:Solving\n",
|
||
"30-Jul 00:08:18:DEBUG:root:Solution norm = 3.0814821107320176\n",
|
||
"30-Jul 00:08:18:DEBUG:root:Starting iteration 2\n",
|
||
"30-Jul 00:08:18:DEBUG:root:Assembling\n",
|
||
"30-Jul 00:08:18:DEBUG:root:Solving\n",
|
||
"30-Jul 00:08:18:DEBUG:root:Solution norm = 0.32007464366194766\n",
|
||
"30-Jul 00:08:18:DEBUG:root:Starting iteration 3\n",
|
||
"30-Jul 00:08:18:DEBUG:root:Assembling\n",
|
||
"30-Jul 00:08:18:DEBUG:root:Solving\n",
|
||
"30-Jul 00:08:18:DEBUG:root:Solution norm = 0.040279810888447135\n",
|
||
"30-Jul 00:08:18:DEBUG:root:Starting iteration 4\n",
|
||
"30-Jul 00:08:18:DEBUG:root:Assembling\n",
|
||
"30-Jul 00:08:18:DEBUG:root:Solving\n",
|
||
"30-Jul 00:08:18:DEBUG:root:Solution norm = 0.000925649536063315\n",
|
||
"30-Jul 00:08:18:DEBUG:root:Starting iteration 5\n",
|
||
"30-Jul 00:08:18:DEBUG:root:Assembling\n",
|
||
"30-Jul 00:08:18:DEBUG:root:Solving\n",
|
||
"30-Jul 00:08:18:DEBUG:root:Solution norm = 1.5582555024825817e-7\n",
|
||
"30-Jul 00:08:18:DEBUG:root:Starting iteration 6\n",
|
||
"30-Jul 00:08:18:DEBUG:root:Assembling\n",
|
||
"30-Jul 00:08:18:DEBUG:root:Solving\n",
|
||
"30-Jul 00:08:18:DEBUG:root:Solution norm = 1.0317166868587156e-14\n",
|
||
"30-Jul 00:08:18:DEBUG:root:Converged in 6 iterations.\n",
|
||
"30-Jul 00:08:18:DEBUG:root:Displacement of element = \n",
|
||
"[-0.39914506095474334 -0.07228582695592464 0.0 0.0\n",
|
||
" -2.1779892317073504 -2.222244754401764 0.0 0.0]\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"delayed_handler (generic function with 4 methods)"
|
||
]
|
||
},
|
||
"execution_count": 49,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
},
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"1 fact verified.\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"facts(\"one element assembly\") do\n",
|
||
" Logging.debug(\"Creating nodes\")\n",
|
||
" n1 = Node(1, Int64[])\n",
|
||
" n2 = Node(2, Int64[])\n",
|
||
" n3 = Node(3, Int64[])\n",
|
||
" n4 = Node(4, Int64[])\n",
|
||
" nodes = [n1.id, n2.id, n3.id, n4.id]\n",
|
||
" coordinates = [10.0 0.0; 10.0 1.0; 0.0 1.0; 0.0 0.0]'\n",
|
||
" attributes = Dict(\n",
|
||
" \"Young\" => 90, \"Poisson\" => 0.25,\n",
|
||
" \"displacement\" => zeros(2, 4),\n",
|
||
" \"displacement nodal force\" => zeros(2, 4),\n",
|
||
" \"displacement tangent stiffness\" => zeros(8, 8))\n",
|
||
" Logging.debug(\"Creating elements\")\n",
|
||
" el = Element(1, nodes, coordinates, attributes)\n",
|
||
" for i=1:10\n",
|
||
" Logging.debug(\"Starting iteration $i\")\n",
|
||
" ass = Assembly(Int64[], Int64[], Float64[], Int64[], Float64[], Dict{Int64,Array{Int64,1}}())\n",
|
||
" ass.gdofs[el.id] = [1, 2, 3, 4, 5, 6, 7, 8]\n",
|
||
" Logging.debug(\"Assembling\")\n",
|
||
" assemble_element!(ass, el)\n",
|
||
" Logging.debug(\"Solving\")\n",
|
||
" du = zeros(2, 4) # must be determined from ass\n",
|
||
" F = [0 0; 0 -2; 0 0; 0 0]'\n",
|
||
" free_dofs = [1, 2, 3, 4]\n",
|
||
"\n",
|
||
" # solution\n",
|
||
" K = sparse(ass.I, ass.J, ass.A)\n",
|
||
" R = full(sparsevec(ass.i, ass.b))\n",
|
||
" R = reshape(R, (2, round(Int, length(R)/2)))\n",
|
||
" du[free_dofs] = K[free_dofs, free_dofs] \\ -(R - F)[free_dofs]\n",
|
||
"\n",
|
||
" Logging.debug(\"Solution norm = $(norm(du))\")\n",
|
||
" #Logging.debug(\"Solution increment = \\n$du\")\n",
|
||
"\n",
|
||
" # update solution back to elements\n",
|
||
" eldu = du[ass.gdofs[el.id]]\n",
|
||
" eldu = reshape(eldu, (2, round(Int, length(eldu)/2)))\n",
|
||
" el.attributes[\"displacement\"] += eldu\n",
|
||
" if norm(du) < 1.0e-9\n",
|
||
" Logging.debug(\"Converged in $i iterations.\")\n",
|
||
" break\n",
|
||
" end\n",
|
||
" end\n",
|
||
" disp = el.attributes[\"displacement\"]\n",
|
||
" Logging.debug(\"Displacement of element = \\n$disp\")\n",
|
||
" @fact norm(disp) => roughly(3.1292483947150043)\n",
|
||
"end"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Seems to be working. But we still need to handle boundary conditions more \"cleverly\" and generalize assembly to several elements (which is not problem)."
|
||
]
|
||
},
|
||
{
|
||
"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": [
|
||
"#(X, u, du, elmap, nodalloads, dirichletbc,\n",
|
||
"# la, mu, N, dNdξ, ipoints, iweights) = one_elem_fixture()\n",
|
||
"function solve_one_element()\n",
|
||
"\n",
|
||
" # create nodes separately ...\n",
|
||
"\n",
|
||
" # .. or create somewhat simpler syntax\n",
|
||
" # nodes = Dict(1 => [0.0, 0.0], 2 => [10.0, 0.0], 3 => [10.0, 1.0], 4 => [0.0, 1.0])\n",
|
||
" # add_nodes(m, \"NALL\", nodes)\n",
|
||
"\n",
|
||
" # create element (hard way)\n",
|
||
" e = new_element()\n",
|
||
" set_element_id(1)\n",
|
||
" set_node_ids(e, [1, 2, 3, 4])\n",
|
||
"\n",
|
||
" # we can set function spaces and integration schema for element-wise ...\n",
|
||
" set_function_space(e, \"Lagrange(1)\") # use linear Lagrange function space to approximate unknown field\n",
|
||
" set_integration_schema(e, \"FPG4\") # use four integration points\n",
|
||
" # or for model as a \"default value\"\n",
|
||
" # set_function_space(m, \"Lagrange\", 1)\n",
|
||
" # set_integration_schema(m, \"FPG4\")\n",
|
||
"\n",
|
||
" # set necessary material parameters\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",
|
||
" # we can add attribute for each element node ...\n",
|
||
" #add_attribute(e, \"lambda\", [la, la, la, la])\n",
|
||
" #add_attribute(e, \"mu\", [mu, mu, mu, mu])\n",
|
||
" # or just one for each element ...\n",
|
||
" add_attribute(e, \"lambda\", lambda)\n",
|
||
" add_attribute(e, \"mu\", mu)\n",
|
||
" # .. or just for model as a default value\n",
|
||
" # add_attribute(m, \"lambda\", lambda)\n",
|
||
" # add_attribute(m, \"mu\", mu)\n",
|
||
" # note that we don't assign attributes to nodes here so we can describe discontinous fields\n",
|
||
" # in attributes\n",
|
||
"\n",
|
||
" # or we can use convenient syntax\n",
|
||
" # e = new_element(element_id=1, node_ids=[1, 2, 3, 4], function_space=\"Lagrange(1)\",\n",
|
||
" # integration_schema=\"FPG4\", attributes=Dict(\"lambda\" => lambda, \"mu\" => mu))\n",
|
||
"\n",
|
||
" elements = [e]\n",
|
||
" add_elements(m, \"EALL\", elements)\n",
|
||
"\n",
|
||
" # boundary conditions are always assignet to sets\n",
|
||
"\n",
|
||
" # element boundary conditions\n",
|
||
" \n",
|
||
" # add load for element surface S1 in normal-tangential coordinate system\n",
|
||
" # add_attribute(e, \"displacement S1 normal load\", 1)\n",
|
||
" # add load for element surface S1 from -1 to -2\n",
|
||
" # add_attribute(e, \"displacement S1 load\", [-1, -2])\n",
|
||
"\n",
|
||
" # nodal boundary conditions\n",
|
||
" # add neumann boundary condition to node 3, in y direction\n",
|
||
" add_attribute(n3, \"displacement 2 load\", -2)\n",
|
||
" # add dirichlet boundary condition to nodes 1 and 2 (encastre)\n",
|
||
" add_attribute(n1, \"displacement\", [0.0, 0.0])\n",
|
||
" # or\n",
|
||
" # add_attribute(n1, \"displacement 1\", 0.0)\n",
|
||
" # add_attribute(n1, \"displacement 2\", 0.0)\n",
|
||
" add_attribute(n2, \"displacement\", [0.0, 0.0])\n",
|
||
" # or, for example, add dirichlet boundary conditions in directions 1 and 3 for node\n",
|
||
" #add_attribute(n2, \"displacement 1,3\", [0.0, 1.0])\n",
|
||
" # or fix all dofs of a nodes in nodeset \"SUPPORT\"\n",
|
||
" # support_bc = add_nodeset(m, \"SUPPORT\", [n1, n2])\n",
|
||
" # add_attribute(support_bc, \"displacement\", 0)\n",
|
||
"\n",
|
||
"\n",
|
||
"\n",
|
||
" # Everything is very general so far. Datamodel is well defined and in this point\n",
|
||
" # we can save or load it to disk\n",
|
||
"\n",
|
||
" # save_model(m, \"mymodel\") # save model to xml/h5 (Xdmf)\n",
|
||
" # m = load_model(\"mymodel\") # load model from file\n",
|
||
"\n",
|
||
" \n",
|
||
" # END OF MODEL DEFINITON\n",
|
||
" \n",
|
||
" # Now we kick in elasticity iterations and solve displacement\n",
|
||
" # field but of course it could be something else too\n",
|
||
"\n",
|
||
"\n",
|
||
" # m1, m2 = make_domain_decomposition(parts=2, keep_in_one_domain=[\"CONTACT_BOUNDARY\"])\n",
|
||
"\n",
|
||
"\n",
|
||
" \n",
|
||
" # In newton iteration, there might be situations where we just want to update RHS\n",
|
||
" # like in radiation problems, it makes no sense to update stiffness matrix in that\n",
|
||
" # case. For this reason local element matrix and force vector can be updated both\n",
|
||
" # or just one of them. This time we don't have anything nonlinear in RHS so we can\n",
|
||
" # calculate it outside of iteration loop\n",
|
||
" p = new_problem(\"displacement\")\n",
|
||
" \n",
|
||
" RHS = zeros(length(nodes)*dofs)\n",
|
||
" \n",
|
||
" for i=1:10\n",
|
||
" \n",
|
||
" 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",
|
||
" return u\n",
|
||
"end\n",
|
||
"\n",
|
||
"u"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": null,
|
||
"metadata": {
|
||
"collapsed": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"\"\"\"\n",
|
||
"#### Parameters\n",
|
||
"X : Array{Float64, 2}\n",
|
||
" \n",
|
||
"\"\"\"\n",
|
||
"function solve_elasticity_increment!(X, u, du, elmap, nodalloads,\n",
|
||
" dirichletbc, lambda, mu, N, dNdchi, ipoints,\n",
|
||
" iweights)\n",
|
||
" if length(size(elmap)) == 1\n",
|
||
" # quick hack for just one element\n",
|
||
" elmap = elmap''\n",
|
||
" end\n",
|
||
" nelnodes, nelements = size(elmap)\n",
|
||
" dim, nnodes = size(u)\n",
|
||
" dofs = dim*nelnodes\n",
|
||
"\n",
|
||
" Imat = Int64[]\n",
|
||
" Jmat = Int64[]\n",
|
||
" Vmat = Float64[]\n",
|
||
" Ivec = Int64[]\n",
|
||
" Vvec = Float64[]\n",
|
||
"\n",
|
||
" # FIXME: different number of nodes/element\n",
|
||
" R = zeros(dim, nelnodes)\n",
|
||
" Kt = zeros(dofs, dofs)\n",
|
||
"\n",
|
||
" # this can be parallelized\n",
|
||
" for i in 1:nelements\n",
|
||
" eldofs = elmap[:,i]\n",
|
||
" calc_local_matrices!(X[:, eldofs], u[:, eldofs], R, Kt, N, dNdchi,\n",
|
||
" lambda[eldofs], mu[eldofs], ipoints, iweights)\n",
|
||
" assemble!(Kt, eldofs, Imat, Jmat, Vmat)\n",
|
||
" assemble!(R, eldofs, Ivec, Vvec)\n",
|
||
" end\n",
|
||
"\n",
|
||
" # add additional neumann boundary conditions to force vector\n",
|
||
" for (i, nodal_load) in enumerate(nodalloads)\n",
|
||
" if nodal_load == 0\n",
|
||
" continue\n",
|
||
" end\n",
|
||
" push!(Ivec, i)\n",
|
||
" push!(Vvec, -nodal_load)\n",
|
||
" end\n",
|
||
"\n",
|
||
" # Create sparse matrix and vector\n",
|
||
" A = sparse(Imat, Jmat, Vmat)\n",
|
||
" b = sparsevec(Ivec, Vvec)\n",
|
||
"\n",
|
||
" # Remove dirichlet boundary conditions\n",
|
||
" free_dofs = find(isnan(dirichletbc))\n",
|
||
" #Imat, Jmat, Vmat = eliminate_boundary_conditions(dirichletbc, Imat, Jmat, Vmat)\n",
|
||
" b = b[free_dofs]\n",
|
||
" A = A[free_dofs, free_dofs]\n",
|
||
"\n",
|
||
" # solution\n",
|
||
" du[free_dofs] = lufact(A) \\ -full(b)\n",
|
||
"end\n",
|
||
"\n",
|
||
"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"
|
||
]
|
||
},
|
||
{
|
||
"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": {
|
||
"image/png": 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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": 4,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stderr",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"27-Jun 23:44:05: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:113\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 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:113\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 2\n",
|
||
"27-Jun 23:44:06:DEBUG:root:Found NODE section\n",
|
||
"27-Jun 23:44:07: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:59\n",
|
||
" in process_section at /Users/jukka/.julia/v0.4/JuliaFEM/src/abaqus_reader.jl:108\n",
|
||
" in parse_abaqus at /Users/jukka/.julia/v0.4/JuliaFEM/src/abaqus_reader.jl:117\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 2\n",
|
||
"27-Jun 23:44:08:DEBUG:root:120 elements found\n",
|
||
"27-Jun 23:44:08:INFO:root:Creating ELSET Body1\n",
|
||
"27-Jun 23:44:08:DEBUG:root:Found NSET section\n",
|
||
"27-Jun 23:44:08:DEBUG:root:Creating node set SUPPORT\n",
|
||
"27-Jun 23:44:08:DEBUG:root:Found NSET section\n",
|
||
"27-Jun 23:44:08:DEBUG:root:Creating node set LOAD\n",
|
||
"27-Jun 23:44:08:DEBUG:root:Found NSET section\n",
|
||
"27-Jun 23:44:08: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": 4,
|
||
"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": 5,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"10x120 Array{Int64,2}:\n",
|
||
" 243 204 259 145 96 96 236 285 … 217 69 154 179 203 96 259\n",
|
||
" 240 199 70 175 88 101 88 179 216 144 114 91 204 267 199\n",
|
||
" 191 175 69 199 236 164 285 178 278 78 278 178 259 95 204\n",
|
||
" 117 130 130 130 178 97 178 83 155 71 218 83 199 97 130\n",
|
||
" 245 207 265 177 141 102 290 12 219 146 20 181 206 268 39\n",
|
||
" 242 208 72 208 290 171 289 182 … 282 152 280 180 263 272 207\n",
|
||
" 244 209 5 202 291 9 287 11 33 79 32 182 262 98 263\n",
|
||
" 1 3 6 174 7 99 237 13 224 74 223 14 205 99 6\n",
|
||
" 2 4 132 176 8 103 8 14 225 51 284 93 207 24 4\n",
|
||
" 196 176 134 4 237 10 11 15 17 80 283 15 39 100 3"
|
||
]
|
||
},
|
||
"execution_count": 5,
|
||
"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",
|
||
" X[:,j] = model[\"nodes\"][j]\n",
|
||
"end\n",
|
||
"\n",
|
||
"for (j, k) in enumerate(keys(model[\"elements\"]))\n",
|
||
" #node_ids = model[\"elements\"][j]\n",
|
||
" elmap[:,j] = model[\"elements\"][j]\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": 6,
|
||
"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": 6,
|
||
"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",
|
||
" dirichletbc[j] = 0.0\n",
|
||
"end\n",
|
||
"dirichletbc"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Shape functions and integration points"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 7,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"dNtet (generic function with 1 method)"
|
||
]
|
||
},
|
||
"execution_count": 7,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"Ntet(xi) = [(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[1]*xi[3]\n",
|
||
" 4*xi[2]*xi[3]\n",
|
||
" 4*xi[3]*(-xi[1] - xi[2] - xi[3] + 1)]\n",
|
||
"\n",
|
||
"dNtet(xi) = [\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",
|
||
"-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] 0 4*xi[1]\n",
|
||
" 0 4*xi[3] 4*xi[2]\n",
|
||
" -4*xi[3] -4*xi[3] -4*xi[1] - 4*xi[2] - 8*xi[3] + 4]"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 8,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"1"
|
||
]
|
||
},
|
||
"execution_count": 8,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"sum(Ntet([0, 1, 1]))"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 9,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"1x4 Array{Float64,2}:\n",
|
||
" 0.0416667 0.0416667 0.0416667 0.0416667"
|
||
]
|
||
},
|
||
"execution_count": 9,
|
||
"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": 10,
|
||
"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": 10,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"model[\"nsets\"][\"LOAD\"]"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 11,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"[100.0,10.0,0.0]\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"#nodalloads[3, perm[82]] = -0.06\n",
|
||
"nodalloads[3, 82] = -50.0\n",
|
||
"println(model[\"nodes\"][82])"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 12,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"iteration 1, norm = 93.13879357262775\n",
|
||
"iteration 2, norm = 14.241640589907869\n",
|
||
"iteration 3, norm = 2.3999534862146534\n",
|
||
"iteration 4, norm = 0.8191634532858331\n",
|
||
"iteration 5, norm = 0.08574651168344295\n",
|
||
"iteration 6, norm = 0.00032306479346201524\n",
|
||
"iteration 7, norm = 8.052462405199464e-9\n",
|
||
"iteration 8, norm = 3.0878906643174355e-14\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"3x298 Array{Float64,2}:\n",
|
||
" -0.0479657 -0.0483971 -0.0497284 … -0.0155295 -0.0150513 -0.0462958\n",
|
||
" -0.474054 -0.418817 -0.254176 -0.229641 -0.283098 -0.694379 \n",
|
||
" 0.232677 0.198051 0.0948355 0.128246 0.162511 0.371043 "
|
||
]
|
||
},
|
||
"execution_count": 12,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
},
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Converged\n"
|
||
]
|
||
}
|
||
],
|
||
"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",
|
||
" println(\"iteration $i, norm = $(norm(du))\")\n",
|
||
" if norm(du) < 1.0e-9\n",
|
||
" println(\"Converged\")\n",
|
||
" break\n",
|
||
" end\n",
|
||
"end\n",
|
||
"u"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 13,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"15.449170689704438"
|
||
]
|
||
},
|
||
"execution_count": 13,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"maximum(abs(u))"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 14,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"(10,120)"
|
||
]
|
||
},
|
||
"execution_count": 14,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"size(elmap)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 15,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"120"
|
||
]
|
||
},
|
||
"execution_count": 15,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"nelements"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 16,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"11x120 Array{Int64,2}:\n",
|
||
" 38 38 38 38 38 38 38 38 … 38 38 38 38 38 38 38\n",
|
||
" 243 204 259 145 96 96 236 285 217 69 154 179 203 96 259\n",
|
||
" 240 199 70 175 88 101 88 179 216 144 114 91 204 267 199\n",
|
||
" 191 175 69 199 236 164 285 178 278 78 278 178 259 95 204\n",
|
||
" 117 130 130 130 178 97 178 83 155 71 218 83 199 97 130\n",
|
||
" 245 207 265 177 141 102 290 12 … 219 146 20 181 206 268 39\n",
|
||
" 242 208 72 208 290 171 289 182 282 152 280 180 263 272 207\n",
|
||
" 244 209 5 202 291 9 287 11 33 79 32 182 262 98 263\n",
|
||
" 1 3 6 174 7 99 237 13 224 74 223 14 205 99 6\n",
|
||
" 2 4 132 176 8 103 8 14 225 51 284 93 207 24 4\n",
|
||
" 196 176 134 4 237 10 11 15 … 17 80 283 15 39 100 3"
|
||
]
|
||
},
|
||
"execution_count": 16,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"elcodes = 0x0026*ones(Int, nelements)\n",
|
||
"elmap2 = [elcodes'\n",
|
||
" elmap]"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 17,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stderr",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"WARNING: int(x) is deprecated, use Int(x) instead.\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"9568"
|
||
]
|
||
},
|
||
"execution_count": 17,
|
||
"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:140\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[17], in expression starting on line 7\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"xdoc, xmodel = JuliaFEM.xdmf.xdmf_new_model()\n",
|
||
"temporal_collection = JuliaFEM.xdmf.xdmf_new_temporal_collection(xmodel)\n",
|
||
"grid = JuliaFEM.xdmf.xdmf_new_grid(temporal_collection; time=0)\n",
|
||
"JuliaFEM.xdmf.xdmf_new_mesh(grid, X, elmap2)\n",
|
||
"#JuliaFEM.xdmf.xdmf_new_field(grid, \"Displacement\", \"nodes\", u)\n",
|
||
"#print(xdoc)\n",
|
||
"JuliaFEM.xdmf.xdmf_save_model(xdoc, \"/tmp/foo3d2.xmf\")"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 18,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"10x2 Array{Int64,2}:\n",
|
||
" 243 145\n",
|
||
" 240 199\n",
|
||
" 191 69\n",
|
||
" 117 130\n",
|
||
" 245 202\n",
|
||
" 242 47\n",
|
||
" 244 148\n",
|
||
" 1 174\n",
|
||
" 2 4\n",
|
||
" 196 134"
|
||
]
|
||
},
|
||
"execution_count": 18,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"elmap[:,[1, 101]]"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 25,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"3x10 Array{Float64,2}:\n",
|
||
" 20.0 30.0 20.0 20.0 25.0 25.0 20.0 20.0 25.0 20.0\n",
|
||
" 0.0 0.0 0.0 10.0 0.0 0.0 0.0 5.0 5.0 5.0\n",
|
||
" 10.0 10.0 0.0 0.0 10.0 5.0 5.0 5.0 5.0 0.0"
|
||
]
|
||
},
|
||
"execution_count": 25,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"tmp = elmap[:,[1]]\n",
|
||
"tmp = reshape(tmp, length(tmp))\n",
|
||
"X[:, tmp]"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 26,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"11x1 Array{Int64,2}:\n",
|
||
" 38\n",
|
||
" 1\n",
|
||
" 2\n",
|
||
" 3\n",
|
||
" 4\n",
|
||
" 5\n",
|
||
" 6\n",
|
||
" 7\n",
|
||
" 8\n",
|
||
" 9\n",
|
||
" 10"
|
||
]
|
||
},
|
||
"execution_count": 26,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"#tmpelmap = [38 1 2 3 4 5 6 7 8 9 10; 38 11 12 13 14 15 16 17 18 19 20]'\n",
|
||
"tmpelmap = [38 1 2 3 4 5 6 7 8 9 10]'"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 48,
|
||
"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=\"298 3\" Format=\"XML\" Precision=\"8\">\n",
|
||
"\t\t20.0 5.0 5.0\n",
|
||
"\t\t25.0 5.0 5.0\n",
|
||
"\t\t40.0 5.0 5.0\n",
|
||
"\t\t42.5 5.0 2.5\n",
|
||
"\t\t47.5 7.5 5.0\n",
|
||
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|
||
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|
||
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|
||
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-0.6133598889995131 0.3702729276182241 0.015004314467624716 -0.585343247022487 0.39329629153147017 0.01458071509855983 -0.5302734140075925 0.3587018974517421 -0.01344375293594734 -0.5032141882644785 0.30108529882614404 -0.3620456247533485 0.5519867699907384 -12.620344556531794 -0.526966243814986 0.5761773089089341 -13.53252924781271 -0.010580716254271554 0.5370526569804701 -11.240538337103064 -0.7590766917007422 0.5424585404804543 -14.06075381984704 -0.2241267810324015 0.5080924245964678 -11.678636409861051 0.12435591418543097 0.4890125752209692 -10.2901175360841 0.5644461793934311 0.4452121362167419 -7.977671709359734 0.6877930605010911 0.1763463728609681 -0.8949858092003476 -0.013854912976747782 -0.44812265379862676 0.26650158133217267 -0.014668310361330275 -0.33793775862863673 0.1972625056180801 -0.014256902850070032 -0.3930499585001261 0.23188288965132975 -0.015529548039433162 -0.22964069733477832 0.12824581547933717 -0.01505131691402543 -0.28309752287511414 0.16251145574210094 -0.04629575533140819 -0.6943785848803764 0.37104295188956193</DataItem>\n",
|
||
" </Attribute>\n",
|
||
" </Grid>\n",
|
||
" </Grid>\n",
|
||
" </Domain>\n",
|
||
"</Xdmf>\n",
|
||
"\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"28476"
|
||
]
|
||
},
|
||
"execution_count": 48,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"using LightXML\n",
|
||
"\n",
|
||
"function xdmf_new_mesh(grid, X, elmap)\n",
|
||
" dim, nnodes = size(X)\n",
|
||
" geometry = new_child(grid, \"Geometry\")\n",
|
||
" set_attribute(geometry, \"Type\", \"XYZ\")\n",
|
||
" dataitem = new_child(geometry, \"DataItem\")\n",
|
||
" set_attribute(dataitem, \"DataType\", \"Float\")\n",
|
||
" set_attribute(dataitem, \"Dimensions\", \"$nnodes $dim\")\n",
|
||
" set_attribute(dataitem, \"Format\", \"XML\")\n",
|
||
" set_attribute(dataitem, \"Precision\", 8)\n",
|
||
" #add_text(dataitem, join(X, \" \"))\n",
|
||
" s = \"\\n\"\n",
|
||
" \n",
|
||
" for i=1:nnodes\n",
|
||
" s *= \"\\t\\t\" * join(X[:,i], \" \") * \"\\n\"\n",
|
||
" end\n",
|
||
" s *= \" \"\n",
|
||
" add_text(dataitem, s)\n",
|
||
"\n",
|
||
" elmap2 = copy(elmap)\n",
|
||
" elmap2[2:end,:] -= 1\n",
|
||
" dim, nelements = size(elmap2)\n",
|
||
"\n",
|
||
" topology = new_child(grid, \"Topology\")\n",
|
||
" #set_attribute(topology, \"Dimensions\", \"1\")\n",
|
||
" set_attribute(topology, \"TopologyType\", \"Mixed\")\n",
|
||
" set_attribute(topology, \"NumberOfElements\", nelements)\n",
|
||
" dataitem = new_child(topology, \"DataItem\")\n",
|
||
" set_attribute(dataitem, \"DataType\", \"Int\")\n",
|
||
" set_attribute(dataitem, \"Dimensions\", \"$nelements $dim\")\n",
|
||
" set_attribute(dataitem, \"Format\", \"XML\")\n",
|
||
" set_attribute(dataitem, \"Precision\", 8)\n",
|
||
" s = \"\\n\"\n",
|
||
" for i=1:nelements\n",
|
||
" s *= \"\\t\\t\" * join(elmap2[:,i], \" \") * \"\\n\"\n",
|
||
" end\n",
|
||
" add_text(dataitem, s)\n",
|
||
" #add_text(dataitem, join(elmap2, \" \"))\n",
|
||
" \n",
|
||
"end\n",
|
||
"\n",
|
||
"xdoc, xmodel = JuliaFEM.xdmf.xdmf_new_model()\n",
|
||
"temporal_collection = JuliaFEM.xdmf.xdmf_new_temporal_collection(xmodel)\n",
|
||
"grid = JuliaFEM.xdmf.xdmf_new_grid(temporal_collection; time=0)\n",
|
||
"xdmf_new_mesh(grid, X, elmap2)\n",
|
||
"JuliaFEM.xdmf.xdmf_new_field(grid, \"Displacement\", \"nodes\", u)\n",
|
||
"print(xdoc)\n",
|
||
"JuliaFEM.xdmf.xdmf_save_model(xdoc, \"/tmp/foo3d.xmf\")"
|
||
]
|
||
}
|
||
],
|
||
"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
|
||
}
|