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JuliaFEM.jl/notebooks/2015-06-25-elasticity-solver-example.ipynb
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Jukka Aho 1aa1ccb4c1 still wondering, does not converge
2015-08-10 23:01:44 +03:00

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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Solving elasticity problems using JuliaFEM\n",
"\n",
"Author(s): Jukka Aho\n",
"\n",
"**Abstract**: A workflow to solve typical elasticity problem. This document also tries to give some quidelines how to develop JuliaFEM."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Bottom-up design\n",
"\n",
"We go piece by piece starting from something simple and going up to more complicated programming model."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Design principle 1*: we introduce new ideas using Notebooks."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Design principle 2*: we use ``Logging``. Forget ``println``."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"Logger(root,DEBUG,Pipe(open, 0 bytes waiting),root)"
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"using Logging\n",
"Logging.configure(level=DEBUG)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Design principle 3*: we write docstrings using [numpy style](https://github.com/numpy/numpy/blob/master/doc/HOWTO_DOCUMENT.rst.txt).\n",
"\n",
"*Design principle 4*: we don't use greek characters in code which is implemented to JuliaFEM. In notebooks they are ok.\n",
"\n",
"*Design principle 5*: we use 4 space indentation like in Python.\n",
"\n",
"First we write some elementary functions to calculate stiffness matrix."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"calc_local_matrices! (generic function with 1 method)"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"\"\"\"\n",
"Calculate local tangent stiffness matrix and residual force vector\n",
"R = T - F for elasticity problem.\n",
"\n",
"Parameters\n",
"----------\n",
"X : Element coordinates\n",
"u : Displacement field\n",
"R : Residual force vector\n",
"K : Tangent stiffness matrix\n",
"basis : Basis functions\n",
"dbasis : Derivative of basis functions\n",
"lambda : Material parameter\n",
"mu : Material parameter\n",
"ipoints : integration points\n",
"iweights : integration weights\n",
"\n",
"Returns\n",
"-------\n",
"None\n",
"\n",
"Notes\n",
"-----\n",
"If material parameters are given in list, they are interpolated to gauss\n",
"points using shape functions.\n",
"\n",
"Examples\n",
"--------\n",
"\n",
"\"\"\"\n",
"function calc_local_matrices!(X, u, R, K, basis, dbasis, lambda_, mu_, ipoints, iweights)\n",
" dim, nnodes = size(X)\n",
" I = eye(dim)\n",
" R[:,:] = 0.0\n",
" K[:,:] = 0.0\n",
"\n",
" dF = zeros(dim, dim)\n",
"\n",
" for m = 1:length(iweights)\n",
" w = iweights[m]\n",
" xi = ipoints[m, :]\n",
" # calculate material parameters\n",
" lambda = typeof(lambda_) == Float64 ? lambda_ : dot(lambda_, basis(xi))\n",
" mu = typeof(mu_) == Float64 ? mu_ : dot(mu_, basis(xi))\n",
" Jt = X*dbasis(xi)\n",
" detJ = det(Jt)\n",
" dbasisdX = dbasis(xi)*inv(Jt)\n",
"\n",
" gradu = u*dbasisdX\n",
" F = I + gradu # Deformation gradient\n",
" E = 1/2*(gradu' + gradu + gradu'*gradu) # Green-Lagrange strain tensor\n",
" S = lambda*trace(E)*I + 2*mu*E # PK2 stress tensor\n",
" P = F*S # PK1 stress tensor\n",
"\n",
" R[:,:] += w*P*dbasisdX'*detJ\n",
"\n",
" for p = 1:nnodes\n",
" for i = 1:dim\n",
" dF[:,:] = 0.0\n",
" dF[i,:] = dbasisdX[p,:]\n",
" dE = 1/2*(F'*dF + dF'*F)\n",
" dS = lambda*trace(dE)*I + 2*mu*dE\n",
" dP = dF*S + F*dS\n",
" for q = 1:nnodes\n",
" for j = 1:dim\n",
" K[dim*(p-1)+i,dim*(q-1)+j] += w*(dP[j,:]*dbasisdX[q,:]')[1]*detJ\n",
" end\n",
" end\n",
" end\n",
" end\n",
"\n",
" end\n",
"end"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Design principle 6*: we test our code. We use FactCheck for testing."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"using FactCheck"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"test solve one element model\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"10-Aug 19:18:44:DEBUG:root:Converged in 6 iterations.\n",
"10-Aug 19:18:45:DEBUG:root:solution vector: \n",
" [0.0 -0.39914506095474317 -0.07228582695592449 0.0\n",
" 0.0 -2.1779892317073504 -2.222244754401764 0.0]\n",
"10-Aug 19:18:45:DEBUG:root:norm of u: 3.1292483947150043\n",
"10-Aug 19:18:45:DEBUG:root:Converged in 6 iterations.\n",
"10-Aug 19:18:45:DEBUG:root:solution vector: \n",
" [0.0 0.7433248532717793 1.0485210147234858 0.0\n",
" 0.0 -2.085766534304891 -1.9606633242166027 0.0]\n",
"10-Aug 19:18:45:DEBUG:root:norm of u: 3.129248394715006\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"2 facts verified.\n"
]
},
{
"data": {
"text/plain": [
"delayed_handler (generic function with 4 methods)"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"facts(\"test solve one element model\") do\n",
" X = [0.0 0.0; 10.0 0.0; 10.0 1.0; 0.0 1.0]'\n",
" F = [0 0; 0 0; 0 -2; 0 0]'\n",
"\n",
" # Material properties\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",
" u = zeros(2, 4)\n",
" du = zeros(2, 4)\n",
" R = zeros(2, 4)\n",
" K = zeros(8, 8)\n",
"\n",
" basis(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",
" dbasis(xi) = [-(1-xi[2])/4.0 -(1-xi[1])/4.0\n",
" (1-xi[2])/4.0 -(1+xi[1])/4.0\n",
" (1+xi[2])/4.0 (1+xi[1])/4.0\n",
" -(1+xi[2])/4.0 (1-xi[1])/4.0]\n",
"\n",
" ipoints = 1/sqrt(3)*[-1 -1; 1 -1; 1 1; -1 1]\n",
" iweights = [1, 1, 1, 1]\n",
" free_dofs = [3, 4, 5, 6]\n",
"\n",
" for i=1:10\n",
" calc_local_matrices!(X, u, R, K, basis, dbasis, la, mu, ipoints, iweights)\n",
" du[free_dofs] = K[free_dofs, free_dofs] \\ -(R - F)[free_dofs]\n",
" u += du\n",
" if norm(du) < 1.0e-9\n",
" Logging.debug(\"Converged in $i iterations.\")\n",
" break\n",
" end\n",
" end\n",
"\n",
" # Tested against Elmer solution\n",
" Logging.debug(\"solution vector: \\n $u\")\n",
" @fact u[2, 3] => roughly(-2.222244754401764)\n",
" norm1 = norm(u)\n",
" Logging.debug(\"norm of u: $(norm(u))\")\n",
"\n",
" # We rotate model a bit and make sure that L2 norm is same\n",
" phi = 30/180*pi\n",
" rmat = [\n",
" cos(phi) -sin(phi)\n",
" sin(phi) cos(phi)]\n",
" X = rmat*X\n",
" F = rmat*F\n",
" u = zeros(2, 4)\n",
" for i=1:10\n",
" calc_local_matrices!(X, u, R, K, basis, dbasis, la, mu, ipoints, iweights)\n",
" du[free_dofs] = K[free_dofs, free_dofs] \\ -(R - F)[free_dofs]\n",
" u += du\n",
" if norm(du) < 1.0e-9\n",
" Logging.debug(\"Converged in $i iterations.\")\n",
" break\n",
" end\n",
" end\n",
" Logging.debug(\"solution vector: \\n $u\")\n",
" Logging.debug(\"norm of u: $(norm(u))\")\n",
" @fact norm(u) => roughly(norm1) \n",
"end"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"One element solutions are not particularly interesting so next step is to create function that assembles global matrix from local matrices. Some data types:"
]
},
{
"cell_type": "code",
"execution_count": 55,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"#type Node\n",
"# id :: Int\n",
"# #elements :: Array{Int64, 1}\n",
"#end"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"type Element\n",
" id :: Int\n",
" node_ids :: Array{Int64, 1}\n",
" coordinates :: Array{Float64, 2}\n",
" attributes :: Dict{ASCIIString, Any}\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"type Assembly\n",
" # LHS\n",
" I :: Array{Int64, 1}\n",
" J :: Array{Int64, 1}\n",
" A :: Array{Float64, 1}\n",
" # RHS\n",
" i :: Array{Int64, 1}\n",
" b :: Array{Float64, 1}\n",
" # global dofs for each element\n",
" gdofs :: Dict{Int64, Array{Int64, 1}}\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 56,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"get_integration_scheme (generic function with 2 methods)"
]
},
"execution_count": 56,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"\"\"\"\n",
"Return shape functions and their derivatives for a element.\n",
"\n",
"Parameters\n",
"----------\n",
"element::Element\n",
"\n",
"Returns\n",
"-------\n",
"tuple (basis, dbasis)\n",
"\"\"\"\n",
"function get_shape_functions(el::Element)\n",
" ndim, nnodes = size(el.coordinates)\n",
" #Logging.debug(\"ndim = $ndim, nnodes=$nnodes\")\n",
" if (nnodes == 4) & (ndim == 2)\n",
" basis(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",
" dbasis(xi) = [-(1-xi[2])/4.0 -(1-xi[1])/4.0\n",
" (1-xi[2])/4.0 -(1+xi[1])/4.0\n",
" (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",
" elseif (nnodes == 10) & (ndim == 3)\n",
" basis(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",
" dbasis(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]\n",
" return basis, dbasis\n",
" end\n",
" throw(\"Unknown function space, ndim=$ndim, nnodes=$nnodes\")\n",
"end\n",
"\n",
"\"\"\"\n",
"\"\"\"\n",
"function get_integration_scheme(el::Element, order=2)\n",
" ndim, nnodes = size(el.coordinates)\n",
" if (nnodes == 4) & (order == 2) & (ndim == 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",
" elseif (nnodes == 10) & (order == 2) & (ndim == 3) # c3d10\n",
" # 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]\n",
" return ipoints, iweights\n",
" end\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 79,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"assemble_element! (generic function with 2 methods)"
]
},
"execution_count": 79,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function assemble_element!(ass::Assembly, el::Element, io=2)\n",
"\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",
" Logging.debug(\"Assemble element to gdofs $gdofs\")\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": 58,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"one element assembly\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"10-Aug 21:03:06:DEBUG:root:Adding nodes to array\n",
"10-Aug 21:03:06:DEBUG:root:Creating elements\n",
"10-Aug 21:03:06:DEBUG:root:Starting iteration 1\n",
"10-Aug 21:03:06:DEBUG:root:Assembling\n",
"10-Aug 21:03:06:DEBUG:root:Solution norm = 3.090022136728999\n",
"10-Aug 21:03:06:DEBUG:root:Starting iteration 2\n",
"10-Aug 21:03:06:DEBUG:root:Assembling\n",
"10-Aug 21:03:06:DEBUG:root:Solution norm = 0.3212131602153504\n",
"10-Aug 21:03:06:DEBUG:root:Starting iteration 3\n",
"10-Aug 21:03:06:DEBUG:root:Assembling\n",
"10-Aug 21:03:06:DEBUG:root:Solution norm = 0.040431781940005365\n",
"10-Aug 21:03:06:DEBUG:root:Starting iteration 4\n",
"10-Aug 21:03:06:DEBUG:root:Assembling\n",
"10-Aug 21:03:06:DEBUG:root:Solution norm = 0.0009291101052064257\n",
"10-Aug 21:03:06:DEBUG:root:Starting iteration 5\n",
"10-Aug 21:03:06:DEBUG:root:Assembling\n",
"10-Aug 21:03:06:DEBUG:root:Solution norm = 1.5638899025378415e-7\n",
"10-Aug 21:03:06:DEBUG:root:Starting iteration 6\n",
"10-Aug 21:03:06:DEBUG:root:Assembling\n",
"10-Aug 21:03:06:DEBUG:root:Solution norm = 1.0355045356935844e-14\n",
"10-Aug 21:03:06:DEBUG:root:Converged in 6 iterations.\n",
"10-Aug 21:03:06: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": 58,
"metadata": {},
"output_type": "execute_result"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"1 fact verified.\n"
]
}
],
"source": [
"facts(\"one element assembly\") do\n",
" # Create model\n",
" #Logging.debug(\"Creating nodes\")\n",
" #n1 = Node(1)\n",
" #n2 = Node(2)\n",
" #n3 = Node(3)\n",
" #n4 = Node(4)\n",
" Logging.debug(\"Adding nodes to array\")\n",
" #nodes = [n1.id, n2.id, n3.id, n4.id]\n",
" node_ids = [1, 2, 3, 4]\n",
" coordinates = [10.0 0.0; 10.0 1.0; 0.0 1.0; 0.0 0.0]'\n",
" attributes = Dict(\"Young\" => 90, \"Poisson\" => 0.25)\n",
" Logging.debug(\"Creating elements\")\n",
" el = Element(1, node_ids, coordinates, attributes)\n",
"\n",
" # Initialize elements ready for solution\n",
" el.attributes[\"displacement\"] = zeros(2, 4)\n",
" el.attributes[\"displacement nodal force\"] = zeros(2, 4)\n",
" el.attributes[\"displacement tangent stiffness\"] = zeros(8, 8)\n",
"\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",
"\n",
" # Boundary conditions\n",
" F = [0 0; 0 -2; 0 0; 0 0]'\n",
" F = reshape(F, prod(size(F)))\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 = R - F\n",
" du = zeros(8) # must be determined from ass\n",
" du[free_dofs] = K[free_dofs, free_dofs] \\ -R[free_dofs]\n",
"\n",
" Logging.debug(\"Solution norm = $(norm(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).\n",
"\n",
"First of all, essential boundary conditions are nothing more than equality constraints saying that value for some degree of freedom is fixed. Elimination is just a special case when this value equals to zero. There is couple of different strategies to handle essential boundary conditions. One option is to force them using Lagrange multipliers which can also be used to create all kind of kinematic constraints also. (For example, contact can be considered as a kinematic constraint.) Another option is to manipulate matrix such a way that constraint is satisfied.\n",
"\n",
"Because we are now going \"bottom-up\", we develop something extremely simple that however deals with the problem:"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"type BC\n",
" dofs :: Array{Int64, 1}\n",
" values :: Array{Float64, 1}\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 82,
"metadata": {
"collapsed": false,
"scrolled": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"solve one element problem\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"10-Aug 22:55:49:DEBUG:root:Creating nodes\n",
"10-Aug 22:55:49:DEBUG:root:Creating elements\n",
"10-Aug 22:55:49:INFO:root:create_ldof2gdofmap: dofs per node: 2\n",
"10-Aug 22:55:49:DEBUG:root:Dict(4=>[7,8],2=>[3,4],3=>[5,6],1=>[1,2])\n",
"10-Aug 22:55:50:INFO:root:solve!: dofs per node: 2\n",
"10-Aug 22:55:50:DEBUG:root:Problem size = 8\n",
"10-Aug 22:55:50:DEBUG:root:Starting iteration 1\n",
"10-Aug 22:55:50:DEBUG:root:Assembling\n",
"10-Aug 22:55:50:DEBUG:root:Assemble element to gdofs [1,2,3,4,5,6,7,8]\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Element stiffness matrix\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"10-Aug 22:55:50:DEBUG:root:Adding Dirichlet boundary conditions\n",
"10-Aug 22:55:50:DEBUG:root:dof 5 => 0.0\n",
"10-Aug 22:55:50:DEBUG:root:dof 6 => 0.0\n",
"10-Aug 22:55:50:DEBUG:root:dof 7 => 0.0\n",
"10-Aug 22:55:50:DEBUG:root:dof 8 => 0.0\n",
"10-Aug 22:55:50:DEBUG:root:Added 4 Lagrange multipliers to model\n",
"10-Aug 22:55:50:DEBUG:root:Adding Neumann boundary conditions\n",
"10-Aug 22:55:50:DEBUG:root:Solving system of equations. Total size = 12\n",
"10-Aug 22:55:50:DEBUG:root:nothing\n",
"10-Aug 22:55:50:DEBUG:root:nothing\n",
"10-Aug 22:55:50:DEBUG:root:Solution norm = 3.0900221367289444\n",
"10-Aug 22:55:50:DEBUG:root:Starting iteration 2\n",
"10-Aug 22:55:50:DEBUG:root:Assembling\n",
"10-Aug 22:55:50:DEBUG:root:Assemble element to gdofs [1,2,3,4,5,6,7,8]\n",
"10-Aug 22:55:50:DEBUG:root:Adding Dirichlet boundary conditions\n",
"10-Aug 22:55:50:DEBUG:root:dof 5 => 0.0\n",
"10-Aug 22:55:50:DEBUG:root:dof 6 => 0.0\n",
"10-Aug 22:55:50:DEBUG:root:dof 7 => 0.0\n",
"10-Aug 22:55:50:DEBUG:root:dof 8 => 0.0\n",
"10-Aug 22:55:50:DEBUG:root:Added 4 Lagrange multipliers to model\n",
"10-Aug 22:55:50:DEBUG:root:Adding Neumann boundary conditions\n",
"10-Aug 22:55:50:DEBUG:root:Solving system of equations. Total size = 12\n",
"10-Aug 22:55:50:DEBUG:root:nothing\n",
"10-Aug 22:55:50:DEBUG:root:nothing\n",
"10-Aug 22:55:50:DEBUG:root:Solution norm = 0.32121316021534363\n",
"10-Aug 22:55:50:DEBUG:root:Starting iteration 3\n",
"10-Aug 22:55:50:DEBUG:root:Assembling\n",
"10-Aug 22:55:50:DEBUG:root:Assemble element to gdofs [1,2,3,4,5,6,7,8]\n",
"10-Aug 22:55:50:DEBUG:root:Adding Dirichlet boundary conditions\n",
"10-Aug 22:55:50:DEBUG:root:dof 5 => 0.0\n",
"10-Aug 22:55:50:DEBUG:root:dof 6 => 0.0\n",
"10-Aug 22:55:50:DEBUG:root:dof 7 => 0.0\n",
"10-Aug 22:55:50:DEBUG:root:dof 8 => 0.0\n",
"10-Aug 22:55:50:DEBUG:root:Added 4 Lagrange multipliers to model\n",
"10-Aug 22:55:50:DEBUG:root:Adding Neumann boundary conditions\n",
"10-Aug 22:55:50:DEBUG:root:Solving system of equations. Total size = 12\n",
"10-Aug 22:55:50:DEBUG:root:nothing\n",
"10-Aug 22:55:50:DEBUG:root:nothing\n",
"10-Aug 22:55:50:DEBUG:root:Solution norm = 0.04043178194002483\n",
"10-Aug 22:55:50:DEBUG:root:Starting iteration 4\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Array(Float64,(8,8)) 8x8 Array{Float64,2}:\n",
" 123.2 -15.0 -118.4 -03.0 -61.6 15.0 56.8 03.0\n",
" -15.0 321.2 03.0 -319.4 15.0 -160.6 -03.0 158.8\n",
" -118.4 03.0 123.2 15.0 56.8 -03.0 -61.6 -15.0\n",
" -03.0 -319.4 15.0 321.2 03.0 158.8 -15.0 -160.6\n",
" -61.6 15.0 56.8 03.0 123.2 -15.0 -118.4 -03.0\n",
" 15.0 -160.6 -03.0 158.8 -15.0 321.2 03.0 -319.4\n",
" 56.8 -03.0 -61.6 -15.0 -118.4 03.0 123.2 15.0\n",
" 03.0 158.8 -15.0 -160.6 -03.0 -319.4 15.0 321.2\n",
"Array(Float64,(12,12)) 12x12 Array{Float64,2}:\n",
" 123.2 -15.0 -118.4 -03.0 -61.6 15.0 56.8 03.0 0.0 0.0 0.0 0.0\n",
" -15.0 321.2 03.0 -319.4 15.0 -160.6 -03.0 158.8 0.0 0.0 0.0 0.0\n",
" -118.4 03.0 123.2 15.0 56.8 -03.0 -61.6 -15.0 0.0 0.0 0.0 0.0\n",
" -03.0 -319.4 15.0 321.2 03.0 158.8 -15.0 -160.6 0.0 0.0 0.0 0.0\n",
" -61.6 15.0 56.8 03.0 123.2 -15.0 -118.4 -03.0 1.0 0.0 0.0 0.0\n",
" 15.0 -160.6 -03.0 158.8 -15.0 321.2 03.0 -319.4 0.0 1.0 0.0 0.0\n",
" 56.8 -03.0 -61.6 -15.0 -118.4 03.0 123.2 15.0 0.0 0.0 1.0 0.0\n",
" 03.0 158.8 -15.0 -160.6 -03.0 -319.4 15.0 321.2 0.0 0.0 0.0 1.0\n",
" 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0\n",
"Array(Float64,(1,12)) 1x12 Array{Float64,2}:\n",
" 0.0 0.0 0.0 02.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
"Element stiffness matrix\n",
"Array(Float64,(8,8)) 8x8 Array{Float64,2}:\n",
" 147.61 36.88 -149.16 -55.03 -66.97 1.91 68.52 16.24\n",
" 36.88 343.08 -48.76 -334.42 1.81 -174.07 10.06 165.4 \n",
" -149.16 -48.76 160.72 65.4 63.17 10.41 -74.73 -27.06\n",
" -55.03 -334.42 65.4 330.06 16.65 163.39 -27.02 -159.04\n",
" -66.97 1.81 63.17 16.65 128.11 -15.44 -124.3 -3.03\n",
" 1.91 -174.07 10.41 163.39 -15.44 338.21 3.11 -327.53\n",
" 68.52 10.06 -74.73 -27.02 -124.3 3.11 130.51 13.85\n",
" 16.24 165.4 -27.06 -159.04 -3.03 -327.53 13.85 321.16\n",
"Array(Float64,(12,12)) 12x12 Array{Float64,2}:\n",
" 147.6 36.9 -149.2 -55.0 -67.0 1.9 68.5 16.2 0.0 0.0 0.0 0.0\n",
" 36.9 343.1 -48.8 -334.4 1.8 -174.1 10.1 165.4 0.0 0.0 0.0 0.0\n",
" -149.2 -48.8 160.7 65.4 63.2 10.4 -74.7 -27.1 0.0 0.0 0.0 0.0\n",
" -55.0 -334.4 65.4 330.1 16.7 163.4 -27.0 -159.0 0.0 0.0 0.0 0.0\n",
" -67.0 1.8 63.2 16.7 128.1 -15.4 -124.3 -03.0 1.0 0.0 0.0 0.0\n",
" 1.9 -174.1 10.4 163.4 -15.4 338.2 3.1 -327.5 0.0 1.0 0.0 0.0\n",
" 68.5 10.1 -74.7 -27.0 -124.3 3.1 130.5 13.8 0.0 0.0 1.0 0.0\n",
" 16.2 165.4 -27.1 -159.0 -03.0 -327.5 13.8 321.2 0.0 0.0 0.0 1.0\n",
" 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0\n",
"Array(Float64,(1,12)) 1x12 Array{Float64,2}:\n",
" -2.3 -15.7 05.0 15.2 -20.2 12.2 17.5 -9.6 0.0 0.0 0.0 0.0\n",
"Element stiffness matrix\n",
"Array(Float64,(8,8)) 8x8 Array{Float64,2}:\n",
" 131.01 35.45 -132.72 -52.73 -60.29 1.77 62.0 15.51\n",
" 35.45 313.79 -46.75 -305.49 1.71 -163.9 9.58 155.6 \n",
" -132.72 -46.75 143.74 62.55 56.75 10.12 -67.77 -25.93\n",
" -52.73 -305.49 62.55 301.12 16.11 153.51 -25.93 -149.13\n",
" -60.29 1.71 56.75 16.11 117.72 -14.75 -114.18 -3.07\n",
" 1.77 -163.9 10.12 153.51 -14.75 327.07 2.86 -316.69\n",
" 62.0 9.58 -67.77 -25.93 -114.18 2.86 119.94 13.49\n",
" 15.51 155.6 -25.93 -149.13 -3.07 -316.69 13.49 310.22\n",
"Array(Float64,(12,12)) 12x12 Array{Float64,2}:\n",
" 131.0 35.4 -132.7 -52.7 -60.3 1.8 62.0 15.5 0.0 0.0 0.0 0.0\n",
" 35.4 313.8 -46.7 -305.5 1.7 -163.9 9.6 155.6 0.0 0.0 0.0 0.0\n",
" -132.7 -46.7 143.7 62.6 56.7 10.1 -67.8 -25.9 0.0 0.0 0.0 0.0\n",
" -52.7 -305.5 62.6 301.1 16.1 153.5 -25.9 -149.1 0.0 0.0 0.0 0.0\n",
" -60.3 1.7 56.7 16.1 117.7 -14.8 -114.2 -3.1 1.0 0.0 0.0 0.0\n",
" 1.8 -163.9 10.1 153.5 -14.8 327.1 2.9 -316.7 0.0 1.0 0.0 0.0\n",
" 62.0 9.6 -67.8 -25.9 -114.2 2.9 119.9 13.5 0.0 0.0 1.0 0.0\n",
" 15.5 155.6 -25.9 -149.1 -3.1 -316.7 13.5 310.2 0.0 0.0 0.0 1.0\n",
" 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0\n",
"Array(Float64,(1,12)) 1x12 Array{Float64,2}:\n",
" -0.0 -0.6 0.1 0.6 -19.7 3.2 19.6 -1.1 0.0 0.0 0.0 0.0\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"10-Aug 22:55:50:DEBUG:root:Assembling\n",
"10-Aug 22:55:50:DEBUG:root:Assemble element to gdofs [1,2,3,4,5,6,7,8]\n",
"10-Aug 22:55:50:DEBUG:root:Adding Dirichlet boundary conditions\n",
"10-Aug 22:55:50:DEBUG:root:dof 5 => 0.0\n",
"10-Aug 22:55:50:DEBUG:root:dof 6 => 0.0\n",
"10-Aug 22:55:50:DEBUG:root:dof 7 => 0.0\n",
"10-Aug 22:55:50:DEBUG:root:dof 8 => 0.0\n",
"10-Aug 22:55:50:DEBUG:root:Added 4 Lagrange multipliers to model\n",
"10-Aug 22:55:50:DEBUG:root:Adding Neumann boundary conditions\n",
"10-Aug 22:55:50:DEBUG:root:Solving system of equations. Total size = 12\n",
"10-Aug 22:55:50:DEBUG:root:nothing\n",
"10-Aug 22:55:50:DEBUG:root:nothing\n",
"10-Aug 22:55:50:DEBUG:root:Solution norm = 0.0009291101052060104\n",
"10-Aug 22:55:50:DEBUG:root:Starting iteration 5\n",
"10-Aug 22:55:50:DEBUG:root:Assembling\n",
"10-Aug 22:55:50:DEBUG:root:Assemble element to gdofs [1,2,3,4,5,6,7,8]\n",
"10-Aug 22:55:50:DEBUG:root:Adding Dirichlet boundary conditions\n",
"10-Aug 22:55:50:DEBUG:root:dof 5 => 0.0\n",
"10-Aug 22:55:50:DEBUG:root:dof 6 => 0.0\n",
"10-Aug 22:55:50:DEBUG:root:dof 7 => 0.0\n",
"10-Aug 22:55:50:DEBUG:root:dof 8 => 0.0\n",
"10-Aug 22:55:50:DEBUG:root:Added 4 Lagrange multipliers to model\n",
"10-Aug 22:55:50:DEBUG:root:Adding Neumann boundary conditions\n",
"10-Aug 22:55:50:DEBUG:root:Solving system of equations. Total size = 12\n",
"10-Aug 22:55:50:DEBUG:root:nothing\n",
"10-Aug 22:55:50:DEBUG:root:nothing\n",
"10-Aug 22:55:50:DEBUG:root:Solution norm = 1.563889898905983e-7\n",
"10-Aug 22:55:50:DEBUG:root:Starting iteration 6\n",
"10-Aug 22:55:50:DEBUG:root:Assembling\n",
"10-Aug 22:55:50:DEBUG:root:Assemble element to gdofs [1,2,3,4,5,6,7,8]\n",
"10-Aug 22:55:50:DEBUG:root:Adding Dirichlet boundary conditions\n",
"10-Aug 22:55:50:DEBUG:root:dof 5 => 0.0\n",
"10-Aug 22:55:50:DEBUG:root:dof 6 => 0.0\n",
"10-Aug 22:55:50:DEBUG:root:dof 7 => 0.0\n",
"10-Aug 22:55:50:DEBUG:root:dof 8 => 0.0\n",
"10-Aug 22:55:50:DEBUG:root:Added 4 Lagrange multipliers to model\n",
"10-Aug 22:55:50:DEBUG:root:Adding Neumann boundary conditions\n",
"10-Aug 22:55:50:DEBUG:root:Solving system of equations. Total size = 12\n",
"10-Aug 22:55:50:DEBUG:root:nothing\n",
"10-Aug 22:55:50:DEBUG:root:nothing\n",
"10-Aug 22:55:50:DEBUG:root:Solution norm = 1.2782462771683917e-14\n",
"10-Aug 22:55:50:DEBUG:root:Converged in 6 iterations.\n",
"10-Aug 22:55:50:DEBUG:root:Displacement of element = \n",
"[-0.3991450609547439 -0.07228582695592495 0.0 0.0\n",
" -2.1779892317073513 -2.2222447544017654 0.0 0.0]\n",
"10-Aug 22:55:50:DEBUG:root:Creating elements\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Element stiffness matrix\n",
"Array(Float64,(8,8)) 8x8 Array{Float64,2}:\n",
" 130.66 36.04 -132.46 -53.26 -60.05 1.58 61.86 15.64\n",
" 36.04 312.24 -47.29 -303.89 1.52 -163.43 9.73 155.09\n",
" -132.46 -47.29 143.55 63.02 56.54 10.29 -67.63 -26.02\n",
" -53.26 -303.89 63.02 299.46 16.27 152.96 -26.02 -148.53\n",
" -60.05 1.52 56.54 16.27 117.21 -14.68 -113.7 -3.11\n",
" 1.58 -163.43 10.29 152.96 -14.68 326.61 2.81 -316.14\n",
" 61.86 9.73 -67.63 -26.02 -113.7 2.81 119.47 13.49\n",
" 15.64 155.09 -26.02 -148.53 -3.11 -316.14 13.49 309.58\n",
"Array(Float64,(12,12)) 12x12 Array{Float64,2}:\n",
" 130.7 36.0 -132.5 -53.3 -60.1 1.6 61.9 15.6 0.0 0.0 0.0 0.0\n",
" 36.0 312.2 -47.3 -303.9 1.5 -163.4 9.7 155.1 0.0 0.0 0.0 0.0\n",
" -132.5 -47.3 143.5 63.0 56.5 10.3 -67.6 -26.0 0.0 0.0 0.0 0.0\n",
" -53.3 -303.9 63.0 299.5 16.3 153.0 -26.0 -148.5 0.0 0.0 0.0 0.0\n",
" -60.1 1.5 56.5 16.3 117.2 -14.7 -113.7 -3.1 1.0 0.0 0.0 0.0\n",
" 1.6 -163.4 10.3 153.0 -14.7 326.6 2.8 -316.1 0.0 1.0 0.0 0.0\n",
" 61.9 9.7 -67.6 -26.0 -113.7 2.8 119.5 13.5 0.0 0.0 1.0 0.0\n",
" 15.6 155.1 -26.0 -148.5 -3.1 -316.1 13.5 309.6 0.0 0.0 0.0 1.0\n",
" 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0\n",
"Array(Float64,(1,12)) 1x12 Array{Float64,2}:\n",
" 0.0 -0.0 -0.0 0.0 -19.9 2.8 19.9 -0.8 0.0 0.0 0.0 0.0\n",
"Element stiffness matrix\n",
"Array(Float64,(8,8)) 8x8 Array{Float64,2}:\n",
" 130.66 36.06 -132.47 -53.28 -60.05 1.57 61.86 15.64\n",
" 36.06 312.22 -47.3 -303.88 1.51 -163.43 9.73 155.08\n",
" -132.47 -47.3 143.56 63.03 56.54 10.29 -67.63 -26.02\n",
" -53.28 -303.88 63.03 299.44 16.27 152.96 -26.02 -148.52\n",
" -60.05 1.51 56.54 16.27 117.21 -14.67 -113.69 -3.11\n",
" 1.57 -163.43 10.29 152.96 -14.67 326.61 2.81 -316.14\n",
" 61.86 9.73 -67.63 -26.02 -113.69 2.81 119.46 13.49\n",
" 15.64 155.08 -26.02 -148.52 -3.11 -316.14 13.49 309.58\n",
"Array(Float64,(12,12)) 12x12 Array{Float64,2}:\n",
" 130.7 36.1 -132.5 -53.3 -60.1 1.6 61.9 15.6 0.0 0.0 0.0 0.0\n",
" 36.1 312.2 -47.3 -303.9 1.5 -163.4 9.7 155.1 0.0 0.0 0.0 0.0\n",
" -132.5 -47.3 143.6 63.0 56.5 10.3 -67.6 -26.0 0.0 0.0 0.0 0.0\n",
" -53.3 -303.9 63.0 299.4 16.3 153.0 -26.0 -148.5 0.0 0.0 0.0 0.0\n",
" -60.1 1.5 56.5 16.3 117.2 -14.7 -113.7 -3.1 1.0 0.0 0.0 0.0\n",
" 1.6 -163.4 10.3 153.0 -14.7 326.6 2.8 -316.1 0.0 1.0 0.0 0.0\n",
" 61.9 9.7 -67.6 -26.0 -113.7 2.8 119.5 13.5 0.0 0.0 1.0 0.0\n",
" 15.6 155.1 -26.0 -148.5 -3.1 -316.1 13.5 309.6 0.0 0.0 0.0 1.0\n",
" 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0\n",
"Array(Float64,(1,12)) 1x12 Array{Float64,2}:\n",
" 0.0 -0.0 0.0 0.0 -19.9 2.8 19.9 -0.8 0.0 0.0 0.0 0.0\n",
"Element stiffness matrix\n",
"Array(Float64,(8,8)) 8x8 Array{Float64,2}:\n",
" 130.66 36.06 -132.47 -53.28 -60.05 1.57 61.86 15.64\n",
" 36.06 312.22 -47.3 -303.88 1.51 -163.43 9.73 155.08\n",
" -132.47 -47.3 143.56 63.03 56.54 10.29 -67.63 -26.02\n",
" -53.28 -303.88 63.03 299.44 16.27 152.96 -26.02 -148.52\n",
" -60.05 1.51 56.54 16.27 117.21 -14.67 -113.69 -3.11\n",
" 1.57 -163.43 10.29 152.96 -14.67 326.61 2.81 -316.14\n",
" 61.86 9.73 -67.63 -26.02 -113.69 2.81 119.46 13.49\n",
" 15.64 155.08 -26.02 -148.52 -3.11 -316.14 13.49 309.58\n",
"Array(Float64,(12,12)) 12x12 Array{Float64,2}:\n",
" 130.7 36.1 -132.5 -53.3 -60.1 1.6 61.9 15.6 0.0 0.0 0.0 0.0\n",
" 36.1 312.2 -47.3 -303.9 1.5 -163.4 9.7 155.1 0.0 0.0 0.0 0.0\n",
" -132.5 -47.3 143.6 63.0 56.5 10.3 -67.6 -26.0 0.0 0.0 0.0 0.0\n",
" -53.3 -303.9 63.0 299.4 16.3 153.0 -26.0 -148.5 0.0 0.0 0.0 0.0\n",
" -60.1 1.5 56.5 16.3 117.2 -14.7 -113.7 -3.1 1.0 0.0 0.0 0.0\n",
" 1.6 -163.4 10.3 153.0 -14.7 326.6 2.8 -316.1 0.0 1.0 0.0 0.0\n",
" 61.9 9.7 -67.6 -26.0 -113.7 2.8 119.5 13.5 0.0 0.0 1.0 0.0\n",
" 15.6 155.1 -26.0 -148.5 -3.1 -316.1 13.5 309.6 0.0 0.0 0.0 1.0\n",
" 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0\n",
"Array(Float64,(1,12)) 1x12 Array{Float64,2}:\n",
" 0.0 -0.0 -0.0 0.0 -19.9 2.8 19.9 -0.8 0.0 0.0 0.0 0.0\n",
"1 fact verified.\n",
"solve two element problem\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"10-Aug 22:55:50:INFO:root:create_ldof2gdofmap: dofs per node: 2\n",
"10-Aug 22:55:50:DEBUG:root:Dict(4=>[7,8],2=>[3,4],3=>[5,6],5=>[9,10],6=>[11,12],1=>[1,2])\n",
"10-Aug 22:55:50:INFO:root:solve!: dofs per node: 2\n",
"10-Aug 22:55:50:DEBUG:root:Problem size = 12\n",
"10-Aug 22:55:50:DEBUG:root:Starting iteration 1\n",
"10-Aug 22:55:50:DEBUG:root:Assembling\n",
"10-Aug 22:55:50:DEBUG:root:Assemble element to gdofs [1,2,3,4,9,10,7,8]\n",
"10-Aug 22:55:50:DEBUG:root:Assemble element to gdofs [3,4,5,6,11,12,9,10]\n",
"10-Aug 22:55:50:DEBUG:root:Adding Dirichlet boundary conditions\n",
"10-Aug 22:55:50:DEBUG:root:dof 1 => 0.0\n",
"10-Aug 22:55:50:DEBUG:root:dof 2 => 0.0\n",
"10-Aug 22:55:50:DEBUG:root:dof 7 => 0.0\n",
"10-Aug 22:55:50:DEBUG:root:dof 8 => 0.0\n",
"10-Aug 22:55:50:DEBUG:root:Added 4 Lagrange multipliers to model\n",
"10-Aug 22:55:50:DEBUG:root:Adding Neumann boundary conditions\n",
"10-Aug 22:55:50:DEBUG:root:Solving system of equations. Total size = 16\n",
"10-Aug 22:55:50:DEBUG:root:nothing\n",
"10-Aug 22:55:50:DEBUG:root:nothing\n",
"10-Aug 22:55:50:DEBUG:root:Solution norm = 12.031677381267034\n",
"10-Aug 22:55:50:DEBUG:root:Starting iteration 2\n",
"10-Aug 22:55:50:DEBUG:root:Assembling\n",
"10-Aug 22:55:50:DEBUG:root:Assemble element to gdofs [1,2,3,4,9,10,7,8]\n",
"10-Aug 22:55:50:DEBUG:root:Assemble element to gdofs [3,4,5,6,11,12,9,10]\n",
"10-Aug 22:55:50:DEBUG:root:Adding Dirichlet boundary conditions\n",
"10-Aug 22:55:50:DEBUG:root:dof 1 => 0.0\n",
"10-Aug 22:55:50:DEBUG:root:dof 2 => 0.0\n",
"10-Aug 22:55:50:DEBUG:root:dof 7 => 0.0\n",
"10-Aug 22:55:50:DEBUG:root:dof 8 => 0.0\n",
"10-Aug 22:55:50:DEBUG:root:Added 4 Lagrange multipliers to model\n",
"10-Aug 22:55:50:DEBUG:root:Adding Neumann boundary conditions\n",
"10-Aug 22:55:50:DEBUG:root:Solving system of equations. Total size = 16\n",
"10-Aug 22:55:50:DEBUG:root:nothing\n",
"10-Aug 22:55:50:DEBUG:root:nothing\n",
"10-Aug 22:55:50:DEBUG:root:Solution norm = 8.151050361276255\n",
"10-Aug 22:55:50:DEBUG:root:Starting iteration 3\n",
"10-Aug 22:55:50:DEBUG:root:Assembling\n",
"10-Aug 22:55:50:DEBUG:root:Assemble element to gdofs [1,2,3,4,9,10,7,8]\n",
"10-Aug 22:55:50:DEBUG:root:Assemble element to gdofs [3,4,5,6,11,12,9,10]\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Element stiffness matrix\n",
"Array(Float64,(8,8)) 8x8 Array{Float64,2}:\n",
" 66.4 15.0 23.6 -03.0 -33.2 -15.0 -56.8 03.0\n",
" 15.0 162.4 03.0 77.6 -15.0 -81.2 -03.0 -158.8\n",
" 23.6 03.0 66.4 -15.0 -56.8 -03.0 -33.2 15.0\n",
" -03.0 77.6 -15.0 162.4 03.0 -158.8 15.0 -81.2\n",
" -33.2 -15.0 -56.8 03.0 66.4 15.0 23.6 -03.0\n",
" -15.0 -81.2 -03.0 -158.8 15.0 162.4 03.0 77.6\n",
" -56.8 -03.0 -33.2 15.0 23.6 03.0 66.4 -15.0\n",
" 03.0 -158.8 15.0 -81.2 -03.0 77.6 -15.0 162.4\n",
"Element stiffness matrix\n",
"Array(Float64,(8,8)) 8x8 Array{Float64,2}:\n",
" 66.4 15.0 23.6 -03.0 -33.2 -15.0 -56.8 03.0\n",
" 15.0 162.4 03.0 77.6 -15.0 -81.2 -03.0 -158.8\n",
" 23.6 03.0 66.4 -15.0 -56.8 -03.0 -33.2 15.0\n",
" -03.0 77.6 -15.0 162.4 03.0 -158.8 15.0 -81.2\n",
" -33.2 -15.0 -56.8 03.0 66.4 15.0 23.6 -03.0\n",
" -15.0 -81.2 -03.0 -158.8 15.0 162.4 03.0 77.6\n",
" -56.8 -03.0 -33.2 15.0 23.6 03.0 66.4 -15.0\n",
" 03.0 -158.8 15.0 -81.2 -03.0 77.6 -15.0 162.4\n",
"Array(Float64,(16,16)) 16x16 Array{Float64,2}:\n",
" 66.4 15.0 23.6 -03.0 0.0 0.0 -56.8 03.0 -33.2 -15.0 0.0 0.0 1.0 0.0 0.0 0.0\n",
" 15.0 162.4 03.0 77.6 0.0 0.0 -03.0 -158.8 -15.0 -81.2 0.0 0.0 0.0 1.0 0.0 0.0\n",
" 23.6 03.0 132.8 0.0 23.6 -03.0 -33.2 15.0 -113.6 0.0 -33.2 -15.0 0.0 0.0 0.0 0.0\n",
" -03.0 77.6 0.0 324.8 03.0 77.6 15.0 -81.2 0.0 -317.6 -15.0 -81.2 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 23.6 03.0 66.4 -15.0 0.0 0.0 -33.2 15.0 -56.8 -03.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 -03.0 77.6 -15.0 162.4 0.0 0.0 15.0 -81.2 03.0 -158.8 0.0 0.0 0.0 0.0\n",
" -56.8 -03.0 -33.2 15.0 0.0 0.0 66.4 -15.0 23.6 03.0 0.0 0.0 0.0 0.0 1.0 0.0\n",
" 03.0 -158.8 15.0 -81.2 0.0 0.0 -15.0 162.4 -03.0 77.6 0.0 0.0 0.0 0.0 0.0 1.0\n",
" -33.2 -15.0 -113.6 0.0 -33.2 15.0 23.6 -03.0 132.8 0.0 23.6 03.0 0.0 0.0 0.0 0.0\n",
" -15.0 -81.2 0.0 -317.6 15.0 -81.2 03.0 77.6 0.0 324.8 -03.0 77.6 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 -33.2 -15.0 -56.8 03.0 0.0 0.0 23.6 -03.0 66.4 15.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 -15.0 -81.2 -03.0 -158.8 0.0 0.0 03.0 77.6 15.0 162.4 0.0 0.0 0.0 0.0\n",
" 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
"Array(Float64,(1,16)) 1x16 Array{Float64,2}:\n",
" 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 02.0 0.0 0.0 0.0 0.0\n",
"Element stiffness matrix\n",
"Array(Float64,(8,8)) 8x8 Array{Float64,2}:\n",
" 520.78 72.26 330.9 62.7 -397.04 -45.87 -454.64 -89.09\n",
" 72.26 461.85 83.07 254.3 -47.57 -243.98 -107.75 -472.18\n",
" 330.9 83.07 874.92 211.87 -895.33 -206.2 -310.49 -88.74\n",
" 62.7 254.3 211.87 708.11 -183.65 -617.73 -90.92 -344.68\n",
" -397.04 -47.57 -895.33 -183.65 983.14 157.73 309.22 73.49\n",
" -45.87 -243.98 -206.2 -617.73 157.73 615.62 94.34 246.08\n",
" -454.64 -107.75 -310.49 -90.92 309.22 94.34 455.91 104.34\n",
" -89.09 -472.18 -88.74 -344.68 73.49 246.08 104.34 570.77\n",
"Element stiffness matrix\n",
"Array(Float64,(8,8)) 8x8 Array{Float64,2}:\n",
" 520.78 72.26 330.9 62.7 -397.04 -45.87 -454.64 -89.09\n",
" 72.26 461.85 83.07 254.3 -47.57 -243.98 -107.75 -472.18\n",
" 330.9 83.07 874.92 211.87 -895.33 -206.2 -310.49 -88.74\n",
" 62.7 254.3 211.87 708.11 -183.65 -617.73 -90.92 -344.68\n",
" -397.04 -47.57 -895.33 -183.65 983.14 157.73 309.22 73.49\n",
" -45.87 -243.98 -206.2 -617.73 157.73 615.62 94.34 246.08\n",
" -454.64 -107.75 -310.49 -90.92 309.22 94.34 455.91 104.34\n",
" -89.09 -472.18 -88.74 -344.68 73.49 246.08 104.34 570.77\n",
"Array(Float64,(16,16)) 16x16 Array{Float64,2}:\n",
" 520.8 72.3 330.9 62.7 0.0 0.0 -454.6 -89.1 -397.0 -45.9 0.0 0.0 1.0 0.0 0.0 0.0\n",
" 72.3 461.9 83.1 254.3 0.0 0.0 -107.8 -472.2 -47.6 -244.0 0.0 0.0 0.0 1.0 0.0 0.0\n",
" 330.9 83.1 1395.7 284.1 330.9 62.7 -310.5 -88.7 -1350.0 -295.3 -397.0 -45.9 0.0 0.0 0.0 0.0\n",
" 62.7 254.3 284.1 1170.0 83.1 254.3 -90.9 -344.7 -291.4 -1089.9 -47.6 -244.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 330.9 83.1 874.9 211.9 0.0 0.0 -310.5 -88.7 -895.3 -206.2 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 62.7 254.3 211.9 708.1 0.0 0.0 -90.9 -344.7 -183.7 -617.7 0.0 0.0 0.0 0.0\n",
" -454.6 -107.8 -310.5 -90.9 0.0 0.0 455.9 104.3 309.2 94.3 0.0 0.0 0.0 0.0 1.0 0.0\n",
" -89.1 -472.2 -88.7 -344.7 0.0 0.0 104.3 570.8 73.5 246.1 0.0 0.0 0.0 0.0 0.0 1.0\n",
" -397.0 -47.6 -1350.0 -291.4 -310.5 -90.9 309.2 73.5 1439.1 262.1 309.2 94.3 0.0 0.0 0.0 0.0\n",
" -45.9 -244.0 -295.3 -1089.9 -88.7 -344.7 94.3 246.1 262.1 1186.4 73.5 246.1 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 -397.0 -47.6 -895.3 -183.7 0.0 0.0 309.2 73.5 983.1 157.7 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 -45.9 -244.0 -206.2 -617.7 0.0 0.0 94.3 246.1 157.7 615.6 0.0 0.0 0.0 0.0\n",
" 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
"Array(Float64,(1,16)) 1x16 Array{Float64,2}:\n",
" -453.5 -212.6 -1168.0 -759.0 -714.5 -546.4 300.0 466.2 1168.0 759.0 868.1 294.8 0.0 0.0 0.0 0.0\n",
"Element stiffness matrix\n",
"Array(Float64,(8,8)) 8x8 Array{Float64,2}:\n",
" 43.42 28.69 48.59 17.79 -57.52 -15.59 -34.48 -30.89\n",
" 28.69 51.46 22.52 33.82 -15.89 -22.99 -35.32 -62.29\n",
" 48.59 22.52 142.25 54.77 -152.3 -53.31 -38.54 -23.98\n",
" 17.79 33.82 54.77 88.5 -48.04 -72.78 -24.51 -49.53\n",
" -57.52 -15.89 -152.3 -48.04 168.56 42.6 41.26 21.33\n",
" -15.59 -22.99 -53.31 -72.78 42.6 67.46 26.29 28.32\n",
" -34.48 -35.32 -38.54 -24.51 41.26 26.29 31.77 33.54\n",
" -30.89 -62.29 -23.98 -49.53 21.33 28.32 33.54 83.5 \n",
"Element stiffness matrix\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"10-Aug 22:55:50:DEBUG:root:Adding Dirichlet boundary conditions\n",
"10-Aug 22:55:50:DEBUG:root:dof 1 => 0.0\n",
"10-Aug 22:55:50:DEBUG:root:dof 2 => 0.0\n",
"10-Aug 22:55:50:DEBUG:root:dof 7 => 0.0\n",
"10-Aug 22:55:50:DEBUG:root:dof 8 => 0.0\n",
"10-Aug 22:55:50:DEBUG:root:Added 4 Lagrange multipliers to model\n",
"10-Aug 22:55:50:DEBUG:root:Adding Neumann boundary conditions\n",
"10-Aug 22:55:50:DEBUG:root:Solving system of equations. Total size = 16\n",
"10-Aug 22:55:50:DEBUG:root:nothing\n",
"10-Aug 22:55:50:DEBUG:root:nothing\n",
"10-Aug 22:55:50:DEBUG:root:Solution norm = 3.886954756970209\n",
"10-Aug 22:55:50:DEBUG:root:Starting iteration 4\n",
"10-Aug 22:55:50:DEBUG:root:Assembling\n",
"10-Aug 22:55:50:DEBUG:root:Assemble element to gdofs [1,2,3,4,9,10,7,8]\n",
"10-Aug 22:55:50:DEBUG:root:Assemble element to gdofs [3,4,5,6,11,12,9,10]\n",
"10-Aug 22:55:50:DEBUG:root:Adding Dirichlet boundary conditions\n",
"10-Aug 22:55:50:DEBUG:root:dof 1 => 0.0\n",
"10-Aug 22:55:50:DEBUG:root:dof 2 => 0.0\n",
"10-Aug 22:55:50:DEBUG:root:dof 7 => 0.0\n",
"10-Aug 22:55:50:DEBUG:root:dof 8 => 0.0\n",
"10-Aug 22:55:50:DEBUG:root:Added 4 Lagrange multipliers to model\n",
"10-Aug 22:55:50:DEBUG:root:Adding Neumann boundary conditions\n",
"10-Aug 22:55:50:DEBUG:root:Solving system of equations. Total size = 16\n",
"10-Aug 22:55:50:DEBUG:root:nothing\n",
"10-Aug 22:55:50:DEBUG:root:nothing\n",
"10-Aug 22:55:50:DEBUG:root:Solution norm = 2.9651628976855293\n",
"10-Aug 22:55:50:DEBUG:root:Starting iteration 5\n",
"10-Aug 22:55:50:DEBUG:root:Assembling\n",
"10-Aug 22:55:50:DEBUG:root:Assemble element to gdofs [1,2,3,4,9,10,7,8]\n",
"10-Aug 22:55:50:DEBUG:root:Assemble element to gdofs [3,4,5,6,11,12,9,10]\n",
"10-Aug 22:55:50:DEBUG:root:Adding Dirichlet boundary conditions\n",
"10-Aug 22:55:50:DEBUG:root:dof 1 => 0.0\n",
"10-Aug 22:55:50:DEBUG:root:dof 2 => 0.0\n",
"10-Aug 22:55:50:DEBUG:root:dof 7 => 0.0\n",
"10-Aug 22:55:50:DEBUG:root:dof 8 => 0.0\n",
"10-Aug 22:55:50:DEBUG:root:Added 4 Lagrange multipliers to model\n",
"10-Aug 22:55:50:DEBUG:root:Adding Neumann boundary conditions\n",
"10-Aug 22:55:50:DEBUG:root:Solving system of equations. Total size = 16\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Array(Float64,(8,8)) 8x8 Array{Float64,2}:\n",
" 43.42 28.69 48.59 17.79 -57.52 -15.59 -34.48 -30.89\n",
" 28.69 51.46 22.52 33.82 -15.89 -22.99 -35.32 -62.29\n",
" 48.59 22.52 142.25 54.77 -152.3 -53.31 -38.54 -23.98\n",
" 17.79 33.82 54.77 88.5 -48.04 -72.78 -24.51 -49.53\n",
" -57.52 -15.89 -152.3 -48.04 168.56 42.6 41.26 21.33\n",
" -15.59 -22.99 -53.31 -72.78 42.6 67.46 26.29 28.32\n",
" -34.48 -35.32 -38.54 -24.51 41.26 26.29 31.77 33.54\n",
" -30.89 -62.29 -23.98 -49.53 21.33 28.32 33.54 83.5 \n",
"Array(Float64,(16,16)) 16x16 Array{Float64,2}:\n",
" 43.4 28.7 48.6 17.8 0.0 0.0 -34.5 -30.9 -57.5 -15.6 0.0 0.0 1.0 0.0 0.0 0.0\n",
" 28.7 51.5 22.5 33.8 0.0 0.0 -35.3 -62.3 -15.9 -23.0 0.0 0.0 0.0 1.0 0.0 0.0\n",
" 48.6 22.5 185.7 83.5 48.6 17.8 -38.5 -24.0 -186.8 -84.2 -57.5 -15.6 0.0 0.0 0.0 0.0\n",
" 17.8 33.8 83.5 140.0 22.5 33.8 -24.5 -49.5 -83.4 -135.1 -15.9 -23.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 48.6 22.5 142.2 54.8 0.0 0.0 -38.5 -24.0 -152.3 -53.3 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 17.8 33.8 54.8 88.5 0.0 0.0 -24.5 -49.5 -48.0 -72.8 0.0 0.0 0.0 0.0\n",
" -34.5 -35.3 -38.5 -24.5 0.0 0.0 31.8 33.5 41.3 26.3 0.0 0.0 0.0 0.0 1.0 0.0\n",
" -30.9 -62.3 -24.0 -49.5 0.0 0.0 33.5 83.5 21.3 28.3 0.0 0.0 0.0 0.0 0.0 1.0\n",
" -57.5 -15.9 -186.8 -83.4 -38.5 -24.5 41.3 21.3 200.3 76.1 41.3 26.3 0.0 0.0 0.0 0.0\n",
" -15.6 -23.0 -84.2 -135.1 -24.0 -49.5 26.3 28.3 76.1 151.0 21.3 28.3 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 -57.5 -15.9 -152.3 -48.0 0.0 0.0 41.3 21.3 168.6 42.6 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 -15.6 -23.0 -53.3 -72.8 0.0 0.0 26.3 28.3 42.6 67.5 0.0 0.0 0.0 0.0\n",
" 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
"Array(Float64,(1,16)) 1x16 Array{Float64,2}:\n",
" 27.5 08.5 22.1 17.8 -5.4 9.3 -21.6 -15.8 -22.1 -17.8 -0.5 -0.0 0.0 0.0 0.0 0.0\n",
"Element stiffness matrix\n",
"Array(Float64,(8,8)) 8x8 Array{Float64,2}:\n",
" 116.19 1.61 71.4 10.34 -89.72 1.21 -97.86 -13.16\n",
" 1.61 96.17 17.73 49.31 0.67 -49.8 -20.01 -95.68\n",
" 71.4 17.73 191.45 46.09 -197.12 -40.75 -65.73 -23.07\n",
" 10.34 49.31 46.09 167.18 -32.77 -134.57 -23.66 -81.92\n",
" -89.72 0.67 -197.12 -32.77 219.04 18.96 67.81 13.14\n",
" 1.21 -49.8 -40.75 -134.57 18.96 135.27 20.58 49.1 \n",
" -97.86 -20.01 -65.73 -23.66 67.81 20.58 95.78 23.09\n",
" -13.16 -95.68 -23.07 -81.92 13.14 49.1 23.09 128.5 \n",
"Element stiffness matrix\n",
"Array(Float64,(8,8)) 8x8 Array{Float64,2}:\n",
" 116.19 1.61 71.4 10.34 -89.72 1.21 -97.86 -13.16\n",
" 1.61 96.17 17.73 49.31 0.67 -49.8 -20.01 -95.68\n",
" 71.4 17.73 191.45 46.09 -197.12 -40.75 -65.73 -23.07\n",
" 10.34 49.31 46.09 167.18 -32.77 -134.57 -23.66 -81.92\n",
" -89.72 0.67 -197.12 -32.77 219.04 18.96 67.81 13.14\n",
" 1.21 -49.8 -40.75 -134.57 18.96 135.27 20.58 49.1 \n",
" -97.86 -20.01 -65.73 -23.66 67.81 20.58 95.78 23.09\n",
" -13.16 -95.68 -23.07 -81.92 13.14 49.1 23.09 128.5 \n",
"Array(Float64,(16,16)) 16x16 Array{Float64,2}:\n",
" 116.2 1.6 71.4 10.3 0.0 0.0 -97.9 -13.2 -89.7 1.2 0.0 0.0 1.0 0.0 0.0 0.0\n",
" 1.6 96.2 17.7 49.3 0.0 0.0 -20.0 -95.7 0.7 -49.8 0.0 0.0 0.0 1.0 0.0 0.0\n",
" 71.4 17.7 307.6 47.7 71.4 10.3 -65.7 -23.1 -295.0 -53.9 -89.7 1.2 0.0 0.0 0.0 0.0\n",
" 10.3 49.3 47.7 263.4 17.7 49.3 -23.7 -81.9 -52.8 -230.3 0.7 -49.8 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 71.4 17.7 191.5 46.1 0.0 0.0 -65.7 -23.1 -197.1 -40.8 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 10.3 49.3 46.1 167.2 0.0 0.0 -23.7 -81.9 -32.8 -134.6 0.0 0.0 0.0 0.0\n",
" -97.9 -20.0 -65.7 -23.7 0.0 0.0 95.8 23.1 67.8 20.6 0.0 0.0 0.0 0.0 1.0 0.0\n",
" -13.2 -95.7 -23.1 -81.9 0.0 0.0 23.1 128.5 13.1 49.1 0.0 0.0 0.0 0.0 0.0 1.0\n",
" -89.7 0.7 -295.0 -52.8 -65.7 -23.7 67.8 13.1 314.8 42.0 67.8 20.6 0.0 0.0 0.0 0.0\n",
" 1.2 -49.8 -53.9 -230.3 -23.1 -81.9 20.6 49.1 42.0 263.8 13.1 49.1 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 -89.7 0.7 -197.1 -32.8 0.0 0.0 67.8 13.1 219.0 19.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 1.2 -49.8 -40.8 -134.6 0.0 0.0 20.6 49.1 19.0 135.3 0.0 0.0 0.0 0.0\n",
" 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
"Array(Float64,(1,16)) 1x16 Array{Float64,2}:\n",
" -02.5 8.8 -27.7 -26.3 -25.2 -35.2 -10.3 26.0 27.7 26.3 38.0 2.3 0.0 0.0 0.0 0.0\n",
"Element stiffness matrix\n",
"Array(Float64,(8,8)) 8x8 Array{Float64,2}:\n",
" 80.58 18.37 53.97 14.28 -64.27 -7.29 -70.28 -25.36\n",
" 18.37 29.48 19.23 20.58 -7.58 -16.78 -30.02 -33.28\n",
" 53.97 19.23 139.54 47.2 -146.69 -42.11 -46.81 -24.33\n",
" 14.28 20.58 47.2 74.51 -36.82 -59.55 -24.66 -35.54\n",
" -64.27 -7.58 -146.69 -36.82 159.26 28.44 51.7 15.96\n",
" -7.29 -16.78 -42.11 -59.55 28.44 56.47 20.96 19.86\n",
" -70.28 -30.02 -46.81 -24.66 51.7 20.96 65.39 33.72\n",
" -25.36 -33.28 -24.33 -35.54 15.96 19.86 33.72 48.96\n",
"Element stiffness matrix\n",
"Array(Float64,(8,8)) 8x8 Array{Float64,2}:\n",
" 80.58 18.37 53.97 14.28 -64.27 -7.29 -70.28 -25.36\n",
" 18.37 29.48 19.23 20.58 -7.58 -16.78 -30.02 -33.28\n",
" 53.97 19.23 139.54 47.2 -146.69 -42.11 -46.81 -24.33\n",
" 14.28 20.58 47.2 74.51 -36.82 -59.55 -24.66 -35.54\n",
" -64.27 -7.58 -146.69 -36.82 159.26 28.44 51.7 15.96\n",
" -7.29 -16.78 -42.11 -59.55 28.44 56.47 20.96 19.86\n",
" -70.28 -30.02 -46.81 -24.66 51.7 20.96 65.39 33.72\n",
" -25.36 -33.28 -24.33 -35.54 15.96 19.86 33.72 48.96\n",
"Array(Float64,(16,16)) 16x16 Array{Float64,2}"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"10-Aug 22:55:50:DEBUG:root:nothing\n",
"10-Aug 22:55:50:DEBUG:root:nothing\n",
"10-Aug 22:55:50:DEBUG:root:Solution norm = 2.638889456564507\n",
"10-Aug 22:55:50:DEBUG:root:Starting iteration 6\n",
"10-Aug 22:55:50:DEBUG:root:Assembling\n",
"10-Aug 22:55:50:DEBUG:root:Assemble element to gdofs [1,2,3,4,9,10,7,8]\n",
"10-Aug 22:55:50:DEBUG:root:Assemble element to gdofs [3,4,5,6,11,12,9,10]\n",
"10-Aug 22:55:50:DEBUG:root:Adding Dirichlet boundary conditions\n",
"10-Aug 22:55:50:DEBUG:root:dof 1 => 0.0\n",
"10-Aug 22:55:50:DEBUG:root:dof 2 => 0.0\n",
"10-Aug 22:55:50:DEBUG:root:dof 7 => 0.0\n",
"10-Aug 22:55:50:DEBUG:root:dof 8 => 0.0\n",
"10-Aug 22:55:50:DEBUG:root:Added 4 Lagrange multipliers to model\n",
"10-Aug 22:55:50:DEBUG:root:Adding Neumann boundary conditions\n",
"10-Aug 22:55:50:DEBUG:root:Solving system of equations. Total size = 16\n",
"10-Aug 22:55:50:DEBUG:root:nothing\n",
"10-Aug 22:55:50:DEBUG:root:nothing\n",
"10-Aug 22:55:50:DEBUG:root:Solution norm = 2.5846689771724556\n",
"10-Aug 22:55:50:DEBUG:root:Starting iteration 7\n",
"10-Aug 22:55:50:DEBUG:root:Assembling\n",
"10-Aug 22:55:50:DEBUG:root:Assemble element to gdofs [1,2,3,4,9,10,7,8]\n",
"10-Aug 22:55:51:DEBUG:root:Assemble element to gdofs [3,4,5,6,11,12,9,10]\n",
"10-Aug 22:55:51:DEBUG:root:Adding Dirichlet boundary conditions\n",
"10-Aug 22:55:51:DEBUG:root:dof 1 => 0.0\n",
"10-Aug 22:55:51:DEBUG:root:dof 2 => 0.0\n",
"10-Aug 22:55:51:DEBUG:root:dof 7 => 0.0\n",
"10-Aug 22:55:51:DEBUG:root:dof 8 => 0.0\n",
"10-Aug 22:55:51:DEBUG:root:Added 4 Lagrange multipliers to model\n",
"10-Aug 22:55:51:DEBUG:root:Adding Neumann boundary conditions\n",
"10-Aug 22:55:51:DEBUG:root:Solving system of equations. Total size = 16\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
":\n",
" 80.6 18.4 54.0 14.3 0.0 0.0 -70.3 -25.4 -64.3 -7.3 0.0 0.0 1.0 0.0 0.0 0.0\n",
" 18.4 29.5 19.2 20.6 0.0 0.0 -30.0 -33.3 -7.6 -16.8 0.0 0.0 0.0 1.0 0.0 0.0\n",
" 54.0 19.2 220.1 65.6 54.0 14.3 -46.8 -24.3 -217.0 -67.5 -64.3 -7.3 0.0 0.0 0.0 0.0\n",
" 14.3 20.6 65.6 104.0 19.2 20.6 -24.7 -35.5 -66.8 -92.8 -7.6 -16.8 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 54.0 19.2 139.5 47.2 0.0 0.0 -46.8 -24.3 -146.7 -42.1 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 14.3 20.6 47.2 74.5 0.0 0.0 -24.7 -35.5 -36.8 -59.6 0.0 0.0 0.0 0.0\n",
" -70.3 -30.0 -46.8 -24.7 0.0 0.0 65.4 33.7 51.7 21.0 0.0 0.0 0.0 0.0 1.0 0.0\n",
" -25.4 -33.3 -24.3 -35.5 0.0 0.0 33.7 49.0 16.0 19.9 0.0 0.0 0.0 0.0 0.0 1.0\n",
" -64.3 -7.6 -217.0 -66.8 -46.8 -24.7 51.7 16.0 224.7 62.2 51.7 21.0 0.0 0.0 0.0 0.0\n",
" -7.3 -16.8 -67.5 -92.8 -24.3 -35.5 21.0 19.9 62.2 105.4 16.0 19.9 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 -64.3 -7.6 -146.7 -36.8 0.0 0.0 51.7 16.0 159.3 28.4 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 -7.3 -16.8 -42.1 -59.6 0.0 0.0 21.0 19.9 28.4 56.5 0.0 0.0 0.0 0.0\n",
" 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
"Array(Float64,(1,16)) 1x16 Array{Float64,2}:\n",
" 28.6 5.9 32.9 14.7 4.3 8.7 -24.6 -14.9 -32.9 -14.7 -8.3 2.2 0.0 0.0 0.0 0.0\n",
"Element stiffness matrix\n",
"Array(Float64,(8,8)) 8x8 Array{Float64,2}:\n",
" 138.24 6.59 72.3 13.02 -91.67 -1.46 -118.87 -18.14\n",
" 6.59 95.68 20.35 47.41 -1.83 -47.79 -25.11 -95.3 \n",
" 72.3 20.35 177.29 48.61 -182.78 -43.91 -66.81 -25.05\n",
" 13.02 47.41 48.61 159.72 -36.21 -128.01 -25.42 -79.12\n",
" -91.67 -1.83 -182.78 -36.21 203.7 23.62 70.75 14.42\n",
" -1.46 -47.79 -43.91 -128.01 23.62 126.88 21.75 48.93\n",
" -118.87 -25.11 -66.81 -25.42 70.75 21.75 114.93 28.77\n",
" -18.14 -95.3 -25.05 -79.12 14.42 48.93 28.77 125.49\n",
"Element stiffness matrix\n",
"Array(Float64,(8,8)) 8x8 Array{Float64,2}:\n",
" 138.24 6.59 72.3 13.02 -91.67 -1.46 -118.87 -18.14\n",
" 6.59 95.68 20.35 47.41 -1.83 -47.79 -25.11 -95.3 \n",
" 72.3 20.35 177.29 48.61 -182.78 -43.91 -66.81 -25.05\n",
" 13.02 47.41 48.61 159.72 -36.21 -128.01 -25.42 -79.12\n",
" -91.67 -1.83 -182.78 -36.21 203.7 23.62 70.75 14.42\n",
" -1.46 -47.79 -43.91 -128.01 23.62 126.88 21.75 48.93\n",
" -118.87 -25.11 -66.81 -25.42 70.75 21.75 114.93 28.77\n",
" -18.14 -95.3 -25.05 -79.12 14.42 48.93 28.77 125.49\n",
"Array(Float64,(16,16)) 16x16 Array{Float64,2}:\n",
" 138.2 6.6 72.3 13.0 0.0 0.0 -118.9 -18.1 -91.7 -1.5 0.0 0.0 1.0 0.0 0.0 0.0\n",
" 6.6 95.7 20.3 47.4 0.0 0.0 -25.1 -95.3 -1.8 -47.8 0.0 0.0 0.0 1.0 0.0 0.0\n",
" 72.3 20.3 315.5 55.2 72.3 13.0 -66.8 -25.0 -301.6 -62.1 -91.7 -1.5 0.0 0.0 0.0 0.0\n",
" 13.0 47.4 55.2 255.4 20.3 47.4 -25.4 -79.1 -61.3 -223.3 -1.8 -47.8 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 72.3 20.3 177.3 48.6 0.0 0.0 -66.8 -25.0 -182.8 -43.9 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 13.0 47.4 48.6 159.7 0.0 0.0 -25.4 -79.1 -36.2 -128.0 0.0 0.0 0.0 0.0\n",
" -118.9 -25.1 -66.8 -25.4 0.0 0.0 114.9 28.8 70.7 21.8 0.0 0.0 0.0 0.0 1.0 0.0\n",
" -18.1 -95.3 -25.0 -79.1 0.0 0.0 28.8 125.5 14.4 48.9 0.0 0.0 0.0 0.0 0.0 1.0\n",
" -91.7 -1.8 -301.6 -61.3 -66.8 -25.4 70.7 14.4 318.6 52.4 70.7 21.8 0.0 0.0 0.0 0.0\n",
" -1.5 -47.8 -62.1 -223.3 -25.0 -79.1 21.8 48.9 52.4 252.4 14.4 48.9 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 -91.7 -1.8 -182.8 -36.2 0.0 0.0 70.7 14.4 203.7 23.6 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 -1.5 -47.8 -43.9 -128.0 0.0 0.0 21.8 48.9 23.6 126.9 0.0 0.0 0.0 0.0\n",
" 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
"Array(Float64,(1,16)) 1x16 Array{Float64,2}:\n",
" -06.5 7.6 -25.7 -24.5 -19.1 -32.0 -4.1 20.8 25.7 24.5 29.7 5.7 0.0 0.0 0.0 0.0\n",
"Element stiffness matrix\n",
"Array(Float64,(8,8)) 8x8 Array{Float64,2}:\n",
" 105.18 18.96 58.01 14.76 -69.33 -6.94 -93.85 -26.77\n",
" 18.96 36.86 19.89 21.5 -7.13 -18.68 -31.72 -39.68\n",
" 58.01 19.89 135.28 46.75 -141.88 -41.41 -51.41 -25.23\n",
" 14.76 21.5 46.75 74.5 -36.07 -59.09 -25.44 -36.91\n",
" -69.33 -7.13 -141.88 -36.07 154.31 27.5 56.9 15.7 \n",
" -6.94 -18.68 -41.41 -59.09 27.5 56.13 20.86 21.65\n",
" -93.85 -31.72 -51.41 -25.44 56.9 20.86 88.36 36.3 \n",
" -26.77 -39.68 -25.23 -36.91 15.7 21.65 36.3 54.93\n",
"Element stiffness matrix\n",
"Array(Float64,(8,8)) 8x8 Array{Float64,2}:\n",
" 105.18 18.96 58.01 14.76 -69.33 -6.94 -93.85 -26.77\n",
" 18.96 36.86 19.89 21.5 -7.13 -18.68 -31.72 -39.68\n",
" 58.01 19.89 135.28 46.75 -141.88 -41.41 -51.41 -25.23\n",
" 14.76 21.5 46.75 74.5 -36.07 -59.09 -25.44 -36.91\n",
" -69.33 -7.13 -141.88 -36.07 154.31 27.5 56.9 15.7 \n",
" -6.94 -18.68 -41.41 -59.09 27.5 56.13 20.86 21.65\n",
" -93.85 -31.72 -51.41 -25.44 56.9 20.86 88.36 36.3 \n",
" -26.77 -39.68 -25.23 -36.91 15.7 21.65 36.3 54.93\n",
"Array(Float64,(16,16)) 16x16 Array{Float64,2}:\n",
" 105.2 19.0 58.0 14.8 0.0 0.0 -93.9 -26.8 -69.3 -6.9 0.0 0.0 1.0 0.0 0.0 0.0\n",
" 19.0 36.9 19.9 21.5 0.0 0.0 -31.7 -39.7 -7.1 -18.7 0.0 0.0 0.0 1.0 0.0 0.0\n",
" 58.0 19.9 240.5 65.7 58.0 14.8 -51.4 -25.2 -235.7 -68.2 -69.3 -6.9 0.0 0.0 0.0 0.0\n",
" 14.8 21.5 65.7 111.4 19.9 21.5 -25.4 -36.9 -67.8 -98.8 -7.1 -18.7 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 58.0 19.9 135.3 46.7 0.0 0.0 -51.4 -25.2 -141.9 -41.4 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 14.8 21.5 46.7 74.5 0.0 0.0 -25.4 -36.9 -36.1 -59.1 0.0 0.0 0.0 0.0\n",
" -93.9 -31.7 -51.4 -25.4 0.0 0.0 88.4 36.3 56.9 20.9 0.0 0.0 0.0 0.0 1.0 0.0\n",
" -26.8 -39.7 -25.2 -36.9 0.0 0.0 36.3 54.9 15.7 21.6 0.0 0.0 0.0 0.0 0.0 1.0\n",
" -69.3 -7.1 -235.7 -67.8 -51.4 -25.4 56.9 15.7 242.7 63.8 56.9 20.9 0.0 0.0 0.0 0.0\n",
" -6.9 -18.7 -68.2 -98.8 -25.2 -36.9 20.9 21.6 63.8 111.1 15.7 21.6 0.0 0.0 0.0 0.0\n",
" 0.0 "
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"10-Aug 22:55:51:DEBUG:root:nothing\n",
"10-Aug 22:55:51:DEBUG:root:nothing\n",
"10-Aug 22:55:51:DEBUG:root:Solution norm = 2.4116101594574446\n",
"10-Aug 22:55:51:DEBUG:root:Displacement of element = \n",
"[-3.0265017801117513 -5.464687844270099 -4.5022205763589715 -2.2188310526354926\n",
" -1.2759688848713764 -6.757003969576785 -7.2218353000897295 -1.8649226742660745]\n"
]
},
{
"data": {
"text/plain": [
"delayed_handler (generic function with 4 methods)"
]
},
"execution_count": 82,
"metadata": {},
"output_type": "execute_result"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.0 -69.3 -7.1 -141.9 -36.1 0.0 0.0 56.9 15.7 154.3 27.5 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 -6.9 -18.7 -41.4 -59.1 0.0 0.0 20.9 21.6 27.5 56.1 0.0 0.0 0.0 0.0\n",
" 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
" 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
"Array(Float64,(1,16)) 1x16 Array{Float64,2}:\n",
" 22.9 4.1 28.6 11.8 5.6 7.6 -19.5 -12.4 -28.6 -11.8 -09.0 2.6 0.0 0.0 0.0 0.0\n",
"0 facts verified.\n"
]
}
],
"source": [
"\"\"\"\n",
"Create local dof to global dof mapping for given elements\n",
"\"\"\"\n",
"function create_ldof2gdofmap(elements; ndofs=2)\n",
" Logging.info(\"create_ldof2gdofmap: dofs per node: $ndofs\")\n",
"\n",
" all_node_ids = Int64[]\n",
" for el in elements\n",
" eldim, elnodes = size(el.coordinates)\n",
" for nid in el.node_ids\n",
" push!(all_node_ids, nid)\n",
" end\n",
" end\n",
" all_node_ids = unique(all_node_ids)\n",
" sort!(all_node_ids)\n",
"\n",
" # Assign global dof for each node\n",
" pdim = 1\n",
" ngdofs = Dict{Int64, Array{Int64,1}}()\n",
" for nid in all_node_ids\n",
" ngdofs[nid] = collect(pdim:pdim+ndofs-1)\n",
" pdim += ndofs\n",
" end\n",
"\n",
" return ngdofs\n",
"end\n",
"\n",
"function solve!(elements, dofmap, neumann_bcs, dirichlet_bcs; ndofs=2, max_iterations=10)\n",
" \n",
" Logging.info(\"solve!: dofs per node: $ndofs\")\n",
" pdim = length(dofmap)*ndofs\n",
" Logging.debug(\"Problem size = $pdim\")\n",
"\n",
" # Initialize elements ready for solution\n",
" for el in elements\n",
" eldim, elnodes = size(el.coordinates)\n",
" el.attributes[\"displacement\"] = zeros(ndofs, elnodes)\n",
" el.attributes[\"displacement nodal force\"] = zeros(ndofs, elnodes)\n",
" el.attributes[\"displacement tangent stiffness\"] = zeros(ndofs*elnodes, ndofs*elnodes)\n",
" end\n",
"\n",
" # Assign global dofs for elements\n",
" gdofs = Dict{Int64, Array{Int64,1}}()\n",
" for el in elements\n",
" gdofs[el.id] = Int64[]\n",
" for nid in el.node_ids\n",
" for ndof in dofmap[nid]\n",
" push!(gdofs[el.id], ndof)\n",
" end\n",
" end\n",
" end\n",
"\n",
" ass = Assembly(Int64[], Int64[], Float64[], Int64[], Float64[], gdofs)\n",
"\n",
" for iter=1:max_iterations\n",
" Logging.debug(\"Starting iteration $iter\")\n",
" ass.I = []\n",
" ass.J = []\n",
" ass.A = []\n",
" ass.i = []\n",
" ass.b = []\n",
" \n",
" Logging.debug(\"Assembling\")\n",
" for el in elements\n",
" assemble_element!(ass, el)\n",
" println(\"Element stiffness matrix\")\n",
" dump(round(el.attributes[\"displacement tangent stiffness\"], 2))\n",
" end\n",
"\n",
" Logging.debug(\"Adding Dirichlet boundary conditions\")\n",
" # Dirichlet boundary conditions\n",
" i = 1\n",
" for bc in dirichlet_bcs\n",
" for (dof, val) in zip(bc.dofs, bc.values)\n",
" Logging.debug(\"dof $dof => $val\")\n",
" push!(ass.I, dof)\n",
" push!(ass.J, pdim+i)\n",
" push!(ass.A, 1)\n",
" push!(ass.I, pdim+i)\n",
" push!(ass.J, dof)\n",
" push!(ass.A, 1)\n",
" push!(ass.i, pdim+i)\n",
" push!(ass.b, 0)\n",
" i += 1\n",
" end\n",
" end\n",
" i -= 1\n",
" Logging.debug(\"Added $i Lagrange multipliers to model\")\n",
"\n",
" Logging.debug(\"Adding Neumann boundary conditions\")\n",
" F = zeros(pdim+i)\n",
" # Neumann boundary conditions\n",
" for bc in neumann_bcs\n",
" for (dof, val) in zip(bc.dofs, bc.values)\n",
" F[dof] += val\n",
" end\n",
" end\n",
"\n",
" Logging.debug(\"Solving system of equations. Total size = $(pdim+i)\")\n",
" # solution\n",
" K = sparse(ass.I, ass.J, ass.A)\n",
" R = full(sparsevec(ass.i, ass.b))\n",
" R = R - F\n",
" Logging.debug(dump(round(full(K), 1)))\n",
" #print_matrix(full(K))\n",
" Logging.debug(dump(round(R', 1)))\n",
"\n",
" du = K \\ -R\n",
"\n",
" solnorm = norm(du[1:pdim])\n",
" Logging.debug(\"Solution norm = $solnorm\")\n",
"\n",
" # update solution back to elements\n",
" for el in elements\n",
"\n",
" eldu = du[ass.gdofs[el.id]]\n",
" eldu = reshape(eldu, (ndofs, round(Int, length(eldu)/ndofs)))\n",
" el.attributes[\"displacement\"] += eldu\n",
" end\n",
" if solnorm < 1.0e-9\n",
" Logging.debug(\"Converged in $iter iterations.\")\n",
" break\n",
" end\n",
" end\n",
"\n",
"end\n",
"\n",
"ENV[\"COLUMNS\"] = 160\n",
"\n",
"facts(\"solve one element problem\") do\n",
" # Create model\n",
" Logging.debug(\"Creating nodes\")\n",
" node_ids = [1, 2, 3, 4]\n",
" coordinates = [10.0 0.0; 10.0 1.0; 0.0 1.0; 0.0 0.0]'\n",
" attributes = Dict(\"Young\" => 90, \"Poisson\" => 0.25)\n",
" Logging.debug(\"Creating elements\")\n",
" el = Element(1, node_ids, coordinates, attributes)\n",
" elements = [el]\n",
" dofmap = create_ldof2gdofmap(elements)\n",
" Logging.debug(dofmap)\n",
" # Boundary conditions\n",
" # here we want to create nodal force for third dof, that is, node id 2, second dof\n",
" bc1 = BC([dofmap[2][2]], [-2.0])\n",
" # dirichlet bc, set dx=dy=0 on support\n",
" bc2 = BC([dofmap[3][1], dofmap[3][2], dofmap[4][1], dofmap[4][2]], [0.0, 0.0, 0.0, 0.0])\n",
" solve!(elements, dofmap, [bc1], [bc2]; max_iterations=7)\n",
" disp = elements[1].attributes[\"displacement\"]\n",
" Logging.debug(\"Displacement of element = \\n$disp\")\n",
" @fact norm(disp) => roughly(3.1292483947150043)\n",
"end\n",
"\n",
"facts(\"solve two element problem\") do\n",
" # Create model\n",
" attributes = Dict(\"Young\" => 90, \"Poisson\" => 0.25)\n",
"\n",
" Logging.debug(\"Creating elements\")\n",
" nids1 = [1, 2, 5, 4]\n",
" coords1 = [0.0 0.0; 5.0 0.0; 5.0 1.0; 0.0 1.0]'\n",
" el1 = Element(1, nids1, coords1, attributes)\n",
" nids2 = [2, 3, 6, 5]\n",
" coords2 = [5.0 0.0; 10.0 0.0; 10.0 1.0; 5.0 1.0]'\n",
" el2 = Element(2, nids2, coords2, attributes)\n",
" elements = [el1, el2]\n",
"\n",
" dofmap = create_ldof2gdofmap(elements)\n",
" Logging.debug(dofmap)\n",
" # Boundary conditions\n",
" # here we want to create nodal force for third dof, that is, node id 2, second dof\n",
" bc1 = BC([dofmap[6][2]], [-2.0])\n",
" # dirichlet bc, set dx=dy=0 on support\n",
" bc2 = BC([dofmap[1][1], dofmap[1][2], dofmap[4][1], dofmap[4][2]], [0.0, 0.0, 0.0, 0.0])\n",
" solve!(elements, dofmap, [bc1], [bc2]; max_iterations=7)\n",
" disp = elements[2].attributes[\"displacement\"]\n",
" Logging.debug(\"Displacement of element = \\n$disp\")\n",
" #@fact norm(disp) => roughly(3.1292483947150043)\n",
"end"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Top-down design\n",
"\n",
"Next we see this problem from \"other direction\", by parsing ABAQUS .inp file and making 3d simulation."
]
},
{
"cell_type": "code",
"execution_count": 74,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"1x1 sparse matrix with 1 Float64 entries:\n",
"\t[1, 1] = 2.0"
]
},
"execution_count": 74,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sparse([1, 1], [1, 1], [1.0, 1.0])"
]
},
{
"cell_type": "code",
"execution_count": 46,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"10-Aug 20:59:55:INFO:root:Registered handlers: Any[\"ELEMENT\",\"NODE\",\"NSET\"]\n",
"10-Aug 20:59:55:DEBUG:root:Found NODE section\n",
"10-Aug 20:59:56:DEBUG:root:Found ELEMENT section\n",
"10-Aug 20:59:57:DEBUG:root:120 elements found\n",
"10-Aug 20:59:57:INFO:root:Creating ELSET Body1\n",
"10-Aug 20:59:57:DEBUG:root:Found NSET section\n",
"10-Aug 20:59:57:DEBUG:root:Creating node set SUPPORT\n",
"10-Aug 20:59:57:DEBUG:root:Found NSET section\n",
"10-Aug 20:59:57:DEBUG:root:Creating node set LOAD\n",
"10-Aug 20:59:57:DEBUG:root:Found NSET section\n",
"10-Aug 20:59:57: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": 46,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"using JuliaFEM.abaqus_reader\n",
"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": 63,
"metadata": {
"collapsed": false,
"scrolled": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"solve 3d elasticity problem\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"10-Aug 21:16:13:DEBUG:root:Creating elements\n",
"10-Aug 21:16:13:INFO:root:dofs per node: 3\n",
"10-Aug 21:16:13:INFO:root:dofs per node: 3\n",
"10-Aug 21:16:13:DEBUG:root:Problem size = 894\n",
"10-Aug 21:16:13:DEBUG:root:Starting iteration 1\n",
"10-Aug 21:16:13:DEBUG:root:Assembling\n",
"10-Aug 21:16:15:DEBUG:root:Adding Dirichlet boundary conditions\n",
"10-Aug 21:16:15:DEBUG:root:Added 27 Lagrange multipliers to model\n",
"10-Aug 21:16:15:DEBUG:root:Adding Neumann boundary conditions\n",
"10-Aug 21:16:15:DEBUG:root:Solving system of equations. Total size = 921\n",
"10-Aug 21:16:15:DEBUG:root:Solution norm = 0.2429242363684311\n",
"10-Aug 21:16:15:DEBUG:root:Starting iteration 2\n",
"10-Aug 21:16:15:DEBUG:root:Assembling\n",
"10-Aug 21:16:16:DEBUG:root:Adding Dirichlet boundary conditions\n",
"10-Aug 21:16:16:DEBUG:root:Added 27 Lagrange multipliers to model\n",
"10-Aug 21:16:16:DEBUG:root:Adding Neumann boundary conditions\n",
"10-Aug 21:16:16:DEBUG:root:Solving system of equations. Total size = 921\n",
"10-Aug 21:16:16:DEBUG:root:Solution norm = 0.220339941648292\n",
"10-Aug 21:16:16:DEBUG:root:Starting iteration 3\n",
"10-Aug 21:16:16:DEBUG:root:Assembling\n",
"10-Aug 21:16:17:DEBUG:root:Adding Dirichlet boundary conditions\n",
"10-Aug 21:16:17:DEBUG:root:Added 27 Lagrange multipliers to model\n",
"10-Aug 21:16:17:DEBUG:root:Adding Neumann boundary conditions\n",
"10-Aug 21:16:17:DEBUG:root:Solving system of equations. Total size = 921\n",
"10-Aug 21:16:18:DEBUG:root:Solution norm = 31.956186974599095\n",
"10-Aug 21:16:18:DEBUG:root:Starting iteration 4\n",
"10-Aug 21:16:18:DEBUG:root:Assembling\n",
"10-Aug 21:16:19:DEBUG:root:Adding Dirichlet boundary conditions\n",
"10-Aug 21:16:19:DEBUG:root:Added 27 Lagrange multipliers to model\n",
"10-Aug 21:16:19:DEBUG:root:Adding Neumann boundary conditions\n",
"10-Aug 21:16:19:DEBUG:root:Solving system of equations. Total size = 921\n",
"10-Aug 21:16:19:DEBUG:root:Solution norm = 411.4719431105651\n",
"10-Aug 21:16:19:DEBUG:root:Starting iteration 5\n",
"10-Aug 21:16:19:DEBUG:root:Assembling\n",
"10-Aug 21:16:21:DEBUG:root:Adding Dirichlet boundary conditions\n",
"10-Aug 21:16:21:DEBUG:root:Added 27 Lagrange multipliers to model\n",
"10-Aug 21:16:21:DEBUG:root:Adding Neumann boundary conditions\n",
"10-Aug 21:16:21:DEBUG:root:Solving system of equations. Total size = 921\n",
"10-Aug 21:16:21:DEBUG:root:Solution norm = 7077.644216187514\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"0 facts verified.\n"
]
},
{
"data": {
"text/plain": [
"delayed_handler (generic function with 4 methods)"
]
},
"execution_count": 63,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"facts(\"solve 3d elasticity problem\") do\n",
"\n",
" attributes = Dict(\"Young\" => 90, \"Poisson\" => 0.25)\n",
"\n",
" Logging.debug(\"Creating elements\")\n",
" elements = Element[]\n",
" coordinates = zeros(3, 10)\n",
" for (elid, node_ids) in model[\"elements\"]\n",
" for (i, nid) in enumerate(node_ids)\n",
" coordinates[:,i] = model[\"nodes\"][nid]\n",
" end\n",
" el = Element(elid, node_ids, coordinates, attributes)\n",
" push!(elements, el)\n",
" end\n",
"\n",
" # create \"dofmap\" so that we know how to assemble global stiffness matrix\n",
" dofmap = create_ldof2gdofmap(elements; ndofs=3)\n",
"\n",
" # Boundary conditions\n",
"\n",
" # dirichlet bc, set dx=dy=dz for all nodes in set SUPPORT\n",
" bc_support = BC(Int64[], Float64[])\n",
" for nid in model[\"nsets\"][\"SUPPORT\"]\n",
" for i=1:3\n",
" push!(bc_support.dofs, dofmap[nid][i])\n",
" push!(bc_support.values, 0.0)\n",
" end\n",
" end\n",
"\n",
" # force boundary condition, put -1 to 2nd dof for each node in set LOAD\n",
" bc_load = BC(Int64[], Float64[])\n",
" for nid in model[\"nsets\"][\"LOAD\"]\n",
" push!(bc_load.dofs, dofmap[nid][2])\n",
" push!(bc_load.values, -0.1)\n",
" end\n",
"\n",
" #solve!(elements, [bc1], [bc2]; max_iterations=7)\n",
" neumann_bcs = [bc_load]\n",
" dirichlet_bcs = [bc_support]\n",
" # ndofs = dimension of unknown field in nodes\n",
" solve!(elements, dofmap, neumann_bcs, dirichlet_bcs; ndofs=3, max_iterations=5)\n",
"# disp = elements[1].attributes[\"displacement\"]\n",
"# Logging.debug(\"Displacement of element = \\n$disp\")\n",
"# @fact norm(disp) => roughly(3.1292483947150043)\n",
"end"
]
},
{
"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": "markdown",
"metadata": {
"collapsed": true
},
"source": [
"## 3d beam with quadratic elements"
]
},
{
"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": "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": [
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"<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",
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-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
}
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