Glassvision/JuliaFEM.jl
1
0
Fork 0
mirror of https://github.com/JuliaFEM/JuliaFEM.jl.git synced 2026-09-17 09:12:09 +00:00
Code Issues Packages Projects Releases Wiki Activity

.

Browse Source
This commit is contained in:
Jukka Aho
2015-10-22 21:11:14 +03:00
parent f5f25a82c3
commit 86e25d5c4e
2 changed files with 145 additions and 88 deletions
Download Patch File Download Diff File Expand all files Collapse all files
notebooks/2015-06-25-elasticity-solver-example.ipynb
+144 -87
View File
@@ -13,18 +13,36 @@
},
{
"cell_type": "code",
"execution_count": 2,
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"WARNING: Base.String is deprecated, use AbstractString instead.\n",
" likely near /home/jukka/.julia/v0.4/Logging/src/Logging.jl:24\n",
"WARNING: Base.String is deprecated, use AbstractString instead.\n",
" likely near /home/jukka/.julia/v0.4/Logging/src/Logging.jl:24\n",
"WARNING: Base.String is deprecated, use AbstractString instead.\n",
" likely near /home/jukka/.julia/v0.4/Logging/src/Logging.jl:24\n",
"WARNING: Base.String is deprecated, use AbstractString instead.\n",
" likely near /home/jukka/.julia/v0.4/Logging/src/Logging.jl:40\n",
"WARNING: Base.String is deprecated, use AbstractString instead.\n",
" likely near /home/jukka/.julia/v0.4/Logging/src/Logging.jl:40\n",
"WARNING: Base.String is deprecated, use AbstractString instead.\n",
" likely near /home/jukka/.julia/v0.4/Logging/src/Logging.jl:40\n"
]
},
{
"data": {
"text/plain": [
"Logger(root,DEBUG,Base.PipeEndpoint(open, 0 bytes waiting),root)"
]
},
"execution_count": 2,
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
@@ -40,7 +58,7 @@
},
{
"cell_type": "code",
"execution_count": 3,
"execution_count": 2,
"metadata": {
"collapsed": false
},
@@ -51,7 +69,7 @@
"CPS4"
]
},
"execution_count": 3,
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
@@ -89,7 +107,7 @@
},
{
"cell_type": "code",
"execution_count": 5,
"execution_count": 40,
"metadata": {
"collapsed": false
},
@@ -97,11 +115,18 @@
{
"data": {
"text/plain": [
"1x8 Array{Float64,2}:\n",
" -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0"
"8-element Array{Float64,1}:\n",
" -189.267 \n",
" 26.1073 \n",
" 5.7554e-13 \n",
" 2.6894e-12 \n",
" -8.73968e-13\n",
" 20.0 \n",
" 189.267 \n",
" -46.1073 "
]
},
"execution_count": 5,
"execution_count": 40,
"metadata": {},
"output_type": "execute_result"
}
@@ -125,22 +150,43 @@
" lambda = young*poisson/((1+poisson)*(1-2*poisson))\n",
" lambda = 2*lambda*mu/(lambda + 2*mu)\n",
"\n",
" invJ = inv(dN*X)\n",
" gradw = dN*invJ\n",
" gradw = dN*inv(dN*X)\n",
" grad(u) = dN*u*inv(dN*(X+u))\n",
" Grad(u) = dN*u*inv(dN*X)\n",
"\n",
" function calc_R(data::Vector)\n",
" # create new field similar to displacement and fill it with data\n",
" f = similar(u, data)\n",
" # kinematics\n",
" gradu = dN*f*invJ\n",
" F = I + gradu # deformation gradient\n",
" E = 1/2*(F'*F - I) # strain\n",
" F = I + Grad(f) # deformation gradient\n",
" C = F'*F\n",
" E = 1/2*(C - I) # strain\n",
" S = 2*mu*E + lambda*trace(E)*I # stress\n",
" return (F*S*gradw')[:]\n",
" P = F*S\n",
" return (P*gradw')[:]\n",
" end\n",
"\n",
" R = calc_R(u[:])\n",
" Kt = ForwardDiff.jacobian(calc_R, u[:])\n",
" function calc_Wint(data::Vector)\n",
" # create new field similar to displacement and fill it with data\n",
" δu = similar(u, data)\n",
" # kinematics\n",
" F = I + Grad(δu) # deformation gradient\n",
" C = F'*F\n",
" E = 1/2*(C - I) # strain\n",
" #E = 1/2*(Grad(δu)' + Grad(δu) + Grad(δu)'*Grad(δu))\n",
" S = 2*mu*E + lambda*trace(E)*I # stress\n",
" δF = Grad(δu)\n",
" #δɛ = 1/2*(δF' + δF)\n",
" #δE = F'*δɛ*F\n",
" #δE = 1/2*(F'*δF + δF'*F)\n",
" #δE = 1/2*(Grad(δu)' + Grad(δu) + Grad(δu)'*Grad(δu))\n",
" δE = 1/2*E # ...???? energy 2x\n",
"\n",
" return trace(S*δE')\n",
" end\n",
"\n",
" R = ForwardDiff.gradient(calc_Wint, u[:])\n",
" Kt = ForwardDiff.hessian(calc_Wint, u[:])\n",
" return Kt, -R\n",
"end\n",
"\n",
@@ -153,42 +199,13 @@
"\n",
"JuliaFEM.has_lhs(equation::CPS4) = true\n",
"JuliaFEM.has_rhs(equation::CPS4) = true\n",
"JuliaFEM.integrate_rhs(equation, 0.0)'"
"\n",
"JuliaFEM.integrate_rhs(equation, Inf)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"8x8 Array{Float64,2}:\n",
" 123.2 15.0 56.8 -3.0 -61.6 -15.0 -118.4 3.0\n",
" 15.0 321.2 3.0 158.8 -15.0 -160.6 -3.0 -319.4\n",
" 56.8 3.0 123.2 -15.0 -118.4 -3.0 -61.6 15.0\n",
" -3.0 158.8 -15.0 321.2 3.0 -319.4 15.0 -160.6\n",
" -61.6 -15.0 -118.4 3.0 123.2 15.0 56.8 -3.0\n",
" -15.0 -160.6 -3.0 -319.4 15.0 321.2 3.0 158.8\n",
" -118.4 -3.0 -61.6 15.0 56.8 3.0 123.2 -15.0\n",
" 3.0 -319.4 15.0 -160.6 -3.0 158.8 -15.0 321.2"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"JuliaFEM.integrate_lhs(equation, 0.0)"
]
},
{
"cell_type": "code",
"execution_count": 20,
"execution_count": 41,
"metadata": {
"collapsed": false
},
@@ -197,18 +214,19 @@
"name": "stdout",
"output_type": "stream",
"text": [
"increment 1, norm = 3.0900221367289094\n"
"increment "
]
},
{
"data": {
"text/plain": [
"2-element Array{Float64,1}:\n",
" -0.399145\n",
" -2.17799 "
"Success :: (line:-1) :: fact was true\n",
" Expression: (interpolate(element,\"displacement\",[1.0,1.0],Inf))[2] --> roughly(-4.15546385452579)\n",
" Expected: -4.15546385452579\n",
" Occurred: -4.155463854525783"
]
},
"execution_count": 20,
"execution_count": 41,
"metadata": {},
"output_type": "execute_result"
},
@@ -216,23 +234,21 @@
"name": "stdout",
"output_type": "stream",
"text": [
"increment 2, norm = 0.32121316021534246\n",
"increment 3, norm = 0.040431781940025155\n",
"increment 4, norm = 0.0009291101052125905\n",
"increment 5, norm = 1.5638899099729665e-7\n",
"increment 6, norm = 1.0201033584846351e-14\n",
"increment 7, norm = 1.3679680786658739e-15\n",
"increment 8, norm = 2.463346396682122e-15\n",
"increment 9, norm = 9.485831749489368e-16\n",
"increment 10, norm = 1.3372608112297287e-15\n"
"1, norm = 5.77653, Wint = 0.000, Wext = 81.525, |Wint-Wext| = 81.52516\n",
"increment 2, norm = 0.99988, Wint = 173.895, Wext = 79.037, |Wint-Wext| = 94.85823\n",
"increment 3, norm = 0.28354, Wint = 87.084, Wext = 82.175, |Wint-Wext| = 4.90953\n",
"increment 4, norm = 0.07071, Wint = 82.548, Wext = 83.100, |Wint-Wext| = 0.55141\n",
"increment 5, norm = 0.00082, Wint = 83.116, Wext = 83.109, |Wint-Wext| = 0.00644\n",
"increment 6, norm = 0.00000, Wint = 83.109, Wext = 83.109, |Wint-Wext| = 0.00000\n",
"83.10927709051566\n"
]
}
],
"source": [
"element = Quad4([1, 2, 3, 4])\n",
"push!(element, FieldSet(\"young\", [Field(0.0, 90.0)]))\n",
"push!(element, FieldSet(\"young\", [Field(0.0, 500.0)]))\n",
"push!(element, FieldSet(\"geometry\", [Field(0.0, Vector[[0.0, 0.0], [10.0, 0.0], [10.0, 1.0], [0.0, 1.0]])]))\n",
"push!(element, FieldSet(\"poisson\", [Field(0.0, 0.25)]))\n",
"push!(element, FieldSet(\"poisson\", [Field(0.0, 0.3)]))\n",
"equation = CPS4(element)\n",
"\n",
"u0 = Field(0.0, Vector[[0.0, 0.0], [0.0, 0.0], [0.0, 0.0], [0.0, 0.0]])\n",
@@ -241,8 +257,8 @@
"du = zeros(8)\n",
"fd = [3, 4, 5, 6]\n",
"f = zeros(8)\n",
"f[6] = -2.0\n",
"for i=1:10\n",
"f[6] = -20.0\n",
"for i=1:6\n",
" A = JuliaFEM.integrate_lhs(equation, 1.0)\n",
" b = JuliaFEM.integrate_rhs(equation, 1.0)\n",
" du[fd] = A[fd,fd] \\ (b[fd]+f[fd])\n",
@@ -251,9 +267,14 @@
" new_field.time = 1.0\n",
" new_field.increment = i\n",
" push!(element[\"displacement\"], new_field)\n",
" println(\"increment $i, norm = $(norm(du))\")\n",
" Wint = (-b'*u)[1]\n",
" Wext = (f'*u)[1]\n",
" W = abs(Wint-Wext)\n",
" @printf(\"increment %2d, norm = %8.5f, Wint = %8.3f, Wext = %8.3f, |Wint-Wext| = %8.5f\\n\", i, norm(du), Wint, Wext, W)\n",
"end\n",
"interpolate(element, \"displacement\", [1.0, -1.0], 1.0)"
"println((f'*u)[1])\n",
"@fact interpolate(element, \"displacement\", [1.0, 1.0], Inf)[2] --> roughly(-4.15546385452579E+00)\n",
"#interpolate(element, \"displacement\", [1.0, 1.0], Inf)[2], (f'*u)[1]"
]
},
{
@@ -265,7 +286,7 @@
},
{
"cell_type": "code",
"execution_count": 7,
"execution_count": 170,
"metadata": {
"collapsed": false
},
@@ -273,11 +294,10 @@
{
"data": {
"text/plain": [
"1x8 Array{Float64,2}:\n",
" -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0"
"get_rhs (generic function with 6 methods)"
]
},
"execution_count": 7,
"execution_count": 170,
"metadata": {},
"output_type": "execute_result"
}
@@ -342,6 +362,9 @@
"\n",
" R = fint\n",
" Kt = K_L + K_NL\n",
"\n",
" print('.')\n",
" \n",
" return Kt, -R\n",
"end\n",
"\n",
@@ -350,14 +373,56 @@
"end\n",
"function JuliaFEM.get_rhs(equation::CPS4, ip, time)\n",
" get_lhs_and_rhs(equation, ip, time)[2]\n",
"end\n",
"\n",
"JuliaFEM.integrate_rhs(equation, 0.0)'"
"end"
]
},
{
"cell_type": "code",
"execution_count": 8,
"execution_count": 172,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
".."
]
},
{
"data": {
"text/plain": [
"8x8 Array{Float64,2}:\n",
" 119.461 13.486 61.8587 … -26.0246 -113.693 2.80625\n",
" 13.486 309.576 15.6443 -148.518 -3.10973 -316.14 \n",
" 61.8587 15.6443 130.663 -53.2776 -60.0524 1.57406\n",
" 9.73233 155.082 36.0593 -303.877 1.51267 -163.427 \n",
" -67.6267 -26.0206 -132.47 63.0312 56.539 10.2937 \n",
" -26.0246 -148.518 -53.2776 … 299.439 16.271 152.956 \n",
" -113.693 -3.10973 -60.0524 16.271 117.207 -14.674 \n",
" 2.80625 -316.14 1.57406 152.956 -14.674 326.611 "
]
},
"execution_count": 172,
"metadata": {},
"output_type": "execute_result"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
".."
]
}
],
"source": [
"JuliaFEM.integrate_lhs(equation, Inf)"
]
},
{
"cell_type": "code",
"execution_count": 169,
"metadata": {
"collapsed": false
},
@@ -365,24 +430,16 @@
{
"data": {
"text/plain": [
"8x8 Array{Float64,2}:\n",
" 123.2 15.0 56.8 -3.0 -61.6 -15.0 -118.4 3.0\n",
" 15.0 321.2 3.0 158.8 -15.0 -160.6 -3.0 -319.4\n",
" 56.8 3.0 123.2 -15.0 -118.4 -3.0 -61.6 15.0\n",
" -3.0 158.8 -15.0 321.2 3.0 -319.4 15.0 -160.6\n",
" -61.6 -15.0 -118.4 3.0 123.2 15.0 56.8 -3.0\n",
" -15.0 -160.6 -3.0 -319.4 15.0 321.2 3.0 158.8\n",
" -118.4 -3.0 -61.6 15.0 56.8 3.0 123.2 -15.0\n",
" 3.0 -319.4 15.0 -160.6 -3.0 158.8 -15.0 321.2"
"2.927103942720631"
]
},
"execution_count": 8,
"execution_count": 169,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"JuliaFEM.integrate_lhs(equation, 0.0)"
"(1/2*u'*JuliaFEM.integrate_lhs(equation, 0.0)*u)[1]"
]
},
{
src/types.jl
+1 -1
View File
@@ -13,7 +13,7 @@ type Field{T}
end
""" Initialize field. """
function Field(time, values)
Field(time, 1, values)
Field(time, 0, values)
end
""" Get length of a field (number of basis functions in practice). """
function Base.length(f::Field)