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},
"execution_count": 72,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"showlibrary(:cmocean)\n",
"# :Plots\n",
"# :cmocean\n",
"# :misc\n",
"# :colorcet\n",
"# :colorbrewer"
]
},
{
"cell_type": "code",
"execution_count": 90,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"getIndex (generic function with 1 method)"
]
},
"execution_count": 90,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"include(\"./julia/FEM.jl\")\n",
"include(\"./julia/data_FEM.jl\")\n",
"include(\"./julia/MBB.jl\")\n",
"include(\"./julia/topologyOptimization.jl\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## FEM vs Topology"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"1.0"
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"nelx=60\n",
"nely=20\n",
"Emin=1e-9\n",
"Emax=1.0"
]
},
{
"cell_type": "code",
"execution_count": 74,
"metadata": {},
"outputs": [],
"source": [
"volfrac=0.5\n",
"problem=MBB(nelx,nely)\n",
"E,f,g,idb,ien,iplane,ndf,nel,nen,nnp,nsd,snu,t,xn,Ke=problem;\n",
"ρ=ones(nel).*volfrac;\n",
"K,F,d,de,Fe=FEM(problem,ρ);\n",
"# ce = reshape(sum((U[edofMat]*KE).*U[edofMat],dims=2),nely,nelx)\n",
"# c = sum(sum((Emin.+xPhys.^penal*(Emax-Emin)).*ce))\n",
"\n",
"sK = reshape(Ke[:,:,1][:]*(Emin.+ρ'.^penal*(Emax-Emin)),64*nelx*nely,1);"
]
},
{
"cell_type": "code",
"execution_count": 81,
"metadata": {},
"outputs": [],
"source": [
"# dofs:\n",
"ndof = 2*(nelx+1)*(nely+1)\n",
"# Allocate design variables (as array), initialize and allocate sens.\n",
"x=volfrac * ones(Float64,nely,nelx)\n",
"xold=copy(x)\n",
"xPhys=copy(x)\n",
"g=0 # must be initialized to use the NGuyen/Paulino OC approach\n",
"dc=zeros(Float64,(nely,nelx))\n",
"\n",
"# FE: Build the index vectors for the for coo matrix format.\n",
"KE=lk()\n",
"nodenrs = reshape(1:(1+nelx)*(1+nely),1+nely,1+nelx)\n",
"edofVec = reshape(2*nodenrs[1:end-1,1:end-1].+1,nelx*nely,1)\n",
"edofMat = repeat(edofVec,1,8).+repeat([0 1 2*nely.+[2 3 0 1] -2 -1],nelx*nely,1)\n",
"iK = convert(Array{Int},reshape(kron(edofMat,ones(8,1))',64*nelx*nely,1))\n",
"jK = convert(Array{Int},reshape(kron(edofMat,ones(1,8))',64*nelx*nely,1))\n",
"# DEFINE LOADS AND SUPPORTS (HALF MBB-BEAM)\n",
"F = sparse([2],[1],[-1.0],2*(nely+1)*(nelx+1),1)\n",
"U = zeros(2*(nely+1)*(nelx+1),1)\n",
"fixeddofs = union(1:2:2*(nely+1),2*(nelx+1)*(nely+1))\n",
"alldofs = 1:(2*(nely+1)*(nelx+1))\n",
"freedofs = setdiff(alldofs,fixeddofs)\n",
"sK = reshape(KE[:]*(Emin.+xPhys[:]'.^penal*(Emax-Emin)),64*nelx*nely,1)\n",
"K = sparse(vec(iK),vec(jK),vec(sK)); \n",
"K = (K+K')/2\n",
"@timed U[freedofs] = K[freedofs,freedofs] \\ Array(F[freedofs])\n",
"# Objective function and sensitivity analysis\n",
"ce = reshape(sum((U[edofMat]*KE).*U[edofMat],dims=2),nely,nelx)\n",
"c = sum(sum((Emin.+xPhys.^penal*(Emax-Emin)).*ce));"
]
},
{
"cell_type": "code",
"execution_count": 82,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"2562×1 SparseMatrixCSC{Float64,Int64} with 1 stored entry:\n",
" [2, 1] = -1.0"
]
},
"execution_count": 82,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"F"
]
},
{
"cell_type": "code",
"execution_count": 83,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"8×8 Array{Float64,2}:\n",
" 0.494505 0.178571 -0.302198 … -0.178571 0.0549451 0.0137363\n",
" 0.178571 0.494505 0.0137363 -0.247253 -0.0137363 -0.302198\n",
" -0.302198 0.0137363 0.494505 -0.0137363 -0.247253 0.178571\n",
" -0.0137363 0.0549451 -0.178571 -0.302198 0.178571 -0.247253\n",
" -0.247253 -0.178571 0.0549451 0.178571 -0.302198 -0.0137363\n",
" -0.178571 -0.247253 -0.0137363 … 0.494505 0.0137363 0.0549451\n",
" 0.0549451 -0.0137363 -0.247253 0.0137363 0.494505 -0.178571\n",
" 0.0137363 -0.302198 0.178571 0.0549451 -0.178571 0.494505"
]
},
"execution_count": 83,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"KE"
]
},
{
"cell_type": "code",
"execution_count": 84,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"2562×2562 SparseMatrixCSC{Float64,Int64} with 32330 stored entries:\n",
" [1 , 1] = 0.0618132\n",
" [2 , 1] = -0.0223214\n",
" [3 , 1] = 0.00686813\n",
" [4 , 1] = -0.00171703\n",
" [43 , 1] = -0.0377747\n",
" [44 , 1] = 0.00171703\n",
" [45 , 1] = -0.0309066\n",
" [46 , 1] = 0.0223214\n",
" [1 , 2] = -0.0223214\n",
" [2 , 2] = 0.0618132\n",
" [3 , 2] = 0.00171703\n",
" [4 , 2] = -0.0377747\n",
" ⋮\n",
" [2520, 2561] = 0.00171703\n",
" [2559, 2561] = 0.00686813\n",
" [2560, 2561] = -0.00171703\n",
" [2561, 2561] = 0.0618132\n",
" [2562, 2561] = -0.0223214\n",
" [2517, 2562] = 0.0223214\n",
" [2518, 2562] = -0.0309066\n",
" [2519, 2562] = -0.00171703\n",
" [2520, 2562] = 0.00686813\n",
" [2559, 2562] = 0.00171703\n",
" [2560, 2562] = -0.0377747\n",
" [2561, 2562] = -0.0223214\n",
" [2562, 2562] = 0.0618132"
]
},
"execution_count": 84,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"K"
]
},
{
"cell_type": "code",
"execution_count": 85,
"metadata": {},
"outputs": [
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