From 69a31706356aaeaaba1a9d13723745ccdbd65926 Mon Sep 17 00:00:00 2001
From: amiraa <amiraa@mit.edu>
Date: Thu, 14 Oct 2021 04:27:01 -0400
Subject: [PATCH] max min thickness
---
voxel_designer/150921_Max_Min_Thickness.ipynb | 16113 ++++++++++++++++
voxel_designer/julia/include/mmaSolver.jl | 8 +-
voxel_designer/julia/include/top2D.jl | 126 +
voxel_designer/out.jpg | Bin 0 -> 1461 bytes
4 files changed, 16245 insertions(+), 2 deletions(-)
create mode 100644 voxel_designer/150921_Max_Min_Thickness.ipynb
create mode 100644 voxel_designer/out.jpg
diff --git a/voxel_designer/150921_Max_Min_Thickness.ipynb b/voxel_designer/150921_Max_Min_Thickness.ipynb
new file mode 100644
index 0000000..a4a74c4
--- /dev/null
+++ b/voxel_designer/150921_Max_Min_Thickness.ipynb
@@ -0,0 +1,16113 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Maximum and Minimum Thickness Constraints\n",
+ "\n",
+ "Trying to re-implement this: https://www.sciencedirect.com/science/article/pii/S0045782514003065\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 330,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Loaded Topology Optimization Library!\n"
+ ]
+ }
+ ],
+ "source": [
+ "include(\"./julia/include/_topologyOptimization.jl\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Top Opt MMA"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 52,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "\"Minimum compliance problem with MMA\""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "text/plain": [
+ "\"ndes: 120 x 60\""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "text/plain": [
+ "\"volfrac: 0.4 rmin: 1.5 penal: 3\""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "text/plain": [
+ "(94.28277445683601, [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0e-9, 1.0e-9 … 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0], :MAXEVAL_REACHED)"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "text/plain": [
+ "\"got 94.28277445683601 after 100 iterations (returned MAXEVAL_REACHED)\""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
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+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " 7.672618 seconds (22.21 k allocations: 6.146 GiB, 6.62% gc time)\n"
+ ]
+ }
+ ],
+ "source": [
+ "nelx=120\n",
+ "nely=60\n",
+ "volfrac=0.4\n",
+ "rmin=1.5\n",
+ "penal=3\n",
+ "maxEval=100\n",
+ "xPhys=topologyOptimizationMMA(nelx,nely,volfrac,rmin,penal,maxEval);\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Skeleton"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 53,
+ "metadata": {},
+ "outputs": [
+ {
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+ ]
+ },
+ "execution_count": 53,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "include(\"./julia/traceskeleton.jl\")\n",
+ "\n",
+ "bim=xPhys.>=0.5;\n",
+ "bim = thinning_zs(bim)\n",
+ "\n",
+ "Plots.heatmap(bim, aspect_ratio=:equal, legend=false, axis=nothing,foreground_color_subplot=colorant\"white\",fc=:grays)\n",
+ "# H,W = size(bim)\n",
+ "# @time q = trace_skeleton(bim,10,999)\n",
+ "# print(\" -->\")\n",
+ "# print(polylines_to_svg(q,W,H))\n",
+ "\n",
+ "# using ColorTypes\n",
+ "# img = convert(Array{ColorTypes.Gray{Bool}}, convert(Array{Bool},bim))\n",
+ "# save(\"out.jpg\",img)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 226,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "60×120 Array{Float64,2}:\n",
+ " 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 … 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n",
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+ " ⋮ ⋮ ⋱ ⋮ \n",
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+ ]
+ },
+ "execution_count": 226,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "using ImageBinarization\n",
+ "imgb = binarize(xPhys, Otsu())"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 224,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "\u001b[32m\u001b[1m Resolving\u001b[22m\u001b[39m package versions...\n",
+ "\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m LazyArtifacts ───────── v1.3.0\n",
+ "\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m HistogramThresholding ─ v0.2.5\n",
+ "\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m Intervals ───────────── v1.5.0\n",
+ "\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m Polynomials ─────────── v2.0.14\n",
+ "\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m ImageBinarization ───── v0.2.7\n",
+ "\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m TimeZones ───────────── v1.5.7\n",
+ "\u001b[32m\u001b[1mUpdating\u001b[22m\u001b[39m `~/.julia/environments/v1.5/Project.toml`\n",
+ " \u001b[90m [cbc4b850] \u001b[39m\u001b[92m+ ImageBinarization v0.2.7\u001b[39m\n",
+ "\u001b[32m\u001b[1mUpdating\u001b[22m\u001b[39m `~/.julia/environments/v1.5/Manifest.toml`\n",
+ " \u001b[90m [2c695a8d] \u001b[39m\u001b[92m+ HistogramThresholding v0.2.5\u001b[39m\n",
+ " \u001b[90m [cbc4b850] \u001b[39m\u001b[92m+ ImageBinarization v0.2.7\u001b[39m\n",
+ " \u001b[90m [d8418881] \u001b[39m\u001b[92m+ Intervals v1.5.0\u001b[39m\n",
+ " \u001b[90m [4af54fe1] \u001b[39m\u001b[92m+ LazyArtifacts v1.3.0\u001b[39m\n",
+ " \u001b[90m [d8a4904e] \u001b[39m\u001b[92m+ MutableArithmetics v0.2.20\u001b[39m\n",
+ " \u001b[90m [f27b6e38] \u001b[39m\u001b[92m+ Polynomials v2.0.14\u001b[39m\n",
+ " \u001b[90m [f269a46b] \u001b[39m\u001b[92m+ TimeZones v1.5.7\u001b[39m\n",
+ "\u001b[32m\u001b[1m Building\u001b[22m\u001b[39m TimeZones → `~/.julia/packages/TimeZones/kDO1y/deps/build.log`\n"
+ ]
+ }
+ ],
+ "source": [
+ "import Pkg; Pkg.add(\"ImageBinarization\")"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 54,
+ "metadata": {},
+ "outputs": [
+ {
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+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "using SignedDistanceFields\n",
+ "xPhys1=xPhys.>=0.5;\n",
+ "\n",
+ "ss=sdf(xPhys1)\n",
+ "ss=sdf(bim)\n",
+ "\n",
+ "display(Plots.heatmap(ss, aspect_ratio=:equal,fc=:grays))\n",
+ "sss=(ss.==-1)\n",
+ "display(Plots.heatmap(sss, aspect_ratio=:equal,fc=:grays))\n",
+ "\n",
+ "tmin=1\n",
+ "tmax=3\n",
+ "\n",
+ "Imin=((ss.>=0) .& (ss.<=tmin))\n",
+ "Imin=( (ss.<=tmin))\n",
+ "\n",
+ "display(Plots.heatmap(Imin, aspect_ratio=:equal,fc=:grays))\n",
+ "\n",
+ "\n",
+ "Imax=((ss.>=0) .& (ss.<=tmax))\n",
+ "Imax=((ss.<=tmax))\n",
+ "\n",
+ "display(Plots.heatmap(Imax, aspect_ratio=:equal,fc=:grays))\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Top Opt MMA with Skeleton"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 284,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "topologyOptimizationMinMaxThickness (generic function with 2 methods)"
+ ]
+ },
+ "execution_count": 284,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "using ImageBinarization\n",
+ "using SignedDistanceFields\n",
+ "include(\"./julia/traceskeleton.jl\")\n",
+ "\n",
+ "function topologyOptimizationMinMaxThickness(nelx,nely,prob,volfrac,rmin,penal,maxEval,tmin,tmax,min_max=true)\n",
+ " # Max and min stiffness\n",
+ " Emin=1e-2;\n",
+ " Emax=1.0;\n",
+ "\n",
+ " # 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",
+ " \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",
+ " \n",
+ " U,F,freedofs=prob(nelx,nely) \n",
+ " \n",
+ " \n",
+ " H,Hs=make_filter(nelx,nely,rmin)\n",
+ "\n",
+ " nel=nely*nelx\n",
+ "\n",
+ " function FA(x::Vector, grad::Vector)\n",
+ "\n",
+ " xPhys=reshape(x,nely,nelx)\n",
+ "\n",
+ " sK = reshape(KE[:]*(Emin.+xPhys[:]'.^penal*(Emax-Emin)),64*nelx*nely,1)\n",
+ " K = sparse(vec(iK),vec(jK),vec(sK)); 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))\n",
+ "\n",
+ " dc = -penal*(Emax-Emin)*xPhys.^(penal-1).*ce\n",
+ " dc[:] = H*(dc[:]./Hs)\n",
+ "\n",
+ " grad[:] .= dc[:]\n",
+ "\n",
+ " return c\n",
+ " end\n",
+ "\n",
+ "\n",
+ "\n",
+ " function G(x::Vector, grad::Vector)\n",
+ " dv = ones(nely,nelx)\n",
+ " dv[:] = H*(dv[:]./Hs)\n",
+ "\n",
+ " grad[:] .= dv[:]\n",
+ "\n",
+ " return (sum(x) - volfrac*nel)\n",
+ " end\n",
+ "\n",
+ " function Gmin(x::Vector, grad::Vector)\n",
+ "\n",
+ " xPhys1=Bool.(binarize(reshape(x,nely,nelx), Otsu()))\n",
+ " #reshape(x,nely,nelx).>=0.5;\n",
+ " bim = thinning_zs(xPhys1) # get the skeleton (check algorithm is correct with matlab (boundary conditions))\n",
+ " ss=sdf(bim) # signed distance field form skeletom\n",
+ " Imin= (ss.<=tmin) # all the ones that respect the min distance\n",
+ " # Imax= (ss.>tmax) # all the ones that respect the max distance\n",
+ " dv = zeros(nely,nelx)\n",
+ " dv[Imin[:]].=2 .*(x[Imin[:]] .-Emax)\n",
+ "\n",
+ "\n",
+ " # dv[:] = H*(dv[:]./Hs)\n",
+ " grad[:] .= dv[:]\n",
+ "\n",
+ " return sum((x[Imin[:]].-Emax).^2)-startt/iterr\n",
+ " end\n",
+ "\n",
+ " function Gmax(x::Vector, grad::Vector)\n",
+ "\n",
+ " xPhys1=Bool.(binarize(reshape(x,nely,nelx), Otsu()))\n",
+ " #reshape(x,nely,nelx).>=0.5;\n",
+ " bim = thinning_zs(xPhys1) # get the skeleton (check algorithm is correct with matlab (boundary conditions))\n",
+ " ss=sdf(bim) # signed distance field form skeletom\n",
+ " #Imin= (ss.<=tmin) # all the ones that respect the min distance\n",
+ " Imax= (ss.>tmax) # all the ones that respect the max distance\n",
+ " dv = zeros(nely,nelx)\n",
+ " dv[Imax[:]].=2 .*(x[Imax[:]] .-Emin)\n",
+ "\n",
+ "\n",
+ " # dv[:] = H*(dv[:]./Hs)\n",
+ " grad[:] .= dv[:]\n",
+ "\n",
+ " return sum((x[Imax[:]].-Emin).^2)-startt/iterr\n",
+ " end\n",
+ "\n",
+ "\n",
+ "\n",
+ " iterr=1\n",
+ " startt=100 #100\n",
+ "\n",
+ " FA(ones(nel)*volfrac, fill(volfrac,nel))\n",
+ " G(ones(nel)*volfrac, fill(volfrac,nel))\n",
+ " Gmin(ones(nel)*volfrac, fill(volfrac,nel))\n",
+ " Gmax(ones(nel)*volfrac, fill(volfrac,nel))\n",
+ " \n",
+ " \n",
+ " \n",
+ " opt = Opt(:LD_MMA, nel)\n",
+ " opt.lower_bounds = fill(Emin,nel)\n",
+ " opt.upper_bounds = fill(Emax,nel)\n",
+ " opt.xtol_rel = 1e-9\n",
+ " \n",
+ "\n",
+ " opt.min_objective = FA\n",
+ " inequality_constraint!(opt, (x,gg) -> G(x,gg), 1e-9)\n",
+ " if min_max\n",
+ " steps=4\n",
+ " opt.maxeval = Int(maxEval/steps)\n",
+ " inequality_constraint!(opt, (x,gg) -> Gmin(x,gg), 1e-4)\n",
+ " inequality_constraint!(opt, (x,gg) -> Gmax(x,gg), 1e-4)\n",
+ " \n",
+ " #display(@time (minf,minx,ret) = optimize(opt, ones(nel).*volfrac))\n",
+ " minx=ones(nel).*volfrac\n",
+ " for i=1:steps\n",
+ " (minf,minx,ret) = optimize(opt, minx)\n",
+ " numevals = opt.numevals # the number of function evaluations\n",
+ " display(\"got $minf after $numevals iterations (returned $ret)\")\n",
+ " display(100/iterr)\n",
+ " iterr+=10\n",
+ " end\n",
+ " else\n",
+ " opt.maxeval = Int(maxEval)\n",
+ " display(@time (minf,minx,ret) = optimize(opt, ones(nel).*volfrac))\n",
+ "\n",
+ " end\n",
+ "\n",
+ " \n",
+ "\n",
+ " xPhys=reshape(minx,nely,nelx)\n",
+ " display(Plots.heatmap(xPhys, aspect_ratio=:equal, legend=false, axis=nothing,fc=:grays))\n",
+ "\n",
+ " return xPhys\n",
+ "end\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 285,
+ "metadata": {},
+ "outputs": [
+ {
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+ "cAAAAAAAognhAAAAAABEE8IBAAAAAIgmhAMAAAAAEE0IBwAAAAAg2lBKGZf8ga21JX8c7KU//vhj\n",
+ "8swLL7ywwBIAAA5B8vew3377batzL7/88k5+XvK/ZbrLly9Pnrl06dICSwDowY1wAAAAAACiCeEA\n",
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+ "AKIJ4QAAAAAARBPCAQAAAACIJoQDAAAAABBNCAcAAAAAIJoQDgAAAABANCEcAAAAAIBoQjgAAAAA\n",
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+ "cAAAAAAAognhAAAAAABEE8IBAAAAAIgmhAMAAAAAEE0IBwAAAAAgmhAOAAAAAEA0IRwAAAAAgGhD\n",
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+ "AAAAIJoQDgAAAABANCEcAAAAAIBoQjgAAAAAANGEcAAAAAAAognhAAAAAABEG0opY+8R0FtrrfcE\n",
+ "QtRae08AAGa01vfGL774YvLMBx98sMAS6Getf7/Jvvrqq8kz77///gJLgEPgRjgAAAAAANGEcAAA\n",
+ "AAAAognhAAAAAABEE8IBAAAAAIgmhAMAAAAAEE0IBwAAAAAgmhAOAAAAAEA0IRwAAAAAgGhDKWXs\n",
+ "PQJStNZ6TyBIrbX3BAA4KGt9l/v1118nz7zyyisLLIHDsNZnRTLfnYBtuBEOAAAAAEA0IRwAAAAA\n",
+ "gGhCOAAAAAAA0YRwAAAAAACiCeEAAAAAAEQTwgEAAAAAiCaEAwAAAAAQTQgHAAAAACDaUEoZe48A\n",
+ "HtRa6z2BELXW3hMAoLvbt29PnnnkkXXeE/JZD/vH97n9dOvWrckzr7322gJLgB7W+aYHAAAAAABb\n",
+ "EsIBAAAAAIgmhAMAAAAAEE0IBwAAAAAgmhAOAAAAAEA0IRwAAAAAgGhCOAAAAAAA0YRwAAAAAACi\n",
+ "DaWUsfcIYD6ttd4TCFJr7T0BAP7l8uXLW5174403Zl4yD5+9gO90+8ezGdbJjXAAAAAAAKIJ4QAA\n",
+ "AAAARBPCAQAAAACIJoQDAAAAABBNCAcAAAAAIJoQDgAAAABANCEcAAAAAIBoQjgAAAAAANGEcAAA\n",
+ "AAAAog2llLH3CGAdWmu9JxCi1tp7AgAh1vp+4rMQ2KVz585Nnrlx48YCS7jn77//njzzzDPPLLAE\n",
+ "uMeNcAAAAAAAognhAAAAAABEE8IBAAAAAIgmhAMAAAAAEE0IBwAAAAAgmhAOAAAAAEA0IRwAAAAA\n",
+ "gGhCOAAAAAAA0YZSyth7BHBYWmu9JxCi1tp7AgAzWus7g88nYK3W+txN53MFdsONcAAAAAAAognh\n",
+ "AAAAAABEE8IBAAAAAIgmhAMAAAAAEE0IBwAAAAAgmhAOAAAAAEA0IRwAAAAAgGhCOAAAAAAA0YZS\n",
+ "yth7BMBptdZ6T2AFNpvN5Jnz588vsASAe9b6GV5r7T0BYBXW+pxfq3/++WfyzNNPP73AEthfboQD\n",
+ "AAAAABBNCAcAAAAAIJoQDgAAAABANCEcAAAAAIBoQjgAAAAAANGEcAAAAAAAognhAAAAAABEE8IB\n",
+ "AAAAAIg2lFLG3iMAemut9Z7ACly7dm3yzMWLFxdYArDfkj9Xa629JwDESP68WCufcyRzIxwAAAAA\n",
+ "gGhCOAAAAAAA0YRwAAAAAACiCeEAAAAAAEQTwgEAAAAAiCaEAwAAAAAQTQgHAAAAACCaEA4AAAAA\n",
+ "QLShlDL2HgGQorXWewIrUWvtPQHgVL7//vvJM88+++wCS3bPsxlgnXwPW9Zff/211bm1vg+Qy41w\n",
+ "AAAAAACiCeEAAAAAAEQTwgEAAAAAiCaEAwAAAAAQTQgHAAAAACCaEA4AAAAAQDQhHAAAAACAaEI4\n",
+ "AAAAAADRhHAAAAAAAKINpZSx9wiAQ/Ptt99OnnnuuefmH8Lq1Vp7TwBCfPjhh1ude/fdd2deMg/P\n",
+ "SwBaa70ncB+fzyzJjXAAAAAAAKIJ4QAAAAAARBPCAQAAAACIJoQDAAAAABBNCAcAAAAAIJoQDgAA\n",
+ "AABANCEcAAAAAIBoQjgAAAAAANGGUsrYewQAp9Na6z2BELXW3hOAztb6meL5BcDS1vqZuVabzWby\n",
+ "zPnz5xdYwtq5EQ4AAAAAQDQhHAAAAACAaEI4AAAAAADRhHAAAAAAAKIJ4QAAAAAARBPCAQAAAACI\n",
+ "JoQDAAAAABBNCAcAAAAAINpQShl7jwCgr9Za7wkEqbX2ngDcZ63Pec8TANZqrZ+96bxbHDY3wgEA\n",
+ "AAAAiCaEAwAAAAAQTQgHAAAAACCaEA4AAAAAQDQhHAAAAACAaEI4AAAAAADRhHAAAAAAAKIJ4QAA\n",
+ "AAAARBtKKWPvEQDkaK31nkCIWmvvCbAKyc9dzwEAyP6s30fXr1+fPHNycrLAEnbNjXAAAAAAAKIJ\n",
+ "4QAAAAAARBPCAQAAAACIJoQDAAAAABBNCAcAAAAAIJoQDgAAAABANCEcAAAAAIBoQjgAAAAAANGG\n",
+ "UsrYewQA3K+11nsCKzCO273GnD17duYlMI+ffvpp8swTTzyxwJLdq7X2ngAAMXx/2j/edfaPG+EA\n",
+ "AAAAAEQTwgEAAAAAiCaEAwAAAAAQTQgHAAAAACCaEA4AAAAAQDQhHAAAAACAaEI4AAAAAADRhHAA\n",
+ "AAAAAKIJ4QAAAAAARBtKKWPvEQAwp9Za7wmswN27dyfPHB8fL7CEQ/DRRx9tde6tt96aeck8aq29\n",
+ "JwAAp+C707K2fSf89NNPZ15yGNwIBwAAAAAgmhAOAAAAAEA0IRwAAAAAgGhCOAAAAAAA0YRwAAAA\n",
+ "AACiCeEAAAAAAEQTwgEAAAAAiCaEAwAAAAAQbSiljL1HAMAatNZ6TyBIrbX3BDpa8/PE7y4AHLY1\n",
+ "v8ck8442zY1wAAAAAACiCeEAAAAAAEQTwgEAAAAAiCaEAwAAAAAQTQgHAAAAACCaEA4AAAAAQDQh\n",
+ "HAAAAACAaEI4AAAAAADRhlLK2HsEAKS4cuXKVudef/31mZdwKGqtvSdwn9Za7wmn4ncJAFjaWt+b\n",
+ "1urQ3/fcCAcAAAAAIJoQDgAAAABANCEcAAAAAIBoQjgAAAAAANGEcAAAAAAAognhAAAAAABEE8IB\n",
+ "AAAAAIgmhAMAAAAAEG0opYy9RwAAD7p58+bkmaOjowWWcAhqrb0nrEJrrfeE2fgdAAD2UfL711qt\n",
+ "9b3RjXAAAAAAAKIJ4QAAAAAARBPCAQAAAACIJoQDAAAAABBNCAcAAAAAIJoQDgAAAABANCEcAAAA\n",
+ "AIBoQjgAAAAAANGEcAAAAAAAog2llLH3CABgPq213hM4MLXW3hNOJflvZa3/TwAAdin5fW8f7ds7\n",
+ "qBvhAAAAAABEE8IBAAAAAIgmhAMAAAAAEE0IBwAAAAAgmhAOAAAAAEA0IRwAAAAAgGhCOAAAAAAA\n",
+ "0YRwAAAAAACiDaWUsfcIAGAdWmu9JxCi1rroz7tx48bkmXPnzi2wZPeW/rcEAEjmO8+y7t69O3nm\n",
+ "+Ph4Jz/LjXAAAAAAAKIJ4QAAAAAARBPCAQAAAACIJoQDAAAAABBNCAcAAAAAIJoQDgAAAABANCEc\n",
+ "AAAAAIBoQjgAAAAAANGGUsrYewQAkOPk5GTyzCeffLLAEli/WmvvCQAA3OfRRx+dPPPLL78ssIR7\n",
+ "tnlvdiMcAAAAAIBoQjgAAAAAANGEcAAAAAAAognhAAAAAABEE8IBAAAAAIgmhAMAAAAAEE0IBwAA\n",
+ "AAAgmhAOAAAAAEC0oZQy9h4BAHC/n3/+efLM448/vsAS6KfW2nsCAAAzaa31nnBQ3AgHAAAAACCa\n",
+ "EA4AAAAAQDQhHAAAAACAaEI4AAAAAADRhHAAAAAAAKIJ4QAAAAAARBPCAQAAAACIJoQDAAAAABBt\n",
+ "KKWMvUcAAMyptdZ7AvxLrbX3BAAAVsL3md1wIxwAAAAAgGhCOAAAAAAA0YRwAAAAAACiCeEAAAAA\n",
+ "AEQTwgEAAAAAiCaEAwAAAAAQTQgHAAAAACCaEA4AAAAAQDQhHAAAAACAaEMpZew9AgCgtx9//HHy\n",
+ "zJNPPrnAEtau1tp7AgAAPKC11ntCV26EAwAAAAAQTQgHAAAAACCaEA4AAAAAQDQhHAAAAACAaEI4\n",
+ "AAAAAADRhHAAAAAAAKIJ4QAAAAAARBPCAQAAAACINpRSxt4jAADW4ObNm5Nnjo6OFljCPqu19p4A\n",
+ "AACn0lrrPWE2boQDAAAAABBNCAcAAAAAIJoQDgAAAABANCEcAAAAAIBoQjgAAAAAANGEcAAAAAAA\n",
+ "ognhAAAAAABEE8IBAAAAAIgmhAMAAAAAEE0IBwAAAAAgmhAOAAAAAEA0IRwAAAAAgGhCOAAAAAAA\n",
+ "0YRwAAAAAACiCeEAAAAAAEQTwgEAAAAAiCaEAwAAAAAQ7UzvAQAA++DHH3+cPHN0dLTAEgAAgN1r\n",
+ "rfWe0JUb4QAAAAAARBPCAQAAAACIJoQDAAAAABBNCAcAAAAAIJoQDgAAAABANCEcAAAAAIBoQjgA\n",
+ "AAAAANGEcAAAAAAAog2llLH3CACAObXWek+Af6m19p4AAMBK+D6zG26EAwAAAAAQTQgHAAAAACCa\n",
+ "EA4AAAAAQDQhHAAAAACAaEI4AAAAAADRhHAAAAAAAKIJ4QAAAAAARBPCAQAAAACIJoQDAAAAABBt\n",
+ "KKWMvUcAANzv559/njzz+OOPL7AE+qm19p4AAMBMWmu9JxwUN8IBAAAAAIgmhAMAAAAAEE0IBwAA\n",
+ "AAAgmhAOAAAAAEA0IRwAAAAAgGhCOAAAAAAA0YRwAAAAAACiCeEAAAAAAEQ703sAAJDl5ORk8swn\n",
+ "n3yywBIAAIDde/TRRyfP/PLLLwss4Z5a6+QZN8IBAAAAAIgmhAMAAAAAEE0IBwAAAAAgmhAOAAAA\n",
+ "AEA0IRwAAAAAgGhCOAAAAAAA0YRwAAAAAACiCeEAAAAAAEQbSilj7xEAwDq01npPIEStddGfd+PG\n",
+ "jckz586dW2DJ7i39bwkAkMx3nmXdvXt38szx8fFOfpYb4QAAAAAARBPCAQAAAACIJoQDAAAAABBN\n",
+ "CAcAAAAAIJoQDgAAAABANCEcAAAAAIBoQjgAAAAAANGEcAAAAAAAog2llLH3CABgPq213hM4MLXW\n",
+ "3hNOJflvZa3/TwAAdin5fW8f7ds7qBvhAAAAAABEE8IBAAAAAIgmhAMAAAAAEE0IBwAAAAAgmhAO\n",
+ "AAAAAEA0IRwAAAAAgGhCOAAAAAAA0YRwAAAAAACiDaWUsfcIAOBBN2/enDxzdHS0wBIOQa2194RV\n",
+ "aK31njAbvwMAwD5Kfv9aq7W+N7oRDgAAAABANCEcAAAAAIBoQjgAAAAAANGEcAAAAAAAognhAAAA\n",
+ "AABEE8IBAAAAAIgmhAMAAAAAEE0IBwAAAAAgmhAOAAAAAEC0M70HAECSK1eubHXu9ddfn3kJh6LW\n",
+ "2nvCQdnm37u1tsASAID18960rEP/7uBGOAAAAAAA0YRwAAAAAACiCeEAAAAAAEQTwgEAAAAAiCaE\n",
+ "AwAAAAAQTQgHAAAAACCaEA4AAAAAQDQhHAAAAACAaEMpZew9AgDWoLXWewJBaq29J9DRmp8nfncB\n",
+ "4LCt+T0mmXe0aW6EAwAAAAAQTQgHAAAAACCaEA4AAAAAQDQhHAAAAACAaEI4AAAAAADRhHAAAAAA\n",
+ "AKIJ4QAAAAAARBPCAQAAAACIdqb3AACYW2ut9wRW4O7du5Nnjo+PF1jCIfjss8+2OvfWW2/NvOTh\n",
+ "bfNMrbUusAQA2DXfnZb10UcfbXXu008/nXnJYXAjHAAAAACAaEI4AAAAAADRhHAAAAAAAKIJ4QAA\n",
+ "AAAARBPCAQAAAACIJoQDAAAAABBNCAcAAAAAIJoQDgAAAABAtKGUMvYeAQD3a631nsAKjON2rzFn\n",
+ "z56deQnM46effpo888QTTyywZPdqrb0nAEAM35/2j3ed/eNGOAAAAAAA0YRwAAAAAACiCeEAAAAA\n",
+ "AEQTwgEAAAAAiCaEAwAAAAAQTQgHAAAAACCaEA4AAAAAQDQhHAAAAACAaEI4AAAAAADRhlLK2HsE\n",
+ "ADlaa70nEKLW2nsCrELyc9dzAACyP+v30fXr1yfPnJycLLCEXXMjHAAAAACAaEI4AAAAAADRhHAA\n",
+ "AAAAAKIJ4QAAAAAARBPCAQAAAACIJoQDAAAAABBNCAcAAAAAIJoQDgAAAABAtDO9BwDQX2ut9wSC\n",
+ "1Fp7T4CDss3fnOc8ACzLZ+9+8l3lsLkRDgAAAABANCEcAAAAAIBoQjgAAAAAANGEcAAAAAAAognh\n",
+ "AAAAAABEE8IBAAAAAIgmhAMAAAAAEE0IBwAAAAAg2lBKGXuPAOB0Wmu9JxCi1tp7AtDZWj9TPL8A\n",
+ "WNpaPzPXarPZTJ45f/78AktYOzfCAQAAAACIJoQDAAAAABBNCAcAAAAAIJoQDgAAAABANCEcAAAA\n",
+ "AIBoQjgAAAAAANGEcAAAAAAAognhAAAAAABEG0opY+8RAIfm22+/nTzz3HPPzT+E1au19p4AhPjw\n",
+ "ww+3Ovfuu+/OvGQenpcAtNZ6T+A+Pp9ZkhvhAAAAAABEE8IBAAAAAIgmhAMAAAAAEE0IBwAAAAAg\n",
+ "mhAOAAAAAEA0IRwAAAAAgGhCOAAAAAAA0YRwAAAAAACiDaWUsfcIgBSttd4TWIlaa+8JAKfy/fff\n",
+ "T5559tlnF1iye57NAOvke9iy/vrrr63OrfV9gFxuhAMAAAAAEE0IBwAAAAAgmhAOAAAAAEA0IRwA\n",
+ "AAAAgGhCOAAAAAAA0YRwAAAAAACiCeEAAAAAAEQTwgEAAAAAiCaEAwAAAAAQbSiljL1HAPTWWus9\n",
+ "gRW4du3a5JmLFy8usARgvyV/rtZae08AiJH8ebFWPudI5kY4AAAAAADRhHAAAAAAAKIJ4QAAAAAA\n",
+ "RBPCAQAAAACIJoQDAAAAABBNCAcAAAAAIJoQDgAAAABANCEcAAAAAIBoZ3oPAPj/aK31nsAKbDab\n",
+ "yTPnz59fYAnAYai1Tp7xGQ6QzXN+Wf/888/kmaeffnqBJbC/3AgHAAAAACCaEA4AAAAAQDQhHAAA\n",
+ "AACAaEI4AAAAAADRhHAAAAAAAKIJ4QAAAAAARBPCAQAAAACIJoQDAAAAABBtKKWMvUcAh6W11nsC\n",
+ "IWqtvScAMKO1vjP4fALWaq3P3XQ+V2A33AgHAAAAACCaEA4AAAAAQDQhHAAAAACAaEI4AAAAAADR\n",
+ "hHAAAAAAAKIJ4QAAAAAARBPCAQAAAACIJoQDAAAAABBtKKWMvUcA69Ba6z2BELXW3hMACLHW9xOf\n",
+ "hcAunTt3bvLMjRs3FljCPX///ffkmWeeeWaBJcA9boQDAAAAABBNCAcAAAAAIJoQDgAAAABANCEc\n",
+ "AAAAAIBoQjgAAAAAANGEcAAAAAAAognhAAAAAABEE8IBAAAAAIh2pvcAYF6ttd4TCFJr7T0BAP7l\n",
+ "6tWrW5174403Zl7ycLZ9R/PZC/hOt388m2Gd3AgHAAAAACCaEA4AAAAAQDQhHAAAAACAaEI4AAAA\n",
+ "AADRhHAAAAAAAKIJ4QAAAAAARBPCAQAAAACIJoQDAAAAABBNCAcAAAAAINpQShl7jwAe1FrrPYEQ\n",
+ "tdbeEwCgu9u3b0+eeeSRdd4T8lkP+8f3uf1069atyTOvvfbaAkuAHtb5pgcAAAAAAFsSwgEAAAAA\n",
+ "iCaEAwAAAAAQTQgHAAAAACCaEA4AAAAAQDQhHAAAAACAaEI4AAAAAADRhHAAAAAAAKINpZSx9whI\n",
+ "0VrrPYEgtdbeEwDgoKz1Xe7XX3+dPPPKK68ssAQOw1qfFcl8dwK24UY4AAAAAADRhHAAAAAAAKIJ\n",
+ "4QAAAAAARBPCAQAAAACIJoQDAAAAABBNCAcAAAAAIJoQDgAAAABANCEcAAAAAIBoQyll7D0Cemut\n",
+ "9Z5AiFpr7wkAwIzW+t74xRdfTJ754IMPFlgC/az17zfZV199NXnm/fffX2AJcAjcCAcAAAAAIJoQ\n",
+ "DgAAAABANCEcAAAAAIBoQjgAAAAAANGEcAAAAAAAognhAAAAAABEE8IBAAAAAIgmhAMAAAAAEG0o\n",
+ "pYy9R8BptdZ6TyDE119/PXnmnXfeWWAJALB2a31HrbX2ngAP+OabbybPPP/88wss4WF5pgD7xo1w\n",
+ "AAAAAACiCeEAAAAAAEQTwgEAAAAAiCaEAwAAAAAQTQgHAAAAACCaEA4AAAAAQDQhHAAAAACAaEI4\n",
+ "AAAAAADRhHAAAAAAAKKd6T2ALE899dTkmR9++GGBJRyK27dvT5559dVXF1gCAPA/X3755eSZN998\n",
+ "c4ElD6e1ttW5WuvMSzgU2/7OsZz33ntv8szVq1cXWAKwe26EAwAAAAAQTQgHAAAAACCaEA4AAAAA\n",
+ "QDQhHAAAAACAaEI4AAAAAADRhHAAAAAAAKIJ4QAAAAAARBPCAQAAAACINpRSxt4j6Ku11nsCB2Yc\n",
+ "px87Z8+eXWAJAEAf33333Vbnjo+PZ14yj1pr7wnMyHfIdfJ3CRw6N8IBAAAAAIgmhAMAAAAAEE0I\n",
+ "BwAAAAAgmhAOAAAAAEA0IRwAAAAAgGhCOAAAAAAA0YRwAAAAAACiCeEAAAAAAEQbSilj7xE8qLXW\n",
+ "ewKcSq219wQAgBjJ3wu8Ny7rxRdfnDxz7dq1BZbwsPytAOyGG+EAAAAAAEQTwgEAAAAAiCaEAwAA\n",
+ "AAAQTQgHAAAAACCaEA4AAAAAQDQhHAAAAACAaEI4AAAAAADRhHAAAAAAAKINpZSx94g1uHDhwuSZ\n",
+ "zz//fIElsHu11t4TAAA4pdZa7wmz8Z66neTfgbW6c+fO5JmXXnppgSUA3ONGOAAAAAAA0YRwAAAA\n",
+ "AACiCeEAAAAAAEQTwgEAAACA/7ZrxyiKRGEURmmoSDAzexswdxHuwB24EcPKKhRch7swcBEViJmC\n",
+ "qZMPAyVDW8+6nhP/tBe6g/bjQTQhHAAAAACAaEI4AAAAAADRhHAAAAAAAKIJ4QAAAAAARPuZz+fP\n",
+ "2iPeqe/72hPgbUoptScAADAByd+Lpvo/cfLvJN1U/+YAvp0X4QAAAAAARBPCAQAAAACIJoQDAAAA\n",
+ "ABBNCAcAAAAAIJoQDgAAAABANCEcAAAAAIBoQjgAAAAAANGEcAAAAAAAognhAAAAAABEa8b+wL7v\n",
+ "x/5I+Dj3+33wZrlcjrAEAACm7XQ6vXS3Wq1+5fN8p52urusGb9q2HWEJADV4EQ4AAAAAQDQhHAAA\n",
+ "AACAaEI4AAAAAADRhHAAAAAAAKIJ4QAAAL8isNQAAALxSURBVAAARBPCAQAAAACIJoQDAAAAABBN\n",
+ "CAcAAAAAINrP4XB4vnK42WzevQXgoz0ej8Gb2Wz20s+6XC6DN+v1evDmer2+9HkAwGc5n88v3S0W\n",
+ "izcvgekrpdSeAMAEeBEOAAAAAEA0IRwAAAAAgGhCOAAAAAAA0YRwAAAAAACiCeEAAAAAAEQTwgEA\n",
+ "AAAAiCaEAwAAAAAQTQgHAAAAACDaz+12e9YeAQAAAHyXUkrtCQB8ES/CAQAAAACIJoQDAAAAABBN\n",
+ "CAcAAAAAIJoQDgAAAABANCEcAAAAAIBoQjgAAAAAANGEcAAAAAAAognhAAAAAABEa2oPAAAAAKbj\n",
+ "eDwO3my32xGWAMDrvAgHAAAAACCaEA4AAAAAQDQhHAAAAACAaEI4AAAAAADRhHAAAAAAAKIJ4QAA\n",
+ "AAAARBPCAQAAAACIJoQDAAAAABCtqT0AAAAAqK+UUnsCALyNF+EAAAAAAEQTwgEAAAAAiCaEAwAA\n",
+ "AAAQTQgHAAAAACCaEA4AAAAAQDQhHAAAAACAaEI4AAAAAADRhHAAAAAAAKIJ4QAAAAAARGtqDwAA\n",
+ "AAD+X9d1gzdt246wBAA+lxfhAAAAAABEE8IBAAAAAIgmhAMAAAAAEE0IBwAAAAAgmhAOAAAAAEA0\n",
+ "IRwAAAAAgGhCOAAAAAAA0YRwAAAAAACiNbUHAAAAAP9WSqk9AQAieBEOAAAAAEA0IRwAAAAAgGhC\n",
+ "OAAAAAAA0YRwAAAAAACiCeEAAAAAAEQTwgEAAAAAiCaEAwAAAAAQTQgHAAAAACBaU3sAAAAAJCml\n",
+ "1J4AAPzFi3AAAAAAAKIJ4QAAAAAARBPCAQAAAACIJoQDAAAAABBNCAcAAAAAIJoQDgAAAABANCEc\n",
+ "AAAAAIBoQjgAAAAAANGa2gMAAADgE+x2u8Gb/X4/whIA4Ld5EQ4AAAAAQDQhHAAAAACAaEI4AAAA\n",
+ "AADRhHAAAAAAAKIJ4QAAAAAARBPCAQAAAACIJoQDAAAAABBNCAcAAAAAINofKgtCUo9z1fQAAAAA\n",
+ "SUVORK5CYII=\n",
+ "\" transform=\"translate(79, 218)\"/>\n",
+ "</g>\n",
+ "</svg>\n"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "text/plain": [
+ "\"got 17641.365849772155 after 50 iterations (returned MAXEVAL_REACHED)\""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "text/plain": [
+ "100.0"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "text/plain": [
+ "\"got 14980.790925317424 after 50 iterations (returned MAXEVAL_REACHED)\""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "text/plain": [
+ "9.090909090909092"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "text/plain": [
+ "\"got 15037.699827732065 after 50 iterations (returned MAXEVAL_REACHED)\""
+ ]
+ },
+ "metadata": {},
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+ {
+ "data": {
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+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "text/plain": [
+ "\"got 15037.699910377938 after 25 iterations (returned XTOL_REACHED)\""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
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+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " 17.100492 seconds (24.40 k allocations: 11.964 GiB, 6.34% gc time)\n"
+ ]
+ }
+ ],
+ "source": [
+ "nelx=160\n",
+ "nely=80\n",
+ "volfrac=0.3\n",
+ "rmin=2\n",
+ "penal=3\n",
+ "maxEval=200\n",
+ "\n",
+ "tmin=1.5\n",
+ "tmax=3.5\n",
+ "\n",
+ "prob=MBB\n",
+ "prob=poiss\n",
+ "\n",
+ "\n",
+ "min_max=false\n",
+ "topologyOptimizationMinMaxThickness(nelx,nely,prob,volfrac,rmin,penal,maxEval,tmin,tmax,min_max);\n",
+ "\n",
+ "min_max=true\n",
+ "xPhys=topologyOptimizationMinMaxThickness(nelx,nely,prob,volfrac,rmin,penal,maxEval,tmin,tmax,min_max);\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 273,
+ "metadata": {},
+ "outputs": [
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+ }
+ ],
+ "source": [
+ "xPhys1=binarize(xPhys, Otsu())\n",
+ "\n",
+ "display(Plots.heatmap(xPhys1, aspect_ratio=:equal, legend=false, axis=nothing, foreground_color_subplot=colorant\"white\",fc=:grays))\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 346,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Gmax (generic function with 1 method)"
+ ]
+ },
+ "execution_count": 346,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "## SUB FUNCTION: MMA\n",
+ "function OCMMAThickness(x, xold1,xold2,c, dc, dv, H, Hs, volfrac, nele, move, beta,loop,low,upp)\n",
+ "\n",
+ " # display(\"min dc $(minimum(dc)),max dc $(maximum(dc))\")\n",
+ " xTilde=copy(x);nelx=size(x)[2];nely=size(x)[1];\n",
+ " \n",
+ " m = 1; # The number of general constraints.\n",
+ " n = nele; # The number of design variables x_j.\n",
+ " xmin = ones(n).*Emin; # Column vector with the lower bounds for the variables x_j.\n",
+ " xmax = ones(n).*Emax; # Column vector with the upper bounds for the variables x_j.\n",
+ " a0 = 1; # The constants a_0 in the term a_0*z.\n",
+ " a = zeros(m); # Column vector with the constants a_i in the terms a_i*z.\n",
+ " c_MMA = 10000*ones(m); # Column vector with the constants c_i in the terms c_i*y_i.\n",
+ " d = zeros(m); # Column vector with the constants d_i in the terms 0.5*d_i*(y_i)^2.\n",
+ " \n",
+ " \n",
+ " # METHOD OF MOVING ASYMPTOTES\n",
+ " xval = x[:];\n",
+ " f0val = c;\n",
+ " df0dx = dc[:];\n",
+ " fval = sum(x[:])/(volfrac*nele) .- 1.0;\n",
+ " dfdx = dv[:]' / (volfrac*nele);\n",
+ " # xmin=max.(0.0, x[:].-move);\n",
+ " # xmax=min.(1, x[:].+move);\n",
+ "\n",
+ "\n",
+ " xmma, ymma, zmma, lam, xsi, eta_, mu, zet, s, low, upp = mmasub(m, n, loop, xval[:], xmin[:], xmax[:], xold1[:], xold2[:], f0val,df0dx,fval,dfdx,low,upp,a0,a,c_MMA,d);\n",
+ "\n",
+ " # Update MMA Variables\n",
+ " xnew = reshape(xmma,nely,nelx);\n",
+ " xTilde[:] = (H*xnew[:] )./Hs; \n",
+ " xPhys = 1 .-exp.(-beta .*xTilde) .+xTilde .*exp.(-beta);\n",
+ " change = maximum(abs.(xnew[:]-x[:] )); x = xnew;\n",
+ " xold2 = copy(xold1);\n",
+ " xold1 = copy(x);\n",
+ "\n",
+ " return x, xPhys, change,low,upp,xold1,xold2\n",
+ "end\n",
+ "\n",
+ "function FA(x::Vector, grad::Vector)\n",
+ "\n",
+ " xPhys=reshape(x,nely,nelx)\n",
+ "\n",
+ " sK = reshape(KE[:]*(Emin.+xPhys[:]'.^penal*(Emax-Emin)),64*nelx*nely,1)\n",
+ " K = sparse(vec(iK),vec(jK),vec(sK)); 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))\n",
+ "\n",
+ " dc = -penal*(Emax-Emin)*xPhys.^(penal-1).*ce\n",
+ " dc[:] = H*(dc[:]./Hs)\n",
+ "\n",
+ " grad[:] .= dc[:]\n",
+ "\n",
+ " return c\n",
+ "end\n",
+ "\n",
+ "\n",
+ "\n",
+ "function G(x::Vector, grad::Vector)\n",
+ " dv = ones(nely,nelx)\n",
+ " dv[:] = H*(dv[:]./Hs)\n",
+ "\n",
+ " grad[:] .= dv[:]\n",
+ "\n",
+ " return (sum(x) - volfrac*nel)\n",
+ "end\n",
+ "\n",
+ "function Gmin(x::Vector, grad::Vector)\n",
+ "\n",
+ " xPhys1=Bool.(binarize(reshape(x,nely,nelx), Otsu()))\n",
+ " #reshape(x,nely,nelx).>=0.5;\n",
+ " bim = thinning_zs(xPhys1) # get the skeleton (check algorithm is correct with matlab (boundary conditions))\n",
+ " ss=sdf(bim) # signed distance field form skeletom\n",
+ " Imin= (ss.<=tmin) # all the ones that respect the min distance\n",
+ " # Imax= (ss.>tmax) # all the ones that respect the max distance\n",
+ " dv = zeros(nely,nelx)\n",
+ " dv[Imin[:]].=2 .*(x[Imin[:]] .-Emax)\n",
+ "\n",
+ "\n",
+ " # dv[:] = H*(dv[:]./Hs)\n",
+ " grad[:] .= dv[:]\n",
+ "\n",
+ " return sum((x[Imin[:]].-Emax).^2)-startt/iterr\n",
+ "end\n",
+ "\n",
+ "function Gmax(x::Vector, grad::Vector)\n",
+ "\n",
+ " xPhys1=Bool.(binarize(reshape(x,nely,nelx), Otsu()))\n",
+ " #reshape(x,nely,nelx).>=0.5;\n",
+ " bim = thinning_zs(xPhys1) # get the skeleton (check algorithm is correct with matlab (boundary conditions))\n",
+ " ss=sdf(bim) # signed distance field form skeletom\n",
+ " #Imin= (ss.<=tmin) # all the ones that respect the min distance\n",
+ " Imax= (ss.>tmax) # all the ones that respect the max distance\n",
+ " dv = zeros(nely,nelx)\n",
+ " dv[Imax[:]].=2 .*(x[Imax[:]] .-Emin)\n",
+ "\n",
+ "\n",
+ " # dv[:] = H*(dv[:]./Hs)\n",
+ " grad[:] .= dv[:]\n",
+ "\n",
+ " return sum((x[Imax[:]].-Emin).^2)-startt/iterr\n",
+ "end"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 347,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "topologyOptimizationMinMaxThickness1 (generic function with 2 methods)"
+ ]
+ },
+ "execution_count": 347,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "using ImageBinarization\n",
+ "using SignedDistanceFields\n",
+ "include(\"./julia/traceskeleton.jl\")\n",
+ "include(\"./julia/include/mmaSolver.jl\");\n",
+ "\n",
+ "\n",
+ "function topologyOptimizationMinMaxThickness1(nelx,nely,prob,volfrac,rmin,penal,maxEval,tmin,tmax,min_max)\n",
+ " # Max and min stiffness\n",
+ " Emin=1e-2;Emax=1.0;\n",
+ "\n",
+ " # 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",
+ " beta = 1;\n",
+ " xPhys = 1 .- exp.(-beta .*x) .+ x * exp.(-beta);\n",
+ "\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",
+ " \n",
+ " # DEFINE LOADS AND SUPPORTS (HALF MBB-BEAM) \n",
+ " U,F,freedofs=prob(nelx,nely) \n",
+ " \n",
+ " \n",
+ " H,Hs=make_filter(nelx,nely,rmin)\n",
+ " \n",
+ "\n",
+ " nel=nely*nelx\n",
+ " \n",
+ " xold1 = copy(x); # xval, one iteration ago (provided that iter>1).\n",
+ " xold2 = copy(x); # xval, two iterations ago (provided that iter>2).\n",
+ " low = ones(nel); # Column vector with the lower asymptotes from the previous iteration (provided that iter>1).\n",
+ " upp = ones(nel); # Column vector with the upper asymptotes from the previous iteration (provided that iter>1).\n",
+ "\n",
+ " \n",
+ " change=1;loop=0;\n",
+ " \n",
+ " for i =1:maxIter\n",
+ " if (change > 0.01)\n",
+ " # Start iteration\n",
+ " loop += 1\n",
+ " # FE-ANALYSIS\n",
+ " sK = reshape(KE[:]*(Emin.+xPhys[:]'.^penal*(Emax-Emin)),64*nelx*nely,1)\n",
+ " K = sparse(vec(iK),vec(jK),vec(sK)); 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",
+ " \n",
+ " c = sum(sum((Emin.+xPhys.^penal*(Emax-Emin)).*ce))\n",
+ " \n",
+ " dc = -penal*(Emax-Emin)*xPhys.^(penal-1).*ce\n",
+ " dv = ones(nely,nelx)\n",
+ " dc[:] = H*(dc[:]./Hs)\n",
+ " dv[:] = H*(dv[:]./Hs)\n",
+ " \n",
+ " \n",
+ " move = 0.2;\n",
+ " \n",
+ " x, xPhys, change, low, upp, xold1, xold2 = OCMMA(x, xold1,xold2,c,dc, dv, H, Hs, volfrac, nel, move, beta,loop,low,upp);\n",
+ "\n",
+ " \n",
+ " m=mean(xPhys[:])\n",
+ " \n",
+ " println(\" It:$loop Obj:$(round.(c,digits=2)) Vol:$(round.(m,digits=2)) ch:$(round.(change,digits=2)) \")\n",
+ " if mod(loop,5)==0\n",
+ " xxx=1 .- clamp.(xPhys,0,1)\n",
+ " display(Plots.heatmap(xxx,xaxis=nothing,showaxis = false,yaxis=nothing,legend=nothing,fc=:grays,clims=(0.0, 1.0),aspect_ratio=:equal))\n",
+ " Plots.heatmap(xxx,xaxis=nothing,showaxis = false,yaxis=nothing,legend=nothing,fc=:grays,clims=(0.0, 1.0),aspect_ratio=:equal)\n",
+ "\n",
+ " end\n",
+ "\n",
+ " xPhys = copy(x)\n",
+ " end\n",
+ " end\n",
+ " \n",
+ " \n",
+ " display(Plots.heatmap(xPhys, aspect_ratio=:equal, legend=false, axis=nothing,fc=:grays))\n",
+ "\n",
+ " return xPhys\n",
+ "end\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 353,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Loaded Topology Optimization Library!\n",
+ " It:1 Obj:16761.01 Vol:0.44 ch:0.44 \n",
+ " It:2 Obj:9147.74 Vol:0.47 ch:0.28 \n",
+ " It:3 Obj:5668.7 Vol:0.45 ch:0.25 \n",
+ " It:4 Obj:5382.14 Vol:0.42 ch:0.24 \n"
+ ]
+ },
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+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " It:20 Obj:3252.68 Vol:0.32 ch:0.13 \n",
+ " It:21 Obj:3184.83 Vol:0.32 ch:0.14 \n"
+ ]
+ },
+ {
+ "ename": "LoadError",
+ "evalue": "\u001b[91mInterruptException:\u001b[39m",
+ "output_type": "error",
+ "traceback": [
+ "\u001b[91mInterruptException:\u001b[39m",
+ "",
+ "Stacktrace:",
+ " [1] subsolv(::Int64, ::Int64, ::Float64, ::Array{Float64,1}, ::Array{Float64,1}, ::Array{Float64,1}, ::Array{Float64,1}, ::Array{Float64,1}, ::Array{Float64,1}, ::Array{Float64,2}, ::Array{Float64,2}, ::Int64, ::Array{Float64,1}, ::Array{Float64,1}, ::Array{Float64,1}, ::Array{Float64,1}) at /Users/amiraabdel-rahman/Dropbox (MIT)/CBA/MetaVoxels/metavoxels-code/voxel_designer/julia/include/mmaSolver.jl:385",
+ " [2] mmasub(::Int64, ::Int64, ::Int64, ::Array{Float64,1}, ::Array{Float64,1}, ::Array{Float64,1}, ::Array{Float64,1}, ::Array{Float64,1}, ::Float64, ::Array{Float64,1}, ::Float64, ::Adjoint{Float64,Array{Float64,1}}, ::Array{Float64,1}, ::Array{Float64,1}, ::Int64, ::Array{Float64,1}, ::Array{Float64,1}, ::Array{Float64,1}) at /Users/amiraabdel-rahman/Dropbox (MIT)/CBA/MetaVoxels/metavoxels-code/voxel_designer/julia/include/mmaSolver.jl:173",
+ " [3] OCMMA(::Array{Float64,2}, ::Array{Float64,2}, ::Array{Float64,2}, ::Float64, ::Array{Float64,2}, ::Array{Float64,2}, ::SparseMatrixCSC{Float64,Int64}, ::Array{Float64,2}, ::Float64, ::Int64, ::Float64, ::Int64, ::Int64, ::Array{Float64,1}, ::Array{Float64,1}) at /Users/amiraabdel-rahman/Dropbox (MIT)/CBA/MetaVoxels/metavoxels-code/voxel_designer/julia/include/top2D.jl:330",
+ " [4] topologyOptimizationMMA1(::Int64, ::Int64, ::typeof(poiss), ::Float64, ::Int64, ::Int64, ::Int64) at /Users/amiraabdel-rahman/Dropbox (MIT)/CBA/MetaVoxels/metavoxels-code/voxel_designer/julia/include/top2D.jl:280",
+ " [5] top-level scope at In[353]:18",
+ " [6] include_string(::Function, ::Module, ::String, ::String) at ./loading.jl:1091"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "include(\"./julia/include/_topologyOptimization.jl\")\n",
+ "nelx=160\n",
+ "nely=80\n",
+ "volfrac=0.3\n",
+ "rmin=2\n",
+ "penal=3\n",
+ "maxEval=200\n",
+ "\n",
+ "tmin=1.5\n",
+ "tmax=3.5\n",
+ "\n",
+ "prob=MBB\n",
+ "# prob=poiss\n",
+ "\n",
+ "\n",
+ "min_max=false\n",
+ "topologyOptimizationMMA1(nelx,nely,prob,volfrac,rmin,penal,maxEval);\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 355,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Loaded Topology Optimization Library!\n",
+ " It:1 Obj:833.54 Vol:0.32 ch:0.41 \n",
+ " It:2 Obj:789.49 Vol:0.34 ch:0.29 \n",
+ " It:3 Obj:512.63 Vol:0.34 ch:0.22 \n",
+ " It:4 Obj:411.27 Vol:0.34 ch:0.21 \n"
+ ]
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+ " It:16 Obj:205.54 Vol:0.33 ch:0.11 \n",
+ " It:17 Obj:202.81 Vol:0.33 ch:0.1 \n",
+ " It:18 Obj:200.51 Vol:0.33 ch:0.1 \n",
+ " It:19 Obj:198.54 Vol:0.33 ch:0.09 \n"
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+ " It:20 Obj:196.83 Vol:0.33 ch:0.09 \n",
+ " It:21 Obj:195.35 Vol:0.33 ch:0.09 \n",
+ " It:22 Obj:194.1 Vol:0.33 ch:0.08 \n",
+ " It:23 Obj:192.99 Vol:0.33 ch:0.08 \n",
+ " It:24 Obj:192.02 Vol:0.33 ch:0.08 \n"
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+ " It:31 Obj:188.05 Vol:0.33 ch:0.06 \n",
+ " It:32 Obj:187.73 Vol:0.33 ch:0.07 \n",
+ " It:33 Obj:187.43 Vol:0.33 ch:0.06 \n",
+ " It:34 Obj:187.13 Vol:0.33 ch:0.07 \n"
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+ " It:35 Obj:186.84 Vol:0.33 ch:0.08 \n",
+ " It:36 Obj:186.57 Vol:0.33 ch:0.08 \n",
+ " It:37 Obj:186.29 Vol:0.33 ch:0.08 \n",
+ " It:38 Obj:186.02 Vol:0.33 ch:0.08 \n",
+ " It:39 Obj:185.74 Vol:0.33 ch:0.06 \n"
+ ]
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+ " It:41 Obj:185.21 Vol:0.33 ch:0.07 \n",
+ " It:42 Obj:184.94 Vol:0.33 ch:0.08 \n",
+ " It:43 Obj:184.66 Vol:0.33 ch:0.08 \n",
+ " It:44 Obj:184.35 Vol:0.33 ch:0.08 \n"
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+ " It:46 Obj:183.74 Vol:0.33 ch:0.08 \n",
+ " It:47 Obj:183.44 Vol:0.33 ch:0.09 \n",
+ " It:48 Obj:183.18 Vol:0.33 ch:0.08 \n",
+ " It:49 Obj:182.98 Vol:0.33 ch:0.09 \n"
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+ "text": [
+ " It:50 Obj:182.78 Vol:0.33 ch:0.06 \n",
+ " It:51 Obj:182.59 Vol:0.33 ch:0.07 \n",
+ " It:52 Obj:182.4 Vol:0.33 ch:0.07 \n",
+ " It:53 Obj:182.22 Vol:0.33 ch:0.07 \n",
+ " It:54 Obj:182.05 Vol:0.33 ch:0.06 \n"
+ ]
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+ " It:55 Obj:181.9 Vol:0.33 ch:0.06 \n",
+ " It:56 Obj:181.76 Vol:0.33 ch:0.07 \n",
+ " It:57 Obj:181.63 Vol:0.33 ch:0.06 \n",
+ " It:58 Obj:181.51 Vol:0.33 ch:0.06 \n",
+ " It:59 Obj:181.4 Vol:0.33 ch:0.06 \n"
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+ {
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+ " It:87 Obj:179.42 Vol:0.33 ch:0.04 \n",
+ " It:88 Obj:179.38 Vol:0.33 ch:0.05 \n",
+ " It:89 Obj:179.34 Vol:0.33 ch:0.05 \n"
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+ " It:103 Obj:178.97 Vol:0.33 ch:0.03 \n",
+ " It:104 Obj:178.95 Vol:0.33 ch:0.03 \n"
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+ " It:106 Obj:178.93 Vol:0.33 ch:0.03 \n",
+ " It:107 Obj:178.92 Vol:0.33 ch:0.03 \n",
+ " It:108 Obj:178.92 Vol:0.33 ch:0.03 \n",
+ " It:109 Obj:178.91 Vol:0.33 ch:0.03 \n"
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+ " It:116 Obj:178.87 Vol:0.33 ch:0.03 \n",
+ " It:117 Obj:178.87 Vol:0.33 ch:0.03 \n",
+ " It:118 Obj:178.86 Vol:0.33 ch:0.03 \n",
+ " It:119 Obj:178.86 Vol:0.33 ch:0.03 \n"
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+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " It:125 Obj:178.81 Vol:0.33 ch:0.03 \n",
+ " It:126 Obj:178.8 Vol:0.33 ch:0.03 \n",
+ " It:127 Obj:178.79 Vol:0.33 ch:0.03 \n",
+ " It:128 Obj:178.78 Vol:0.33 ch:0.03 \n",
+ " It:129 Obj:178.77 Vol:0.33 ch:0.02 \n"
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+ " It:136 Obj:178.73 Vol:0.33 ch:0.03 \n",
+ " It:137 Obj:178.72 Vol:0.33 ch:0.03 \n",
+ " It:138 Obj:178.71 Vol:0.33 ch:0.03 \n",
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+ " It:151 Obj:178.41 Vol:0.33 ch:0.03 \n",
+ " It:152 Obj:178.4 Vol:0.33 ch:0.03 \n",
+ " It:153 Obj:178.39 Vol:0.33 ch:0.03 \n",
+ " It:154 Obj:178.39 Vol:0.33 ch:0.03 \n"
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+ " It:167 Obj:178.37 Vol:0.33 ch:0.03 \n",
+ " It:168 Obj:178.37 Vol:0.33 ch:0.03 \n",
+ " It:169 Obj:178.36 Vol:0.33 ch:0.03 \n"
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+ " It:182 Obj:178.31 Vol:0.33 ch:0.03 \n",
+ " It:183 Obj:178.3 Vol:0.33 ch:0.03 \n",
+ " It:184 Obj:178.3 Vol:0.33 ch:0.03 \n"
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+ " It:188 Obj:178.28 Vol:0.33 ch:0.03 \n",
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+ " It:195 Obj:178.22 Vol:0.33 ch:0.03 \n",
+ " It:196 Obj:178.21 Vol:0.33 ch:0.03 \n",
+ " It:197 Obj:178.2 Vol:0.33 ch:0.03 \n",
+ " It:198 Obj:178.19 Vol:0.33 ch:0.03 \n",
+ " It:199 Obj:178.18 Vol:0.33 ch:0.03 \n"
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+ "\" transform=\"translate(79, 218)\"/>\n",
+ "</g>\n",
+ "</svg>\n"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " It:200 Obj:178.17 Vol:0.33 ch:0.04 \n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "include(\"./julia/include/_topologyOptimization.jl\")\n",
+ "nelx=80\n",
+ "nely=40\n",
+ "volfrac=0.3\n",
+ "rmin=2\n",
+ "penal=3\n",
+ "maxEval=200\n",
+ "\n",
+ "tmin=1.5\n",
+ "tmax=3.5\n",
+ "\n",
+ "prob=MBB\n",
+ "# prob=poiss\n",
+ "\n",
+ "\n",
+ "min_max=false\n",
+ "topologyOptimizationMMA1(nelx,nely,prob,volfrac,rmin,penal,maxEval);\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Julia 1.5.3",
+ "language": "julia",
+ "name": "julia-1.5"
+ },
+ "language_info": {
+ "file_extension": ".jl",
+ "mimetype": "application/julia",
+ "name": "julia",
+ "version": "1.5.3"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/voxel_designer/julia/include/mmaSolver.jl b/voxel_designer/julia/include/mmaSolver.jl
index e71490d..d492f8a 100644
--- a/voxel_designer/julia/include/mmaSolver.jl
+++ b/voxel_designer/julia/include/mmaSolver.jl
@@ -84,11 +84,15 @@ function mmasub(m,n,iter,xval,xmin,xmax,xold1,xold2,f0val,df0dx,fval,dfdx,low,up
#epsimin = sqrt(m+n)*10^(-9);
epsimin = 10^(-7);
raa0 = 0.00001;
- move = 0.5;
+
+ move = 0.5;# FOR COMPLIANT
# move = 1.0;
+
albefa = 0.1;
- asyinit = 0.5;
+
+ asyinit = 0.5;# FOR COMPLIANT
# asyinit = 0.01;
+
asyincr = 1.2;
asydecr = 0.7;
eeen = ones(n);
diff --git a/voxel_designer/julia/include/top2D.jl b/voxel_designer/julia/include/top2D.jl
index 19452f4..a9b83bb 100644
--- a/voxel_designer/julia/include/top2D.jl
+++ b/voxel_designer/julia/include/top2D.jl
@@ -213,6 +213,132 @@ function topologyOptimizationMMA(nelx,nely,volfrac,rmin,penal,maxEval)
return xPhys
end
+
+include("./mmaSolver.jl");
+function topologyOptimizationMMA1(nelx,nely,prob,volfrac,rmin,penal,maxIter)
+ # Max and min stiffness
+ Emin=1e-2;Emax=1.0;
+
+ # dofs:
+ ndof = 2*(nelx+1)*(nely+1)
+ # Allocate design variables (as array), initialize and allocate sens.
+ x=volfrac .* ones(Float64,nely,nelx)
+ xold=copy(x)
+ xPhys=copy(x)
+ beta = 1;
+ xPhys = 1 .- exp.(-beta .*x) .+ x * exp.(-beta);
+
+ g=0 # must be initialized to use the NGuyen/Paulino OC approach
+ dc=zeros(Float64,(nely,nelx))
+
+ # FE: Build the index vectors for the for coo matrix format.
+ KE=lk()
+ nodenrs = reshape(1:(1+nelx)*(1+nely),1+nely,1+nelx)
+ edofVec = reshape(2*nodenrs[1:end-1,1:end-1].+1,nelx*nely,1)
+ edofMat = repeat(edofVec,1,8).+repeat([0 1 2*nely.+[2 3 0 1] -2 -1],nelx*nely,1)
+ iK = convert(Array{Int},reshape(kron(edofMat,ones(8,1))',64*nelx*nely,1))
+ jK = convert(Array{Int},reshape(kron(edofMat,ones(1,8))',64*nelx*nely,1))
+
+ # DEFINE LOADS AND SUPPORTS (HALF MBB-BEAM)
+ U,F,freedofs=prob(nelx,nely)
+
+
+ H,Hs=make_filter(nelx,nely,rmin)
+
+
+ nel=nely*nelx
+
+ xold1 = copy(x); # xval, one iteration ago (provided that iter>1).
+ xold2 = copy(x); # xval, two iterations ago (provided that iter>2).
+ low = ones(nel); # Column vector with the lower asymptotes from the previous iteration (provided that iter>1).
+ upp = ones(nel); # Column vector with the upper asymptotes from the previous iteration (provided that iter>1).
+
+
+ change=1;loop=0;
+
+ for i =1:maxIter
+ if (change > 0.01)
+ # Start iteration
+ loop += 1
+ # FE-ANALYSIS
+ sK = reshape(KE[:]*(Emin.+xPhys[:]'.^penal*(Emax-Emin)),64*nelx*nely,1)
+ K = sparse(vec(iK),vec(jK),vec(sK)); K = (K+K')/2
+ @timed U[freedofs] = K[freedofs,freedofs] \ Array(F[freedofs])
+ # Objective function and sensitivity analysis
+ ce = reshape(sum((U[edofMat]*KE).*U[edofMat],dims=2),nely,nelx)
+
+ c = sum(sum((Emin.+xPhys.^penal*(Emax-Emin)).*ce))
+
+ dc = -penal*(Emax-Emin)*xPhys.^(penal-1).*ce
+ dv = ones(nely,nelx)
+ dc[:] = H*(dc[:]./Hs)
+ dv[:] = H*(dv[:]./Hs)
+
+
+ move = 0.2;
+
+ x, xPhys, change, low, upp, xold1, xold2 = OCMMA(x, xold1,xold2,c,dc, dv, H, Hs, volfrac, nel, move, beta,loop,low,upp);
+
+
+ m=mean(xPhys[:])
+
+ println(" It:$loop Obj:$(round.(c,digits=2)) Vol:$(round.(m,digits=2)) ch:$(round.(change,digits=2)) ")
+ if mod(loop,5)==0
+ xxx=1 .- clamp.(xPhys,0,1)
+ display(Plots.heatmap(xxx,xaxis=nothing,showaxis = false,yaxis=nothing,legend=nothing,fc=:grays,clims=(0.0, 1.0),aspect_ratio=:equal))
+ Plots.heatmap(xxx,xaxis=nothing,showaxis = false,yaxis=nothing,legend=nothing,fc=:grays,clims=(0.0, 1.0),aspect_ratio=:equal)
+
+ end
+
+ xPhys = copy(x)
+ end
+ end
+
+
+ display(Plots.heatmap(xPhys, aspect_ratio=:equal, legend=false, axis=nothing,fc=:grays))
+
+ return xPhys
+end
+
+
+## SUB FUNCTION: MMA
+function OCMMA(x, xold1,xold2,c, dc, dv, H, Hs, volfrac, nele, move, beta,loop,low,upp)
+
+ # display("min dc $(minimum(dc)),max dc $(maximum(dc))")
+ xTilde=copy(x);nelx=size(x)[2];nely=size(x)[1];
+
+ m = 1; # The number of general constraints.
+ n = nele; # The number of design variables x_j.
+ xmin = ones(n).*Emin; # Column vector with the lower bounds for the variables x_j.
+ xmax = ones(n).*Emax; # Column vector with the upper bounds for the variables x_j.
+ a0 = 1; # The constants a_0 in the term a_0*z.
+ a = zeros(m); # Column vector with the constants a_i in the terms a_i*z.
+ c_MMA = 10000*ones(m); # Column vector with the constants c_i in the terms c_i*y_i.
+ d = zeros(m); # Column vector with the constants d_i in the terms 0.5*d_i*(y_i)^2.
+
+
+ # METHOD OF MOVING ASYMPTOTES
+ xval = x[:];
+ f0val = c;
+ df0dx = dc[:];
+ fval = sum(x[:])/(volfrac*nele) .- 1.0;
+ dfdx = dv[:]' / (volfrac*nele);
+ # xmin=max.(0.0, x[:].-move);
+ # xmax=min.(1, x[:].+move);
+
+
+ xmma, ymma, zmma, lam, xsi, eta_, mu, zet, s, low, upp = mmasub(m, n, loop, xval[:], xmin[:], xmax[:], xold1[:], xold2[:], f0val,df0dx,fval,dfdx,low,upp,a0,a,c_MMA,d);
+
+ # Update MMA Variables
+ xnew = reshape(xmma,nely,nelx);
+ xTilde[:] = (H*xnew[:] )./Hs;
+ xPhys = 1 .-exp.(-beta .*xTilde) .+xTilde .*exp.(-beta);
+ change = maximum(abs.(xnew[:]-x[:] )); x = xnew;
+ xold2 = copy(xold1);
+ xold1 = copy(x);
+
+ return x, xPhys, change,low,upp,xold1,xold2
+end
#########################################################################################################
function CompliantTopologyOptimization(nelx,nely,volfrac,rmin,penal,maxIter,Load,Support,Spring,DOut)
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literal 0
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--
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