top88.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
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   "source": [
    "# Code topology optimization top88\n",
    "\n",
    "Robin Grapin"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "using SparseArrays\n",
    "using LinearAlgebra\n",
    "using Plots\n",
    "using Statistics\n",
    "using SuiteSparse\n",
    "E0 = 1;\n",
    "Emin = 1e-9;\n",
    "nu = 0.3;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "top88 (generic function with 1 method)"
      ]
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     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
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   "source": [
    "function top88(nelx,nely,volfrac,penal,rmin,ft)\n",
    "        \n",
    "    A11 = [12  3 -6 -3;  3 12  3  0; -6  3 12 -3; -3  0 -3 12]\n",
    "    A12 = [-6 -3  0  3; -3 -6 -3 -6;  0 -3 -6  3;  3 -6  3 -6]\n",
    "    B11 = [-4  3 -2  9;  3 -4 -9  4; -2 -9 -4 -3;  9  4 -3 -4]\n",
    "    B12 = [ 2 -3  4 -9; -3  2  9 -2;  4  9  2  3; -9 -2  3  2]\n",
    "    KE = 1/(1-nu^2)/24*([A11 A12;A12' A11]+nu*[B11 B12;B12' B11])\n",
    "\n",
    "    nodenrs = reshape(1:(1+nelx)*(1+nely),1+nely,1+nelx); #number of the nodes in columns\n",
    "    edofVec = reshape(2*nodenrs[1:end-1,1:end-1].+1,nelx*nely,1) ;#1st dof of each element (x top left)\n",
    "    edofMat = zeros(nelx*nely, 8); #every line i contains the 8 dof of the ith element\n",
    "    noeudsvoisins = [0 1 2*nely.+[2 3 0 1] -2 -1];\n",
    "    for i = 1:8\n",
    "        for j = 1:nelx*nely\n",
    "            edofMat[j,i]= edofVec[j]+ noeudsvoisins[i] ;\n",
    "        end\n",
    "    end\n",
    "        #meshing\n",
    "    iK = reshape(kron(edofMat,ones(8,1))',64*nelx*nely,1);# line to build  K\n",
    "    jK = reshape(kron(edofMat,ones(1,8))',64*nelx*nely,1);# columns\n",
    "    #F = spzeros(2*(nely+1)*(nelx+1),1); F[2,1] = -1; impossible to solve in Julia with F sparse\n",
    "    F = zeros(2*(nely+1)*(nelx+1),1); F[2,1] = -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",
    "        #filtering is linear + chain's rule -> matricial opration with operator H\n",
    "    iH = ones(nelx*nely*(2*(convert(Int64,ceil(rmin)-1))+1)^2);#lines H\n",
    "    jH = ones(size(iH));# columns\n",
    "    sH = zeros(size(iH));# values\n",
    "    k = 0;\n",
    "    for i1 = 1:nelx\n",
    "        for j1 = 1:nely\n",
    "            e1 = (i1-1)*nely+j1;\n",
    "            for i2 = max(i1-(ceil(rmin)-1),1):min(i1+(ceil(rmin)-1),nelx)\n",
    "                for j2 = max(j1-(ceil(rmin)-1),1):min(j1+(ceil(rmin)-1),nely)\n",
    "                    e2 = (i2-1)*nely+j2;\n",
    "                    k = k+1;\n",
    "                    iH[k] = e1;\n",
    "                    jH[k] = e2;\n",
    "                    sH[k] = max(0,rmin-sqrt((i1-i2)^2+(j1-j2)^2));\n",
    "                end\n",
    "            end\n",
    "        end\n",
    "    end\n",
    "    H = sparse(iH,jH,sH);# matrix of the Hei\n",
    "    Hs = [sum(H[i,:]) for i = 1:(size(H)[1])];# sum of the Hei for e fixed -> coeffs used to divide in the filter\n",
    "        #variables\n",
    "    x = volfrac*ones(nely,nelx);\n",
    "    xPhys = x; #new variable for the density filter\n",
    "    loop = 0;\n",
    "    change = 1;\n",
    "    cValues = []\n",
    "    while change > 0.01\n",
    "        loop = loop + 1;\n",
    "        sK = [j*((i+Emin)^penal) for i in ((E0-Emin)*xPhys[:]') for j in KE[:] ];#new values EF\n",
    "        K = sparse(iK[:],jK[:],sK); K = (K+K')/2;# force to be symmetric\n",
    "        KK = cholesky(K[freedofs,freedofs]);\n",
    "        U[freedofs] = KK\\F[freedofs];\n",
    "        \n",
    "            # analyse, objective function\n",
    "        edM = [convert(Int64,i) for i in edofMat] ;#to index by int\n",
    "        mat = (U[edM]*KE).*U[edM];\n",
    "        ce = reshape([sum(mat[i,:]) for i = 1:(size(mat)[1])],nely,nelx);\n",
    "        c = sum(sum((Emin*ones(size(xPhys)).+(xPhys.^penal)*(E0-Emin)).*ce));\n",
    "        push!(cValues,c)\n",
    "        dc = -penal*(E0-Emin)*xPhys.^(penal-1).*ce;\n",
    "        dv = ones(nely,nelx);\n",
    "        \n",
    "            #filtering\n",
    "        if ft == 1\n",
    "            dc[:] = H*(x[:].*dc[:])./Hs./max(1e-3,maximum(x[:]));\n",
    "        elseif ft == 2\n",
    "            dc[:] = H*(dc[:]./Hs);\n",
    "            dv[:] = H*(dv[:]./Hs);\n",
    "        end\n",
    "            #Lagrangian multiplicators research, upload of the density x\n",
    "        l1 = 0; l2 = 1e9; move = 0.2;\n",
    "        xnew = zeros(nely, nelx);\n",
    "        while (l2-l1)/(l1+l2) > 1e-3\n",
    "            lmid = 0.5*(l2+l1);\n",
    "            RacBe = sqrt.(-dc./dv/lmid) ;\n",
    "            XB = x.*RacBe ;\n",
    "            for i = 1:nelx\n",
    "                for j = 1:nely\n",
    "                    xji = x[j,i];\n",
    "                    xnew[j,i]= max(0.001,max(xji-move,min(1,min(xji+move,XB[j,i]))));\n",
    "                end\n",
    "            end  \n",
    "            if ft == 1\n",
    "                xPhys = xnew;\n",
    "            elseif ft == 2 # if we chose the density filter\n",
    "                xPhys[:] = (H*xnew[:])./Hs;\n",
    "            end\n",
    "            if sum(xPhys[:]) > volfrac*nelx*nely\n",
    "                l1 = lmid;\n",
    "            else \n",
    "                l2 = lmid; \n",
    "            end\n",
    "        end\n",
    "        change = maximum(abs.(x-xnew));\n",
    "        x = xnew;\n",
    "        println(\"loop = \", loop, \"Change = \", change ,\" c = \", c , \" densité struct = \", mean(x) )\n",
    "        if loop == 25\n",
    "            return heatmap(x), loop, cValues\n",
    "        end\n",
    "    end\n",
    "    return heatmap(x) , loop , cValues\n",
    "end"
   ]
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  {
   "cell_type": "code",
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    {
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     "text": [
      "loop = 1Change = 0.2 c = 240.55295821333357 densité struct = 0.4998520540677216\n",
      "loop = 2Change = 0.20000000000000007 c = 142.29012812657385 densité struct = 0.4999542563374929\n",
      "loop = 3Change = 0.20000000000000007 c = 101.29042745369344 densité struct = 0.5002055990575279\n",
      "loop = 4Change = 0.20000000000000007 c = 80.66559467707458 densité struct = 0.5000701665640235\n",
      "loop = 5Change = 0.20000000000000007 c = 70.50380077726645 densité struct = 0.4999593512379233\n",
      "loop = 6Change = 0.20000000000000007 c = 62.76373407502861 densité struct = 0.5001263852461102\n",
      "loop = 7Change = 0.20000000000000007 c = 57.569456923643784 densité struct = 0.5001217271799653\n",
      "loop = 8Change = 0.20000000000000007 c = 53.32531768875428 densité struct = 0.49999885176338427\n",
      "loop = 9Change = 0.20000000000000007 c = 50.258491516100314 densité struct = 0.5000234485734937\n",
      "loop = 10Change = 0.20000000000000007 c = 48.810735392503446 densité struct = 0.49996998889121175\n",
      "loop = 11Change = 0.20000000000000007 c = 48.11940887678135 densité struct = 0.49999081703082715\n",
      "loop = 12Change = 0.19999999999999996 c = 47.70674371910807 densité struct = 0.49999294864112553\n",
      "loop = 13Change = 0.19999999999999996 c = 47.47118107678733 densité struct = 0.5000210417378071\n",
      "loop = 14Change = 0.19999999999999996 c = 47.343485675725475 densité struct = 0.49999779464942384\n",
      "loop = 15Change = 0.19999999999999996 c = 47.23921449548786 densité struct = 0.5000143110161442\n",
      "loop = 16Change = 0.20000000000000007 c = 47.127973767283066 densité struct = 0.49998472196384736\n",
      "loop = 17Change = 0.19999999999999996 c = 46.99585044365262 densité struct = 0.5000125225561436\n",
      "loop = 18Change = 0.20000000000000007 c = 46.79670069347179 densité struct = 0.5000083286540311\n",
      "loop = 19Change = 0.18506658737457893 c = 46.53871598798251 densité struct = 0.49999955724585887\n",
      "loop = 20Change = 0.19999999999999996 c = 46.30448641143472 densité struct = 0.5000122818824602\n",
      "loop = 21Change = 0.14493080658471336 c = 46.23496928553922 densité struct = 0.49999427568541704\n",
      "loop = 22Change = 0.16818799250749072 c = 46.18414430101558 densité struct = 0.5000030432254848\n",
      "loop = 23Change = 0.15922828772115738 c = 46.1377939278308 densité struct = 0.49999559660075166\n",
      "loop = 24Change = 0.17029341991518365 c = 46.095353434995985 densité struct = 0.4999986841813368\n",
      "loop = 25Change = 0.19999999999999996 c = 46.05217114719343 densité struct = 0.5000025072101839\n"
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   "source": [
    "h,l,c = top88(50,33,0.5, 3,2,1);\n",
    "#h : final mass repartition\n",
    "plot(1:l,c,title = \"sensity evolution\", label = \"sensity c\") #evolution of c during the process\n",
    "xlabel!(\"iteration\")"
   ]
  },
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     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "h"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Original code top88 by Ole Sigmund"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "syntax: invalid escape sequence",
     "output_type": "error",
     "traceback": [
      "syntax: invalid escape sequence",
      ""
     ]
    }
   ],
   "source": [
    "\"\"\"\n",
    "%%%% AN 88 LINE TOPOLOGY OPTIMIZATION CODE Nov, 2010 %%%%\n",
    "function top88(nelx,nely,volfrac,penal,rmin,ft)\n",
    "%% MATERIAL PROPERTIES\n",
    "E0 = 1;\n",
    "Emin = 1e-9;\n",
    "nu = 0.3;\n",
    "%% PREPARE FINITE ELEMENT ANALYSIS\n",
    "A11 = [12  3 -6 -3;  3 12  3  0; -6  3 12 -3; -3  0 -3 12];\n",
    "A12 = [-6 -3  0  3; -3 -6 -3 -6;  0 -3 -6  3;  3 -6  3 -6];\n",
    "B11 = [-4  3 -2  9;  3 -4 -9  4; -2 -9 -4 -3;  9  4 -3 -4];\n",
    "B12 = [ 2 -3  4 -9; -3  2  9 -2;  4  9  2  3; -9 -2  3  2];\n",
    "KE = 1/(1-nu^2)/24*([A11 A12;A12' A11]+nu*[B11 B12;B12' B11]);\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 = repmat(edofVec,1,8)+repmat([0 1 2*nely+[2 3 0 1] -2 -1],nelx*nely,1);\n",
    "iK = reshape(kron(edofMat,ones(8,1))',64*nelx*nely,1);\n",
    "jK = reshape(kron(edofMat,ones(1,8))',64*nelx*nely,1);\n",
    "% DEFINE LOADS AND SUPPORTS (HALF MBB-BEAM)\n",
    "F = sparse(2,1,-1,2*(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",
    "%% PREPARE FILTER\n",
    "iH = ones(nelx*nely*(2*(ceil(rmin)-1)+1)^2,1);\n",
    "jH = ones(size(iH));\n",
    "sH = zeros(size(iH));\n",
    "k = 0;\n",
    "for i1 = 1:nelx\n",
    "  for j1 = 1:nely\n",
    "    e1 = (i1-1)*nely+j1;\n",
    "    for i2 = max(i1-(ceil(rmin)-1),1):min(i1+(ceil(rmin)-1),nelx)\n",
    "      for j2 = max(j1-(ceil(rmin)-1),1):min(j1+(ceil(rmin)-1),nely)\n",
    "        e2 = (i2-1)*nely+j2;\n",
    "        k = k+1;\n",
    "        iH(k) = e1;\n",
    "        jH(k) = e2;\n",
    "        sH(k) = max(0,rmin-sqrt((i1-i2)^2+(j1-j2)^2));\n",
    "      end\n",
    "    end\n",
    "  end\n",
    "end\n",
    "H = sparse(iH,jH,sH);\n",
    "Hs = sum(H,2);\n",
    "%% INITIALIZE ITERATION\n",
    "x = repmat(volfrac,nely,nelx);\n",
    "xPhys = x;\n",
    "loop = 0;\n",
    "change = 1;\n",
    "%% START ITERATION\n",
    "while change > 0.01\n",
    "  loop = loop + 1;\n",
    "  %% FE-ANALYSIS\n",
    "  sK = reshape(KE(:)*(Emin+xPhys(:)'.^penal*(E0-Emin)),64*nelx*nely,1);\n",
    "  K = sparse(iK,jK,sK); K = (K+K')/2;\n",
    "  U(freedofs) = K(freedofs,freedofs)\\F(freedofs);\n",
    "  %% OBJECTIVE FUNCTION AND SENSITIVITY ANALYSIS\n",
    "  ce = reshape(sum((U(edofMat)*KE).*U(edofMat),2),nely,nelx);\n",
    "  c = sum(sum((Emin+xPhys.^penal*(E0-Emin)).*ce));\n",
    "  dc = -penal*(E0-Emin)*xPhys.^(penal-1).*ce;\n",
    "  dv = ones(nely,nelx);\n",
    "  %% FILTERING/MODIFICATION OF SENSITIVITIES\n",
    "  if ft == 1\n",
    "    dc(:) = H*(x(:).*dc(:))./Hs./max(1e-3,x(:));\n",
    "  elseif ft == 2\n",
    "    dc(:) = H*(dc(:)./Hs);\n",
    "    dv(:) = H*(dv(:)./Hs); %dv est dc filtre\n",
    "  end\n",
    "  %% OPTIMALITY CRITERIA UPDATE OF DESIGN VARIABLES AND PHYSICAL DENSITIES\n",
    "  l1 = 0; l2 = 1e9; move = 0.2;\n",
    "  while (l2-l1)/(l1+l2) > 1e-3\n",
    "    lmid = 0.5*(l2+l1);\n",
    "    xnew = max(0,max(x-move,min(1,min(x+move,x.*sqrt(-dc./dv/lmid)))));\n",
    "    if ft == 1\n",
    "      xPhys = xnew;\n",
    "    elseif ft == 2\n",
    "      xPhys(:) = (H*xnew(:))./Hs;\n",
    "    end\n",
    "    if sum(xPhys(:)) > volfrac*nelx*nely, l1 = lmid; else l2 = lmid; end\n",
    "  end\n",
    "  change = max(abs(xnew(:)-x(:)));\n",
    "  x = xnew;\n",
    "  %% PRINT RESULTS\n",
    "  fprintf(' It.:%5i Obj.:%11.4f Vol.:%7.3f ch.:%7.3f\\n',loop,c, ... \n",
    "    mean(xPhys(:)),change);\n",
    "  %% PLOT DENSITIES\n",
    "  colormap(gray); imagesc(1-xPhys); caxis([0 1]); axis equal; axis off; drawnow;\n",
    "end\n",
    "%\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loop = 1Change = 0.2 c = 181.02944558470028 densité struct = 0.49995144886389187\n",
      "loop = 2Change = 0.20000000000000007 c = 87.70747378137004 densité struct = 0.5001614594571799\n",
      "loop = 3Change = 0.20000000000000007 c = 51.266856533836275 densité struct = 0.4998727321391105\n",
      "loop = 4Change = 0.20000000000000007 c = 37.10721162015415 densité struct = 0.5000877840247414\n",
      "loop = 5Change = 0.20000000000000007 c = 33.47226987144041 densité struct = 0.5000324691873671\n",
      "loop = 6Change = 0.20000000000000007 c = 31.701271804970467 densité struct = 0.5000380819496312\n",
      "loop = 7Change = 0.20000000000000007 c = 30.68077904834976 densité struct = 0.4999725989288342\n",
      "loop = 8Change = 0.20000000000000007 c = 30.056612408090903 densité struct = 0.4999948254123275\n",
      "loop = 9Change = 0.20000000000000007 c = 29.697007899595246 densité struct = 0.4999901086505678\n",
      "loop = 10Change = 0.20000000000000007 c = 29.509405391607785 densité struct = 0.4999967663977346\n",
      "loop = 11Change = 0.20000000000000007 c = 29.38356139873617 densité struct = 0.5000018543167374\n",
      "loop = 12Change = 0.20000000000000007 c = 29.292020865461083 densité struct = 0.5000056006525868\n",
      "loop = 13Change = 0.19999999999999996 c = 29.242405104392603 densité struct = 0.4999983961274466\n",
      "loop = 14Change = 0.19999999999999996 c = 29.20736430960941 densité struct = 0.5000011934646945\n",
      "loop = 15Change = 0.19999999999999996 c = 29.187038379599663 densité struct = 0.5000010560456092\n",
      "loop = 16Change = 0.19999999999999996 c = 29.17646552587081 densité struct = 0.4999990036073323\n",
      "loop = 17Change = 0.19999999999999996 c = 29.16804630459116 densité struct = 0.5000009111491894\n",
      "loop = 18Change = 0.19999999999999996 c = 29.159652759679492 densité struct = 0.5000036457225333\n",
      "loop = 19Change = 0.19999999999999996 c = 29.1514975967792 densité struct = 0.4999997711818767\n",
      "loop = 20Change = 0.19999999999999996 c = 29.144847980842343 densité struct = 0.5000036966266692\n",
      "loop = 21Change = 0.20000000000000007 c = 29.138851524864197 densité struct = 0.5000031425181569\n",
      "loop = 22Change = 0.19999999999999996 c = 29.133919112325113 densité struct = 0.5000032434819417\n",
      "loop = 23Change = 0.20000000000000007 c = 29.12907726110656 densité struct = 0.500002823479393\n",
      "loop = 24Change = 0.20000000000000007 c = 29.123976206463112 densité struct = 0.49999588458445904\n",
      "loop = 25Change = 0.20000000000000007 c = 29.118662087008154 densité struct = 0.5000009009005556\n",
      " 20.341404 seconds (156.44 M allocations: 6.358 GiB, 9.61% gc time)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(Plot{Plots.GRBackend() n=1}, 25, Any[181.02944558470028, 87.70747378137004, 51.266856533836275, 37.10721162015415, 33.47226987144041, 31.701271804970467, 30.68077904834976, 30.056612408090903, 29.697007899595246, 29.509405391607785  …  29.17646552587081, 29.16804630459116, 29.159652759679492, 29.1514975967792, 29.144847980842343, 29.138851524864197, 29.133919112325113, 29.12907726110656, 29.123976206463112, 29.118662087008154])"
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