top99.ipynb

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  {
   "cell_type": "markdown",
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   "source": [
    "## Translation in Julia of Ole Sigmund top99 code\n",
    "\n",
    "Robin Grapin"
   ]
  },
  {
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   "source": [
    "#imports\n",
    "using SparseArrays\n",
    "using Plots\n",
    "\n",
    "# 2 dofs only : x and y\n",
    "# material properties\n",
    "E = 1.; \n",
    "nu = 0.3;\n",
    "k=[ 1/2-nu/6   1/8+nu/8 -1/4-nu/12 -1/8+3*nu/8 -1/4+nu/12 -1/8-nu/8  nu/6  1/8-3*nu/8];\n",
    "#elementary matrix of stiffness\n",
    "KE = E/(1-nu^2)*[ k[1] k[2] k[3] k[4] k[5] k[6] k[7] k[8];\n",
    "                  k[2] k[1] k[8] k[7] k[6] k[5] k[4] k[3];\n",
    "                  k[3] k[8] k[1] k[6] k[7] k[4] k[5] k[2];\n",
    "                  k[4] k[7] k[6] k[1] k[8] k[3] k[2] k[5];\n",
    "                  k[5] k[6] k[7] k[8] k[1] k[2] k[3] k[4];\n",
    "                  k[6] k[5] k[4] k[3] k[2] k[1] k[8] k[7];\n",
    "                  k[7] k[4] k[5] k[2] k[3] k[8] k[1] k[6];\n",
    "                  k[8] k[3] k[2] k[5] k[4] k[7] k[6] k[1]];\n"
   ]
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  {
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    {
     "data": {
      "text/plain": [
       "top (generic function with 1 method)"
      ]
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     "execution_count": 2,
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   "source": [
    "function top(nelx,nely,volfrac,penal,rmin)\n",
    "    \n",
    "    # applied stress F[2,1] = -1 -> on the secod dof (y) of the first pixel (top left corner), we add an elementary effort (-1) in the direction of the top\n",
    "    ddl = 2*(nely+1)*(nelx+1) #dofs\n",
    "    F= zeros(ddl);\n",
    "    F[2] = -1; \n",
    "    \n",
    "    #fixed and free nodes ( here teh problem is the half beam MBB)    \n",
    "    fixeddofs   = union(1:2:2*(nely+1),[ddl]); #some dofs (x) are artificially fixed to materialize the symmetry\n",
    "    alldofs     = 1:ddl;\n",
    "    freedofs    = setdiff(alldofs,fixeddofs);\n",
    "    \n",
    "    x = volfrac * ones(nely,nelx) ; #uniform repartition of the mass at the beginning\n",
    "    loop = 0; \n",
    "    change = 1.; #arbitrary, to start the loop\n",
    "    dc = zeros(nely,nelx);\n",
    "    cValues = []\n",
    "    while change > 0.01  \n",
    "        loop += 1;\n",
    "        xold = x; # xold is the old mass repartition      \n",
    "        c = 0.; # objective function here :  the energy of deformation\n",
    "        U = FE(nelx,nely,x,penal, freedofs, fixeddofs,F);\n",
    "        for ely = 1:nely\n",
    "            for elx = 1:nelx\n",
    "                n1 = (nely+1)*(elx-1)+ely; \n",
    "                n2 = (nely+1)* elx   +ely;\n",
    "                Ue = append!([U[2*n1-1]],append!([U[2*n1]],append!([U[2*n2-1]],append!([U[2*n2]],append!([U[2*n2+1]],append!([U[2*n2+2]],append!([U[2*n1+1]],[U[2*n1+2]]))))))); #the 4 nodes of the element\n",
    "                c = c + x[ely,elx]^penal*Ue'*KE*Ue; # elementary participation to Edeformation\n",
    "                dc[ely,elx] = -penal*x[ely,elx]^(penal-1)*Ue'*KE*Ue; # dc/dx (Xe)\n",
    "            end\n",
    "        end\n",
    "        push!(cValues,c)\n",
    "        dc = check(nelx,nely,rmin,x,dc);\n",
    "        x  = OC(nelx,nely,x,volfrac,dc);\n",
    "        change = maximum(abs.(x-xold));\n",
    "        println(\"change = \", change, \"c = \", c);\n",
    "        if loop==25\n",
    "            return x,cValues,loop\n",
    "        end\n",
    "    end\n",
    "    return x,cVlaues,loop\n",
    "end"
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     "data": {
      "text/plain": [
       "OC (generic function with 1 method)"
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   "source": [
    "function OC(nelx,nely,x,volfrac,dc)  # new mass repartition\n",
    "    l1 = 0; l2 = 100000; move = 0.2;\n",
    "    xnew = zeros(nely,nelx);    \n",
    "    while (l2-l1 > 1e-4) #research of the lagrangian multilicator through dichotomy\n",
    "        lmid = 0.5*(l2+l1);\n",
    "        RacBe = sqrt.(-dc/lmid) ; # sqrt(Be) = -dc/(l * dv) and Xe* Be^1/2 .  xnew € [x-move, x+move]\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 sum(sum(xnew)) - volfrac*nelx*nely > 0;\n",
    "            l1 = lmid;\n",
    "        else\n",
    "            l2 = lmid;\n",
    "        end\n",
    "    end\n",
    "    return xnew\n",
    "end"
   ]
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   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
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    {
     "data": {
      "text/plain": [
       "FE (generic function with 1 method)"
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     "execution_count": 4,
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   "source": [
    "function FE(nelx,nely,x,penal, freedofs, fixeddofs, F) #Creation of the global stifness matrix, resolution of the displacements\n",
    "    K = spzeros(2*(nelx+1)*(nely+1), 2*(nelx+1)*(nely+1)); # sparse matrix of the global stifness  \n",
    "    U = zeros(2*(nely+1)*(nelx+1));\n",
    "    for elx = 1:nelx\n",
    "      for ely = 1:nely # loop for every element\n",
    "        n1 = (nely+1)*(elx-1)+ely; #node on the left top of the element \n",
    "        n2 = (nely+1)* elx   +ely; #right top\n",
    "        edof = [2*n1-1; 2*n1; 2*n2-1; 2*n2; 2*n2+1; 2*n2+2; 2*n1+1; 2*n1+2]; # the 2 dofs of each of the 4 nodes of the element\n",
    "        K[edof,edof] += x[ely,elx]^penal*KE; # c(x) = sum on e( Xe^p * Ue' * KE * Ue) => K = (Xe^p*KE)e\n",
    "      end\n",
    "    end\n",
    "    U[freedofs] = K[freedofs,freedofs] \\ F[freedofs]; \n",
    "    U[fixeddofs] .= 0;\n",
    "    return U\n",
    "end"
   ]
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   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "check (generic function with 1 method)"
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     "execution_count": 5,
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   "source": [
    "function check(nelx,nely,rmin,x,dc) # filtering to be sure of he existence of solutions\n",
    "    dcn=zeros(nely,nelx); #filtered dc/dx . Hf = Rmin - dist(e,f)\n",
    "    for i = 1:nelx\n",
    "      for j = 1:nely\n",
    "        sum=0.0;\n",
    "        for k = max(i-floor(rmin),1):min(i+floor(rmin),nelx)\n",
    "          for l = max(j-floor(rmin),1):min(j+floor(rmin),nely)\n",
    "            fac = rmin-sqrt((i-k)^2+(j-l)^2);\n",
    "            sum = sum+max(0,fac); \n",
    "            dcn[j,i] += max(0,fac)*x[l,k]*dc[l,k];\n",
    "          end\n",
    "        end\n",
    "        dcn[j,i] = dcn[j,i]/(x[j,i]*sum);\n",
    "      end\n",
    "    end\n",
    "    return dcn\n",
    "end"
   ]
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     "text": [
      "change = 0.2c = 240.55295797268946\n",
      "change = 0.20000000000000007c = 142.17900808909855\n",
      "change = 0.20000000000000007c = 101.96705996828744\n",
      "change = 0.20000000000000007c = 82.42009077779126\n",
      "change = 0.20000000000000007c = 73.87933102804553\n",
      "change = 0.2c = 67.57751539753602\n",
      "change = 0.1692438717135697c = 63.42635663032229\n",
      "change = 0.1424340357866224c = 61.05609760474731\n",
      "change = 0.1631616850400155c = 59.394304215155074\n",
      "change = 0.13707745286782547c = 57.96507558910982\n",
      "change = 0.1740902643107608c = 56.48944702364758\n",
      "change = 0.17714069897131868c = 54.71453615940355\n",
      "change = 0.20000000000000007c = 52.795844691904534\n",
      "change = 0.20000000000000007c = 51.239015326952234\n",
      "change = 0.17179597655086665c = 50.239263702718546\n",
      "change = 0.13231951929612018c = 49.62505117567204\n",
      "change = 0.13291514575716343c = 49.212430268245164\n",
      "change = 0.11549171936232808c = 48.86540750738922\n",
      "change = 0.07971416509444079c = 48.598735760243834\n",
      "change = 0.06776078298011257c = 48.525640846747436\n",
      "change = 0.06300303461168522c = 48.5276739516173\n",
      "change = 0.05943577612896134c = 48.525458538129584\n",
      "change = 0.05989339848623065c = 48.539686423218065\n",
      "change = 0.06064221843348605c = 48.54046047474225\n",
      "change = 0.060780743457553854c = 48.53892612636884\n"
     ]
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     "output_type": "execute_result"
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   ],
   "source": [
    "x,c,l = top(50,33,0.5,3,2);\n",
    "plot(1:l,c,title = \"sensity evolution top99\", label = \"sensity c\") #evolution of c during the process\n",
    "xlabel!(\"iteration\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
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      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c2 = [ 240.55295821333357,\n",
    " 142.29012812657385,\n",
    " 101.29042745369344,\n",
    "  80.66559467707458,\n",
    "  70.50380077726645,\n",
    "  62.76373407502861,\n",
    "  57.569456923643784,\n",
    "  53.32531768875428,\n",
    "  50.258491516100314,\n",
    "  48.810735392503446,\n",
    "  48.11940887678135,\n",
    "  47.70674371910807,\n",
    "  47.47118107678733,\n",
    "  47.343485675725475,\n",
    "  47.23921449548786,\n",
    "  47.127973767283066,\n",
    "  46.99585044365262,\n",
    "  46.79670069347179,\n",
    "  46.53871598798251,\n",
    "  46.30448641143472,\n",
    "  46.23496928553922,\n",
    "  46.18414430101558,\n",
    "  46.1377939278308,\n",
    "  46.095353434995985,\n",
    "  46.05217114719343]#values for 25 iterations of top88 : top88(50,33,0.5, 3,2,1);\n",
    "heatmap(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
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    "  46.09535345946886,\n",
    "  46.05217117865928]#25 it topFD"
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   ],
   "source": [
    "plot(1:l, [c,c2,c3],title = \"sensity evolution\", label = [\"top99\" \"top88\" \"topFD\"], ylim = (45,50)) #comparation\n",
    "xlabel!(\"iterations\")"
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