Mircrostructure Truss.ipynb

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       "  2232.76,1486.45 2232.76,1355.96 2256.76,1355.96 2232.76,1355.96 2232.76,1207.49 2256.76,1207.49 2232.76,1207.49 2232.76,1059.02 2256.76,1059.02 2232.76,1059.02 \n",
       "  2232.76,910.544 2256.76,910.544 2232.76,910.544 2232.76,762.072 2256.76,762.072 2232.76,762.072 2232.76,613.6 2256.76,613.6 2232.76,613.6 2232.76,465.128 \n",
       "  2256.76,465.128 2232.76,465.128 2232.76,316.656 2256.76,316.656 2232.76,316.656 2232.76,168.183 2256.76,168.183 2232.76,168.183 2232.76,47.2441 \n",
       "  \"/>\n",
       "</svg>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df=6\n",
    "display(heatmap(reshape(U[edofMat][:,df],nely,nelx)))\n",
    "display(heatmap((reshape(de'[:,df],nelx,nely)')))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9600"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "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))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Topology with new FEM"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "topologyOptimizationFEMCode (generic function with 2 methods)"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function topologyOptimizationFEMCode(MBB,nelx,nely,volfrac,rmin ,penal)\n",
    "    anim=Animation()\n",
    "    \n",
    "    display(\"Minimum compliance problem with OC\")\n",
    "    display(\"ndes: $nelx x $nely\")\n",
    "    display(\"volfrac: $volfrac rmin: $rmin penal: $penal\")\n",
    "    # Max and min stiffness\n",
    "    Emin=1e-9\n",
    "    Emax=1.0\n",
    "    # dofs:\n",
    "    ndof = 2*(nelx+1)*(nely+1)\n",
    "    # Allocate design variables (as array), initialize and allocate sens.\n",
    "    x=volfrac * ones(Float64,nelx,nely)\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,(nelx,nely))\n",
    "    \n",
    "    \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",
    "    \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",
    "    \n",
    "    \n",
    "    # Prepare filter\n",
    "    iH = ones(convert(Int,nelx*nely*(2*(ceil(rmin)-1)+1)^2),1)\n",
    "    jH = ones(Int,size(iH))\n",
    "    sH = zeros(size(iH))\n",
    "    k = 0;\n",
    "    for i1 = 1:nely\n",
    "        for j1 = 1:nelx\n",
    "            e1 = (i1-1)*nelx+j1\n",
    "            for i2 = max(i1-(ceil(rmin)-1),1):min(i1+(ceil(rmin)-1),nely)\n",
    "                for j2 = max(j1-(ceil(rmin)-1),1):min(j1+(ceil(rmin)-1),nelx)\n",
    "                    e2 = (i2-1)*nelx+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(vec(iH),vec(jH),vec(sH))\n",
    "    Hs = sum(H,dims=2)\n",
    "    ###################################################\n",
    "    loop = 0\n",
    "    change = 1\n",
    "    maxIter=1000\n",
    "    # Start iteration\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",
    "#             c = sum(sum((Emin.+xPhys.^penal*(Emax-Emin)).*ce))\n",
    "            \n",
    "            \n",
    "            K,F,d,de,Fe=FEM(problem,(Emin.+xPhys[:]'.^penal*(Emax-Emin)));\n",
    "            \n",
    "            # Objective function and sensitivity analysis\n",
    "            ce = reshape(sum((de'*Ke[:,:,1]).*de',dims=2),nelx,nely)\n",
    "            c = sum(sum((Emin.+xPhys.^penal*(Emax-Emin)).*ce))\n",
    "\n",
    "        \n",
    "            \n",
    "            dc = -penal*(Emax-Emin)*xPhys.^(penal-1).*ce\n",
    "            dv = ones(nelx,nely)\n",
    "            dc[:] = H*(dc[:]./Hs)\n",
    "            dv[:] = H*(dv[:]./Hs)\n",
    "            # OPTIMALITY CRITERIA UPDATE OF DESIGN VARIABLES AND PHYSICAL DENSITIES\n",
    "            l1 = 0; l2 = 1e9; xnew = 0\n",
    "            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.((0.0.-dc)./dv./lmid)))))\n",
    "                xPhys[:] = (H*xnew[:])./Hs\n",
    "                xPhys[:] = (xnew[:])\n",
    "                if sum(xPhys[:]) > volfrac*nelx*nely\n",
    "                    l1 = lmid\n",
    "                else\n",
    "                    l2 = lmid\n",
    "                end\n",
    "            end\n",
    "            change = maximum(abs.(xnew[:].-x[:]))\n",
    "            x = xnew\n",
    "            m=mean(xPhys[:])\n",
    "            display(\" It:$loop Obj:$c Vol:$m ch:$change \")\n",
    "            if loop<20||mod(loop,10)==0\n",
    "                xxx=1 .- clamp.(xPhys,0,1)\n",
    "                display(heatmap(xxx',xaxis=nothing,yaxis=nothing,legend=nothing,fc=:grays,clims=(0.0, 1.0),aspect_ratio=:equal))\n",
    "                heatmap(xxx',xaxis=nothing,yaxis=nothing,legend=nothing,fc=:grays,clims=(0.0, 1.0),aspect_ratio=:equal)\n",
    "                frame(anim)\n",
    "            end\n",
    "\n",
    "            xPhys = copy(x)\n",
    "        end\n",
    "    end\n",
    "    return xPhys,anim\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"Minimum compliance problem with OC\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\"ndes: 60 x 20\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\"volfrac: 0.4 rmin: 5.4 penal: 3.0\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\" It:1 Obj:19.668400255357035 Vol:0.39984401223926097 ch:0.20000000000000007 \""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
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