Topology Optimization 3D.ipynb

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      ]
     },
     "execution_count": 211,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Default input parameters\n",
    "volfrac=0.3\n",
    "rmin=5.4\n",
    "penal=3.0\n",
    "ft=1 # ft==0 -> sens, ft==1 -> dens\n",
    "maxIter=300\n",
    "\n",
    "xPhys=CompliantTopologyOptimization(nelx,nely,volfrac,rmin,penal,maxIter,Load,Support,Spring,DOut)\n",
    "Gray.(xPhys)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 219,
   "metadata": {},
   "outputs": [
    {
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       " Gray{Float64}(0.0)  Gray{Float64}(0.0)     Gray{Float64}(1.0)\n",
       " Gray{Float64}(0.0)  Gray{Float64}(0.0)  …  Gray{Float64}(1.0)\n",
       " Gray{Float64}(0.0)  Gray{Float64}(0.0)     Gray{Float64}(1.0)\n",
       " Gray{Float64}(0.0)  Gray{Float64}(0.0)     Gray{Float64}(1.0)\n",
       " Gray{Float64}(0.0)  Gray{Float64}(0.0)     Gray{Float64}(1.0)\n",
       " Gray{Float64}(0.0)  Gray{Float64}(0.0)     Gray{Float64}(1.0)\n",
       " Gray{Float64}(0.0)  Gray{Float64}(0.0)  …  Gray{Float64}(1.0)\n",
       " Gray{Float64}(0.0)  Gray{Float64}(0.0)     Gray{Float64}(1.0)\n",
       " Gray{Float64}(0.0)  Gray{Float64}(0.0)     Gray{Float64}(1.0)\n",
       " Gray{Float64}(0.0)  Gray{Float64}(0.0)     Gray{Float64}(1.0)\n",
       " Gray{Float64}(0.0)  Gray{Float64}(0.0)     Gray{Float64}(1.0)"
      ]
     },
     "execution_count": 219,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Gray.(xPhys) \n",
    "# Gray.(xPhys[end:-1:1,:])\n",
    "xxx=vcat(xPhys[end:-1:1,:],xPhys)\n",
    "Gray.(1 .- xxx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Minimum compliance problem with OC\n",
      "ndes: 60 x 20\n",
      "volfrac: 0.4 rmin: 1.5 penal: 3.0\n",
      "43200.0\n",
      "103240\n",
      " It:1 Obj:11962.173009116676 Vol:0.20000000000000004 ch:0.2 \n",
      " It:2 Obj:95697.37360469432 Vol:0.10003192232531125 ch:0.2 \n",
      " It:3 Obj:443324.00864808855 Vol:0.09992310479005387 ch:0.2 \n",
      " It:4 Obj:261711.62634145602 Vol:0.10005840821677169 ch:0.20000000000000007 \n",
      " It:5 Obj:212337.65131232055 Vol:0.0999302797155729 ch:0.19625397260153898 \n",
      " It:6 Obj:173600.36667067034 Vol:0.09997607369868877 ch:0.20000000000000007 \n",
      " It:7 Obj:150410.42135775986 Vol:0.10000424615611908 ch:0.20000000000000004 \n",
      " It:8 Obj:127962.62611283705 Vol:0.10001121054088659 ch:0.20000000000000007 \n",
      " It:9 Obj:115748.95888814985 Vol:0.10001051804635554 ch:0.20000000000000004 \n",
      " It:10 Obj:101896.02980106752 Vol:0.10005930238832814 ch:0.20000000000000007 \n",
      " It:11 Obj:92870.819138467 Vol:0.10000767044190365 ch:0.20000000000000007 \n",
      " It:12 Obj:77333.24862763958 Vol:0.1000313303877065 ch:0.20000000000000007 \n",
      " It:13 Obj:63185.45205754813 Vol:0.10005399943208382 ch:0.20000000000000007 \n",
      " It:14 Obj:44615.46041004278 Vol:0.10002516939486478 ch:0.20000000000000007 \n",
      " It:15 Obj:30026.553522955586 Vol:0.09993984769191196 ch:0.20000000000000007 \n",
      " It:16 Obj:20458.60894323521 Vol:0.1000105041382848 ch:0.20000000000000007 \n",
      " It:17 Obj:14796.9576929131 Vol:0.10004563921285352 ch:0.20000000000000007 \n",
      " It:18 Obj:11689.991348003325 Vol:0.10002412204538359 ch:0.20000000000000007 \n",
      " It:19 Obj:9777.743061585443 Vol:0.09995485236705179 ch:0.19885557573355161 \n",
      " It:20 Obj:8698.735638262868 Vol:0.10001338062693803 ch:0.20000000000000007 \n",
      " It:21 Obj:8018.38620941117 Vol:0.10003446046665654 ch:0.19999999999999996 \n",
      " It:22 Obj:7589.324880715997 Vol:0.10002981514947144 ch:0.20000000000000007 \n",
      " It:23 Obj:7313.995072436354 Vol:0.09997267393797218 ch:0.20000000000000007 \n",
      " It:24 Obj:7150.919750170102 Vol:0.09999780635551031 ch:0.19999999999999996 \n",
      " It:25 Obj:7019.325907819124 Vol:0.10003180964102867 ch:0.2 \n",
      " It:26 Obj:6933.648772862865 Vol:0.1000000107218357 ch:0.20000000000000007 \n",
      " It:27 Obj:6857.248699070812 Vol:0.10002132314453623 ch:0.20000000000000007 \n",
      " It:28 Obj:6785.471205514017 Vol:0.10000878217503993 ch:0.19999999999999996 \n",
      " It:29 Obj:6712.7067632384405 Vol:0.10001545977515192 ch:0.20000000000000007 \n",
      " It:30 Obj:6663.372991530805 Vol:0.09998785153499634 ch:0.20000000000000007 \n",
      " It:31 Obj:6605.298326006589 Vol:0.100002790222736 ch:0.20000000000000007 \n",
      " It:32 Obj:6545.118814467589 Vol:0.09997705394839049 ch:0.19999999999999996 \n",
      " It:33 Obj:6493.163371942648 Vol:0.10000561240420652 ch:0.19999999999999996 \n",
      " It:34 Obj:6462.683787149101 Vol:0.1000199498590172 ch:0.06896591828759169 \n",
      " It:35 Obj:6435.582422822976 Vol:0.09997608734592617 ch:0.06781187294843538 \n",
      " It:36 Obj:6429.968633739874 Vol:0.10001454616197661 ch:0.06207410605698738 \n",
      " It:37 Obj:6409.361380200666 Vol:0.09999510478718628 ch:0.07794262983960704 \n",
      " It:38 Obj:6402.98368285262 Vol:0.09999183549405839 ch:0.1125199390780357 \n",
      " It:39 Obj:6389.438287596747 Vol:0.1000118010975279 ch:0.1389470708708721 \n",
      " It:40 Obj:6376.178848434467 Vol:0.1000214859143916 ch:0.12102927984841105 \n",
      " It:41 Obj:6365.541213080839 Vol:0.10001752253826204 ch:0.07754866991032161 \n",
      " It:42 Obj:6360.367422969659 Vol:0.09999989383035515 ch:0.04558881484770072 \n",
      " It:43 Obj:6356.908542177172 Vol:0.09997466163142618 ch:0.04345603776201157 \n",
      " It:44 Obj:6355.107350969029 Vol:0.10001176128209288 ch:0.03966477535115731 \n",
      " It:45 Obj:6344.77797380835 Vol:0.10000738828057165 ch:0.03896852480838131 \n",
      " It:46 Obj:6340.4823359575375 Vol:0.09998042643384684 ch:0.03659724921934471 \n",
      " It:47 Obj:6339.5312005802625 Vol:0.10001196394488891 ch:0.0360018749154819 \n",
      " It:48 Obj:6329.347883098046 Vol:0.10000531991100053 ch:0.03695694175265418 \n",
      " It:49 Obj:6325.687818154467 Vol:0.10002570817437942 ch:0.03789334425915983 \n",
      " It:50 Obj:6316.564168963778 Vol:0.10002493519245974 ch:0.055393789843103586 \n",
      " It:51 Obj:6311.139053740666 Vol:0.09998800017918325 ch:0.0859321946509031 \n",
      " It:52 Obj:6307.486965388899 Vol:0.1000042836040583 ch:0.14589092337465165 \n",
      " It:53 Obj:6291.833920571402 Vol:0.09998999521241729 ch:0.19999999999999996 \n",
      " It:54 Obj:6274.778086142693 Vol:0.0999745241332703 ch:0.19999999999999996 \n",
      " It:55 Obj:6263.756580464783 Vol:0.10001757139857773 ch:0.12339151198976261 \n",
      " It:56 Obj:6249.590612264951 Vol:0.10001471919823081 ch:0.03393557048493612 \n",
      " It:57 Obj:6246.955077132851 Vol:0.10002026383383009 ch:0.030889175145225378 \n",
      " It:58 Obj:6242.505599081329 Vol:0.10002288265065219 ch:0.03113382883154925 \n",
      " It:59 Obj:6241.418162824504 Vol:0.10000598809542666 ch:0.029794598771932357 \n",
      " It:60 Obj:6241.637660034608 Vol:0.09998886200665405 ch:0.02826848990458941 \n",
      " It:61 Obj:6244.124537024549 Vol:0.09999197470397495 ch:0.02677465046454952 \n",
      " It:62 Obj:6242.062864729367 Vol:0.1000265943738417 ch:0.026892116905973484 \n",
      " It:63 Obj:6238.134972463837 Vol:0.10001452303944443 ch:0.025508996466282907 \n",
      " It:64 Obj:6239.191630903352 Vol:0.10001667649089008 ch:0.024095982280584294 \n",
      " It:65 Obj:6239.815370906206 Vol:0.1000220086127212 ch:0.0227262480236895 \n",
      " It:66 Obj:6238.51903666902 Vol:0.1000141123977851 ch:0.022060040951965232 \n",
      " It:67 Obj:6241.021001945366 Vol:0.09997394732317427 ch:0.026559935404875973 \n",
      " It:68 Obj:6246.20374135815 Vol:0.09999486372093687 ch:0.033082895010146246 \n",
      " It:69 Obj:6244.601007938554 Vol:0.09999249864194229 ch:0.042040665448560416 \n",
      " It:70 Obj:6245.311828949899 Vol:0.1000111458761327 ch:0.05520411256424096 \n",
      " It:71 Obj:6244.884792609323 Vol:0.0999745998760748 ch:0.07414248276700663 \n",
      " It:72 Obj:6250.634463236177 Vol:0.09997552106911871 ch:0.10268620577876214 \n",
      " It:73 Obj:6252.075237073141 Vol:0.10002720012824859 ch:0.14309563640818507 \n",
      " It:74 Obj:6244.9543496194365 Vol:0.10000909904151413 ch:0.18692118160888527 \n",
      " It:75 Obj:6250.07243740379 Vol:0.09998496071360496 ch:0.17556586638831329 \n",
      " It:76 Obj:6254.4760169714955 Vol:0.10002090931055113 ch:0.03288225374296361 \n",
      " It:77 Obj:6247.703135463185 Vol:0.09999838143730506 ch:0.03096925612617074 \n",
      " It:78 Obj:6248.64073562217 Vol:0.09997995134758025 ch:0.03016880464279903 \n",
      " It:79 Obj:6250.331781033963 Vol:0.10001536426257478 ch:0.028039723586798737 \n",
      " It:80 Obj:6243.153179079924 Vol:0.10002010061424182 ch:0.025522694013984437 \n",
      " It:81 Obj:6242.342965019074 Vol:0.10000588661179727 ch:0.024590193343981603 \n",
      " It:82 Obj:6242.525046494369 Vol:0.09998948728141173 ch:0.02388389547815417 \n",
      " It:83 Obj:6244.213674716348 Vol:0.09997815425522781 ch:0.02312526266349535 \n",
      " It:84 Obj:6243.7826260431575 Vol:0.10001365238769758 ch:0.02145658092118008 \n",
      " It:85 Obj:6238.3330756658015 Vol:0.09997513097726052 ch:0.02052166914564746 \n",
      " It:86 Obj:6242.226840002589 Vol:0.09998100988304252 ch:0.020339400576534605 \n",
      " It:87 Obj:6240.627355901734 Vol:0.10001031840741392 ch:0.018809408793178495 \n",
      " It:88 Obj:6235.035716074013 Vol:0.09997392322329453 ch:0.018223260408825714 \n",
      " It:89 Obj:6239.828585690256 Vol:0.09998544163880546 ch:0.018104787241738918 \n",
      " It:90 Obj:6236.402568315815 Vol:0.10000727586949484 ch:0.016937240749467453 \n",
      " It:91 Obj:6233.115703696965 Vol:0.09998489653981422 ch:0.016459403522395666 \n",
      " It:92 Obj:6234.955705718511 Vol:0.09998256313491552 ch:0.016550187000648586 \n",
      " It:93 Obj:6234.732316266455 Vol:0.10002415614644149 ch:0.015588261990220675 \n",
      " It:94 Obj:6227.768624259415 Vol:0.09998292391169454 ch:0.015273145102023655 \n",
      " It:95 Obj:6233.462987867732 Vol:0.10000432790655907 ch:0.015484233579348694 \n",
      " It:96 Obj:6229.015964003502 Vol:0.10002371651380833 ch:0.01472649582899771 \n",
      " It:97 Obj:6226.360898970592 Vol:0.10000884142789236 ch:0.014529243458483443 \n",
      " It:98 Obj:6227.484805740067 Vol:0.10000541323914322 ch:0.014845089429374292 \n",
      " It:99 Obj:6227.644500964738 Vol:0.09999450009012957 ch:0.014897779837103775 \n",
      " It:100 Obj:6228.05844895467 Vol:0.09998423871633567 ch:0.015187766871117059 \n",
      " It:101 Obj:6229.102732495178 Vol:0.09997622352279435 ch:0.015319186311104516 \n",
      " It:102 Obj:6229.065534147116 Vol:0.100020742825454 ch:0.015031871064862257 \n",
      " It:103 Obj:6222.756365927963 Vol:0.09998349235335385 ch:0.01485725363437762 \n",
      " It:104 Obj:6227.286248181783 Vol:0.10000131676890502 ch:0.015343269837616913 \n",
      " It:105 Obj:6224.324756593172 Vol:0.099971968348639 ch:0.015340402636165207 \n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " It:106 Obj:6227.569143028177 Vol:0.0999804520524124 ch:0.015658564061982516 \n",
      " It:107 Obj:6225.8335234054475 Vol:0.10001576076966325 ch:0.015190868230883392 \n",
      " It:108 Obj:6220.334862435072 Vol:0.09998618234804564 ch:0.015098005611570209 \n",
      " It:109 Obj:6224.354236748468 Vol:0.10000172623218913 ch:0.015139128272545432 \n",
      " It:110 Obj:6221.15785045815 Vol:0.0999747790711943 ch:0.014931122688629339 \n",
      " It:111 Obj:6224.605615726193 Vol:0.09998629286356783 ch:0.014703007928933032 \n",
      " It:112 Obj:6221.90827880178 Vol:0.10001940364389035 ch:0.013980046957357828 \n",
      " It:113 Obj:6217.241294856585 Vol:0.09999852464629884 ch:0.013439222926343142 \n",
      " It:114 Obj:6219.612243319665 Vol:0.10000906353432452 ch:0.012962916447419398 \n",
      " It:115 Obj:6217.691957866182 Vol:0.09999403081565213 ch:0.012307985852295505 \n",
      " It:116 Obj:6219.140275861796 Vol:0.0999984196538965 ch:0.011658284706703048 \n",
      " It:117 Obj:6218.041950005164 Vol:0.09998768201256349 ch:0.010918487683398218 \n",
      " It:118 Obj:6218.9100970322725 Vol:0.09998910291446012 ch:0.010194971365736424 \n",
      " It:119 Obj:6218.259918631438 Vol:0.09998159206822199 ch:0.009442670664909378 \n"
     ]
    },
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       " \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<svg xmlns=\"http://www.w3.org/2000/svg\" version=\"1.1\"\n",
       "     width=\"25mm\" height=\"25mm\" viewBox=\"0 0 1 1\">\n",
       "    <rect width=\"1\" height=\"1\" fill=\"#FFFFFF\" stroke=\"none\"/>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "Gray{Float64}(1.0)"
      ]
     },
     "execution_count": 175,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function topologyOptimization3d(nelx,nely,nelz,volfrac,rmin,penal)\n",
    "    function lk_H8(nu)\n",
    "        A = [32 6 -8 6 -6 4 3 -6 -10 3 -3 -3 -4 -8;\n",
    "            -48 0 0 -24 24 0 0 0 12 -12 0 12 12 12];\n",
    "        k = 1/144*A'*[1; nu];\n",
    "\n",
    "        K1 = [k[1]   k[2]   k[2]   k[3]  k[5]  k[5];\n",
    "              k[2]   k[1]   k[2]   k[4]  k[6]  k[7];\n",
    "              k[2]   k[2]   k[1]   k[4]  k[7]  k[6];\n",
    "              k[3]   k[4]   k[4]   k[1]  k[8]  k[8];\n",
    "              k[5]   k[6]   k[7]   k[8]  k[1]  k[2];\n",
    "              k[5]   k[7]   k[6]   k[8]  k[2]  k[1]];\n",
    "        K2 = [k[9]   k[8]   k[12]  k[6]  k[4]  k[7];\n",
    "              k[8]   k[9]   k[12]  k[5]  k[3]  k[5];\n",
    "              k[10]  k[10]  k[13]  k[7]  k[4]  k[6];\n",
    "              k[6]   k[5]   k[11]  k[9]  k[2]  k[10];\n",
    "              k[4]   k[3]   k[5]   k[2]  k[9]  k[12]\n",
    "              k[11]  k[4]   k[6]   k[12] k[10] k[13]];\n",
    "        K3 = [k[6]   k[7]   k[4]   k[9]  k[12] k[8];\n",
    "              k[7]   k[6]   k[4]   k[10] k[13] k[10];\n",
    "              k[5]   k[5]   k[3]   k[8]  k[12] k[9];\n",
    "              k[9]   k[10]  k[2]   k[6]  k[11] k[5];\n",
    "              k[12]  k[13]  k[10]  k[11] k[6]  k[4];\n",
    "              k[2]   k[12]  k[9]   k[4]  k[5]  k[3]];\n",
    "        K4 = [k[14]  k[11]  k[11]  k[13] k[10] k[10];\n",
    "              k[11]  k[14]  k[11]  k[12] k[9]  k[8];\n",
    "              k[11]  k[11]  k[14]  k[12] k[8]  k[9];\n",
    "              k[13]  k[12]  k[12]  k[14] k[7]  k[7];\n",
    "              k[10]  k[9]   k[8]   k[7]  k[14] k[11];\n",
    "              k[10]  k[8]   k[9]   k[7]  k[11] k[14]];\n",
    "        K5 = [k[1]   k[2]   k[8]   k[3]  k[5]  k[4];\n",
    "              k[2]   k[1]   k[8]   k[4]  k[6]  k[11];\n",
    "              k[8]   k[8]   k[1]   k[5]  k[11] k[6];\n",
    "              k[3]   k[4]   k[5]   k[1]  k[8]  k[2];\n",
    "              k[5]   k[6]   k[11]  k[8]  k[1]  k[8];\n",
    "              k[4]   k[11]  k[6]   k[2]  k[8]  k[1]];\n",
    "        K6 = [k[14]  k[11]  k[7]   k[13] k[10] k[12];\n",
    "              k[11]  k[14]  k[7]   k[12] k[9]  k[2];\n",
    "              k[7]   k[7]   k[14]  k[10] k[2]  k[9];\n",
    "              k[13]  k[12]  k[10]  k[14] k[7]  k[11];\n",
    "              k[10]  k[9]   k[2]   k[7]  k[14] k[7];\n",
    "              k[12]  k[2]   k[9]   k[11] k[7]  k[14]];\n",
    "        KE = 1/((nu+1)*(1-2*nu))*[ K1  K2  K3  K4;K2'  K5  K6  K3';K3' K6  K5' K2';K4  K3  K2  K1'];\n",
    "\n",
    "        return KE\n",
    "    end\n",
    "    println(\"Minimum compliance problem with OC\")\n",
    "    println(\"ndes: $nelx x $nely\")\n",
    "    println(\"volfrac: $volfrac rmin: $rmin penal: $penal\")\n",
    "    # Max and min stiffness\n",
    "    Emin=1e-9\n",
    "    Emax=1.0\n",
    "    nu=0.3\n",
    "    # dofs:\n",
    "    ndof = 3*(nelx+1)*(nely+1)*(nelz+1)\n",
    "    # Allocate design variables (as array), initialize and allocate sens.\n",
    "    x=volfrac * ones(Float64,nely,nelx,nelz)\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,nelz))\n",
    "    \n",
    "    # FE: Build the index vectors for the for coo matrix format.\n",
    "    KE=lk_H8(nu)\n",
    "    nele = nelx*nely*nelz\n",
    "    \n",
    "    nodenrs = reshape(1:(1+nelx)*(1+nely)*(1+nelz),1+nely,1+nelx,1+nelz)\n",
    "    edofVec = reshape(3*nodenrs[1:end-1,1:end-1,1:end-1].+1,nelx*nely*nelz,1)\n",
    "    edofMat = repeat(edofVec,1,24).+repeat([0 1 2 3*nely.+[3 4 5 0 1 2] -3 -2 -1 3*(nely+1)*(nelx+1).+[0 1 2 3*nely.+[3 4 5 0 1 2] -3 -2 -1]],nelx*nely*nelz,1)\n",
    "        \n",
    "    iK = convert(Array{Int},reshape(kron(edofMat,ones(24,1))',24*24*nele,1))\n",
    "    jK = convert(Array{Int},reshape(kron(edofMat,ones(1,24))',24*24*nele,1))\n",
    "    \n",
    "    \n",
    "    \n",
    "    \n",
    "    # USER-DEFINED LOAD DOFs\n",
    "    m= Matlab.meshgrid(nelx:nelx, 0:0, 0:nelz)\n",
    "    il=m[1]\n",
    "    jl=m[2]\n",
    "    kl=m[3]\n",
    "    loadnid = kl.*(nelx+1).*(nely+1).+il.*(nely+1).+(nely+1 .-jl)\n",
    "    loaddof = 3 .*loadnid[:] .- 1; \n",
    "    # USER-DEFINED SUPPORT FIXED DOFs\n",
    "    m= Matlab.meshgrid(0:0,0:nely,0:nelz)# Coordinates\n",
    "    iif=m[1]\n",
    "    jf=m[2]\n",
    "    kf=m[3]\n",
    "    fixednid = kf.*(nelx+1).*(nely+1) .+iif .*(nely .+1) .+(nely .+1 .-jf) # Node IDs\n",
    "    fixeddof = [3 .*fixednid[:]; 3 .*fixednid[:].-1; 3 .*fixednid[:].-2] # DOFs\n",
    "    \n",
    "    \n",
    "    # DEFINE LOADS AND SUPPORTS (HALF MBB-BEAM)\n",
    "    F= sparse(loaddof,fill(1,length(loaddof)),fill(-1,length(loaddof)),ndof,1);\n",
    "    U = zeros(ndof,1)\n",
    "    alldofs = 1:ndof\n",
    "    freedofs = setdiff(1:ndof,fixeddof)\n",
    "    \n",
    "    \n",
    "    \n",
    "    # Prepare filter\n",
    "    #iH = ones(convert(Int,nele*(2*(ceil(rmin)-1)+1)^2),1)\n",
    "    #jH = ones(Int,size(iH))\n",
    "    #sH = zeros(size(iH))\n",
    "    iH=[]\n",
    "    jH=[]\n",
    "    sH=[]\n",
    "    k = 0\n",
    "\n",
    "    for k1 = 1:nelz\n",
    "        for i1 = 1:nelx\n",
    "            for j1 = 1:nely\n",
    "                e1 = (k1-1)*nelx*nely + (i1-1)*nely+j1\n",
    "                for k2 = max(k1-(ceil(rmin)-1),1):min(k1+(ceil(rmin)-1),nelz)\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 = (k2-1)*nelx*nely + (i2-1)*nely+j2;\n",
    "                            k = k+1;\n",
    "                            append!(iH, e1  )\n",
    "                            append!(jH, e2  )\n",
    "                            append!(sH, max(0.0,rmin-sqrt((i1-i2)^2+(j1-j2)^2+(k1-k2)^2) ))\n",
    "                            \n",
    "                        end\n",
    "                    end\n",
    "                end\n",
    "            end\n",
    "        end\n",
    "    end\n",
    "    iH=reshape(iH,length(iH),1)\n",
    "    jH=reshape(jH,length(jH),1)\n",
    "    sH=reshape(convert(Array{Float64}, sH),length(sH),1)\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)),24*24*nelx*nely*nelz,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,nelz)\n",
    "            c = sum(sum(sum((Emin.+xPhys.^penal*(Emax-Emin)).*ce)))\n",
    "            \n",
    "            dc = -penal*(Emax-Emin)*xPhys.^(penal-1).*ce\n",
    "            dv = ones(nely,nelx,nelz)\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; move = 0.2; xnew = 0\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",
    "                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",
    "            println(\" It:$loop Obj:$c Vol:$m ch:$change \")\n",
    "\n",
    "            xPhys = copy(x)\n",
    "        end\n",
    "    end\n",
    "    return xPhys\n",
    "end\n",
    "nelx=60\n",
    "nely=20\n",
    "nelz=4\n",
    "volfrac=0.4\n",
    "rmin=1.5\n",
    "penal=3.0\n",
    "\n",
    "xPhys=topologyOptimization3d(nelx,nely,nelz,volfrac,rmin,penal)\n",
    "Gray.(xPhys[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 201,
   "metadata": {},
   "outputs": [
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