Topology Optimization 3D.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: Precompiling VectorizedRoutines [0e69188a-a5d4-5622-b4e4-a72373136fc5]\n",
      "└ @ Base loading.jl:1242\n"
     ]
    }
   ],
   "source": [
    "using LinearAlgebra\n",
    "using Plots\n",
    "import JSON\n",
    "using SparseArrays\n",
    "using Images\n",
    "using StaticArrays, BenchmarkTools\n",
    "using VectorizedRoutines"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# based on https://paulino.ce.gatech.edu/conferences/papers/11pereira_anefficientandcompact.pdf and http://www.topopt.mek.dtu.dk/apps-and-software and https://github.com/blademwang11/Topopt/blob/master/top.jl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 208,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Minimum compliance problem with OC\n",
      "ndes: 180 x 60\n",
      "volfrac: 0.4 rmin: 5.4 penal: 3.0\n",
      " It:1 Obj:2027.5045897869754 Vol:0.40009542277892857 ch:0.20000000000000007 \n",
      " It:2 Obj:1114.7016909445497 Vol:0.39999020279385833 ch:0.20000000000000007 \n",
      " It:3 Obj:753.4184494393503 Vol:0.3999502677408073 ch:0.20000000000000007 \n",
      " It:4 Obj:589.4415635399109 Vol:0.3999064413649337 ch:0.20000000000000007 \n",
      " It:5 Obj:523.5760184027803 Vol:0.39979707078545607 ch:0.20000000000000007 \n",
      " It:6 Obj:488.20184734540385 Vol:0.40009815713720864 ch:0.20000000000000007 \n",
      " It:7 Obj:461.50052379589266 Vol:0.39996756594927774 ch:0.18770060047517856 \n",
      " It:8 Obj:436.72776763237124 Vol:0.39997068078062337 ch:0.20000000000000007 \n",
      " It:9 Obj:410.4692046583736 Vol:0.3999688727716305 ch:0.18787745329341016 \n",
      " It:10 Obj:384.72649110474407 Vol:0.39986313163500126 ch:0.20000000000000007 \n",
      " It:11 Obj:357.16627586508287 Vol:0.3999089619253164 ch:0.20000000000000007 \n",
      " It:12 Obj:330.7267430567433 Vol:0.3999587977615742 ch:0.20000000000000007 \n",
      " It:13 Obj:306.3854736897865 Vol:0.4000005457148307 ch:0.20000000000000007 \n",
      " It:14 Obj:288.2315743878585 Vol:0.3999937032654836 ch:0.20000000000000007 \n",
      " It:15 Obj:274.1857794613026 Vol:0.4000924533597078 ch:0.20000000000000007 \n",
      " It:16 Obj:264.94569800587306 Vol:0.39991093897094926 ch:0.20000000000000007 \n",
      " It:17 Obj:258.778788272396 Vol:0.40001652314033975 ch:0.20000000000000007 \n",
      " It:18 Obj:253.94126738777538 Vol:0.4000506838849397 ch:0.20000000000000007 \n",
      " It:19 Obj:250.66709616220618 Vol:0.39995490846201837 ch:0.20000000000000007 \n",
      " It:20 Obj:248.25606527431827 Vol:0.3999689511352107 ch:0.20000000000000007 \n",
      " It:21 Obj:245.94860165486534 Vol:0.3999625987049225 ch:0.20000000000000007 \n",
      " It:22 Obj:243.74888320454812 Vol:0.40001523279698936 ch:0.20000000000000007 \n",
      " It:23 Obj:241.74248423356713 Vol:0.3999991521014942 ch:0.20000000000000007 \n",
      " It:24 Obj:240.15060386653911 Vol:0.39998006686729326 ch:0.19999999999999996 \n",
      " It:25 Obj:238.9851828092882 Vol:0.3999868095951767 ch:0.20000000000000007 \n",
      " It:26 Obj:238.2883622637742 Vol:0.3999890832908555 ch:0.20000000000000007 \n",
      " It:27 Obj:237.70769589450794 Vol:0.39999265369511483 ch:0.20000000000000007 \n",
      " It:28 Obj:237.2033385405354 Vol:0.3999873297303694 ch:0.20000000000000007 \n",
      " It:29 Obj:236.7785782018123 Vol:0.4000004750882039 ch:0.20000000000000007 \n",
      " It:30 Obj:236.38528197169884 Vol:0.40000930032038495 ch:0.20000000000000007 \n",
      " It:31 Obj:236.01340184664818 Vol:0.39999547693055404 ch:0.20000000000000007 \n",
      " It:32 Obj:235.68010033105958 Vol:0.3999863076827155 ch:0.20000000000000007 \n",
      " It:33 Obj:235.34882677219787 Vol:0.399983492944396 ch:0.20000000000000007 \n",
      " It:34 Obj:235.00188861867923 Vol:0.3999783526503072 ch:0.20000000000000007 \n",
      " It:35 Obj:234.58246976540124 Vol:0.40001220457009634 ch:0.20000000000000007 \n",
      " It:36 Obj:234.05200277972634 Vol:0.40000949855543694 ch:0.19999999999999996 \n",
      " It:37 Obj:233.55899380756705 Vol:0.4000110177511946 ch:0.18617336635466353 \n",
      " It:38 Obj:233.27010786399626 Vol:0.4000069938539628 ch:0.17978142653742213 \n",
      " It:39 Obj:233.11518441068577 Vol:0.4000063017627396 ch:0.20000000000000007 \n",
      " It:40 Obj:232.97338235727568 Vol:0.40000306597933594 ch:0.20000000000000007 \n",
      " It:41 Obj:232.84740529927114 Vol:0.40000893315187996 ch:0.19389816395843684 \n",
      " It:42 Obj:232.72590359510704 Vol:0.4000186686660424 ch:0.18505513698340847 \n",
      " It:43 Obj:232.61140255654325 Vol:0.400016677927953 ch:0.19999999999999996 \n",
      " It:44 Obj:232.4992077261653 Vol:0.4000186108562634 ch:0.20000000000000007 \n",
      " It:45 Obj:232.3858313790211 Vol:0.39997875918956705 ch:0.18327746197747163 \n",
      " It:46 Obj:232.30661116189532 Vol:0.40000973547322244 ch:0.19999999999999996 \n",
      " It:47 Obj:232.15853579148654 Vol:0.40001168068250686 ch:0.19999999999999996 \n",
      " It:48 Obj:232.053578645034 Vol:0.4000093199237478 ch:0.1905299525710673 \n",
      " It:49 Obj:231.9449504778675 Vol:0.4000029303868017 ch:0.20000000000000007 \n",
      " It:50 Obj:231.85252598763685 Vol:0.39999374282219546 ch:0.19999999999999996 \n",
      " It:51 Obj:231.7803279999307 Vol:0.4000061150743422 ch:0.20000000000000007 \n",
      " It:52 Obj:231.70429963617062 Vol:0.40000693539397547 ch:0.19999999999999996 \n",
      " It:53 Obj:231.64871048345847 Vol:0.39999783954100687 ch:0.19999999999999996 \n",
      " It:54 Obj:231.60544645904872 Vol:0.4000038082639503 ch:0.19999999999999996 \n",
      " It:55 Obj:231.5490138260903 Vol:0.4000031973739572 ch:0.20000000000000007 \n",
      " It:56 Obj:231.51023671347502 Vol:0.39999194653001385 ch:0.19999999999999996 \n",
      " It:57 Obj:231.4813083608297 Vol:0.39999922260188936 ch:0.19999999999999996 \n",
      " It:58 Obj:231.4378185297698 Vol:0.39998697695130736 ch:0.20000000000000007 \n",
      " It:59 Obj:231.42354630492807 Vol:0.40000608616923794 ch:0.20000000000000007 \n",
      " It:60 Obj:231.3741601994792 Vol:0.4000044769429046 ch:0.20000000000000007 \n",
      " It:61 Obj:231.35808804896516 Vol:0.4000047745231512 ch:0.19999999999999996 \n",
      " It:62 Obj:231.33046713293854 Vol:0.4000023069999686 ch:0.19999999999999996 \n",
      " It:63 Obj:231.31242226625997 Vol:0.40000604490383124 ch:0.20000000000000007 \n",
      " It:64 Obj:231.2859561188247 Vol:0.4000088288999765 ch:0.19999999999999996 \n",
      " It:65 Obj:231.26388971006176 Vol:0.3999902272723369 ch:0.20000000000000007 \n",
      " It:66 Obj:231.26360775967555 Vol:0.4000028436763249 ch:0.2 \n",
      " It:67 Obj:231.21052887334906 Vol:0.39998363387917835 ch:0.20000000000000007 \n",
      " It:68 Obj:231.16126282828367 Vol:0.3999966595140699 ch:0.20000000000000007 \n",
      " It:69 Obj:231.00955474316663 Vol:0.3999948093069101 ch:0.2 \n",
      " It:70 Obj:230.84962914564034 Vol:0.3999994675102865 ch:0.20000000000000007 \n",
      " It:71 Obj:230.72174862728477 Vol:0.4000070854760428 ch:0.10831384065901184 \n",
      " It:72 Obj:230.6652257431345 Vol:0.3999979551430493 ch:0.10467794427747956 \n",
      " It:73 Obj:230.65216672164127 Vol:0.4000137571485584 ch:0.11465852537583232 \n",
      " It:74 Obj:230.62407943059083 Vol:0.39998860392602525 ch:0.10727277810298819 \n",
      " It:75 Obj:230.64000357471792 Vol:0.3999999847837149 ch:0.09043574537315746 \n",
      " It:76 Obj:230.60332563808464 Vol:0.39999633016805797 ch:0.09966436564085313 \n",
      " It:77 Obj:230.6029927416497 Vol:0.40000815018720576 ch:0.10568588951008007 \n",
      " It:78 Obj:230.58424001449677 Vol:0.400012237813244 ch:0.0857765548662438 \n",
      " It:79 Obj:230.57582506098322 Vol:0.3999922812211131 ch:0.09163559738827798 \n",
      " It:80 Obj:230.59135657580924 Vol:0.40000796430569163 ch:0.10038008813144539 \n",
      " It:81 Obj:230.55945926383777 Vol:0.40000784951599655 ch:0.09343351317216542 \n",
      " It:82 Obj:230.5560907696892 Vol:0.4000125145408255 ch:0.1047787660774191 \n",
      " It:83 Obj:230.5416919096785 Vol:0.40000971837483695 ch:0.10241141085253858 \n",
      " It:84 Obj:230.5386959339299 Vol:0.4000013776524882 ch:0.1001918822636847 \n",
      " It:85 Obj:230.5379249281579 Vol:0.40000766033727647 ch:0.08117966609068494 \n",
      " It:86 Obj:230.52403122345746 Vol:0.4000118783484707 ch:0.09106458518806149 \n",
      " It:87 Obj:230.52192392948672 Vol:0.4000005918048181 ch:0.09968899731685321 \n",
      " It:88 Obj:230.53975249216543 Vol:0.4000012273360151 ch:0.10993967990187825 \n",
      " It:89 Obj:230.53879340153085 Vol:0.39999496378883914 ch:0.08373973218385711 \n",
      " It:90 Obj:230.54443930328696 Vol:0.3999959315381369 ch:0.09356921335699042 \n",
      " It:91 Obj:230.54567825614973 Vol:0.4000062213930901 ch:0.1040387746496565 \n",
      " It:92 Obj:230.54346314286468 Vol:0.3999921436372145 ch:0.11365156776338747 \n",
      " It:93 Obj:230.56712462359442 Vol:0.399999515576815 ch:0.10713271479092734 \n",
      " It:94 Obj:230.54644444174556 Vol:0.4000097301170341 ch:0.08436647674690345 \n",
      " It:95 Obj:230.52790300922828 Vol:0.39999166429831345 ch:0.08181782489274836 \n",
      " It:96 Obj:230.54581782342933 Vol:0.3999921044174427 ch:0.08772236436718661 \n",
      " It:97 Obj:230.53555644656538 Vol:0.39999879026960117 ch:0.09300957627295148 \n",
      " It:98 Obj:230.52939863197176 Vol:0.40000229020843686 ch:0.10287740536142964 \n",
      " It:99 Obj:230.52201967556425 Vol:0.40000942491006114 ch:0.11407316014985758 \n",
      " It:100 Obj:230.5143220195186 Vol:0.40001105549662835 ch:0.08851946352667905 \n",
      " It:101 Obj:230.5093273235246 Vol:0.39999182987697646 ch:0.0965405661451545 \n",
      " It:102 Obj:230.5298516523536 Vol:0.3999900863850748 ch:0.10720168704035149 \n",
      " It:103 Obj:230.52559198178662 Vol:0.4000084142015186 ch:0.10033559971908346 \n",
      " It:104 Obj:230.5016900582213 Vol:0.3999978597615209 ch:0.11006873909633441 \n",
      " It:105 Obj:230.52081745179677 Vol:0.4000010895851494 ch:0.08658069717768568 \n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " It:106 Obj:230.51132470848992 Vol:0.39999947831401633 ch:0.09643395346865746 \n",
      " It:107 Obj:230.51171441015492 Vol:0.4000082830708686 ch:0.10680940157333807 \n",
      " It:108 Obj:230.50451233709833 Vol:0.399997570234539 ch:0.11598006529983185 \n",
      " It:109 Obj:230.52453728239152 Vol:0.399990521141379 ch:0.10908467195033222 \n",
      " It:110 Obj:230.5275773026536 Vol:0.39998979904982274 ch:0.10092390101429727 \n",
      " It:111 Obj:230.53013534123662 Vol:0.3999907263706001 ch:0.09067101524408527 \n",
      " It:112 Obj:230.52974587932454 Vol:0.3999989623616449 ch:0.10085857119458874 \n",
      " It:113 Obj:230.5271799269135 Vol:0.3999919348988265 ch:0.11008409476681824 \n",
      " It:114 Obj:230.54855229371913 Vol:0.3999920718452961 ch:0.10900180315672758 \n",
      " It:115 Obj:230.55158447390113 Vol:0.3999896485271591 ch:0.1095730412959961 \n",
      " It:116 Obj:230.55914068311336 Vol:0.40001112222536994 ch:0.07875514932727634 \n",
      " It:117 Obj:230.53553019985182 Vol:0.40000955223062806 ch:0.0885769151877358 \n",
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      " It:119 Obj:230.57259148031483 Vol:0.4000035664826363 ch:0.11024101864302271 \n",
      " It:120 Obj:230.5733632730787 Vol:0.39999038856788016 ch:0.10732711078162382 \n",
      " It:121 Obj:230.60011600076842 Vol:0.3999980124666443 ch:0.08403713944101132 \n",
      " It:122 Obj:230.5835697183139 Vol:0.40000594209746043 ch:0.09357551025154975 \n",
      " It:123 Obj:230.58776259800567 Vol:0.40000382992354094 ch:0.10280483032184629 \n",
      " It:124 Obj:230.60677028269117 Vol:0.39999532684948763 ch:0.11321479785698918 \n",
      " It:125 Obj:230.63272714212167 Vol:0.3999924424734859 ch:0.11350920836970979 \n",
      " It:126 Obj:230.6450324474306 Vol:0.40000784284550367 ch:0.09362909438067024 \n",
      " It:127 Obj:230.63331504634988 Vol:0.4000044307302197 ch:0.09963209641199655 \n",
      " It:128 Obj:230.66071323958326 Vol:0.4000016074862809 ch:0.09886603383294557 \n",
      " It:129 Obj:230.6685160231628 Vol:0.3999950345293098 ch:0.11096744623460353 \n",
      " It:130 Obj:230.68123232474105 Vol:0.3999974344036957 ch:0.12078380364341168 \n",
      " It:131 Obj:230.68621396923368 Vol:0.3999943759590862 ch:0.07720741591453695 \n",
      " It:132 Obj:230.6943644359299 Vol:0.39999627024259016 ch:0.08835928775399415 \n",
      " It:133 Obj:230.698405158678 Vol:0.4000052458324285 ch:0.10038579062527675 \n",
      " It:134 Obj:230.69990964389723 Vol:0.4000012819356083 ch:0.111405915776432 \n",
      " It:135 Obj:230.72469982234676 Vol:0.3999906951851086 ch:0.12225522850157589 \n",
      " It:136 Obj:230.7550242959922 Vol:0.40001057667239903 ch:0.07750808872834275 \n",
      " It:137 Obj:230.7279773227763 Vol:0.3999941896904671 ch:0.0878630227174585 \n",
      " It:138 Obj:230.76312080793247 Vol:0.39999535031719113 ch:0.10001036730349822 \n",
      " It:139 Obj:230.76494240298913 Vol:0.3999993916680073 ch:0.11290544596639485 \n",
      " It:140 Obj:230.7720606080953 Vol:0.39999007905922773 ch:0.1244583292340169 \n",
      " It:141 Obj:230.79901431668856 Vol:0.40000399750018417 ch:0.09087802016701774 \n",
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      " It:199 Obj:231.18329250246524 Vol:0.4000055330384655 ch:0.15206876386094348 \n",
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      " It:211 Obj:231.55363504686667 Vol:0.400001354222054 ch:0.132229488409073 \n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " It:212 Obj:231.57415523712532 Vol:0.4000021861958535 ch:0.1489130175089115 \n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " It:318 Obj:233.12008883289565 Vol:0.3999966755259199 ch:0.07597745966619346 \n",
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      " It:379 Obj:232.9162843783382 Vol:0.40000091695836754 ch:0.15361242329505742 \n",
      " It:380 Obj:232.90543468059462 Vol:0.3999931472734841 ch:0.13917261222599475 \n",
      " It:381 Obj:232.91266430026388 Vol:0.4000039333471483 ch:0.1572971929396315 \n",
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      " It:383 Obj:232.9390826886314 Vol:0.39999830777069983 ch:0.11688580318063241 \n",
      " It:384 Obj:232.9439668329782 Vol:0.39999418294721145 ch:0.1529836957708438 \n",
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      " It:388 Obj:232.92422787698408 Vol:0.4000029160170022 ch:0.13677260953424675 \n",
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      " It:391 Obj:232.93021513847265 Vol:0.40000436532825157 ch:0.19999999999999996 \n",
      " It:392 Obj:232.9280433356386 Vol:0.3999953090967681 ch:0.17922280333686036 \n",
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      " It:410 Obj:231.95407931924154 Vol:0.3999981096944779 ch:0.19999999999999996 \n",
      " It:411 Obj:231.7411857329647 Vol:0.40000138029928756 ch:0.19999999999999996 \n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " It:425 Obj:231.23481488882828 Vol:0.3999989003524051 ch:0.02977305873425079 \n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " It:530 Obj:230.22794617074794 Vol:0.399999831081099 ch:0.13325885630719858 \n",
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      " It:558 Obj:229.87361065603397 Vol:0.399998331345411 ch:0.035717819132630946 \n",
      " It:559 Obj:229.8737329578988 Vol:0.3999970060282363 ch:0.03702926649118299 \n",
      " It:560 Obj:229.8735599181166 Vol:0.3999968668114749 ch:0.04296598207321234 \n",
      " It:561 Obj:229.87258124227094 Vol:0.39999821048318746 ch:0.050570242885853156 \n",
      " It:562 Obj:229.8703318865553 Vol:0.40000126718209855 ch:0.05934162582744157 \n",
      " It:563 Obj:229.86636579974208 Vol:0.400005628181322 ch:0.06913756403743637 \n",
      " It:564 Obj:229.86035931687945 Vol:0.3999943991813287 ch:0.07857343403589817 \n",
      " It:565 Obj:229.864024312104 Vol:0.4000040085943452 ch:0.08996389394818272 \n",
      " It:566 Obj:229.8511485756922 Vol:0.399999585847094 ch:0.09894227258952548 \n",
      " It:567 Obj:229.8495931127626 Vol:0.4000003943370058 ch:0.10869201526402505 \n",
      " It:568 Obj:229.843988233731 Vol:0.4000061085495233 ch:0.11860446785227319 \n",
      " It:569 Obj:229.8340254106913 Vol:0.4000077271284675 ch:0.08682022063993605 \n",
      " It:570 Obj:229.82315797527718 Vol:0.39999472834383193 ch:0.10474648956497101 \n",
      " It:571 Obj:229.81925138779008 Vol:0.4000052348548874 ch:0.12688378374453546 \n",
      " It:572 Obj:229.79271663981257 Vol:0.4000034541323844 ch:0.1481037369109972 \n",
      " It:573 Obj:229.77249353814108 Vol:0.4000049496556882 ch:0.13121041194661442 \n",
      " It:574 Obj:229.7467921544736 Vol:0.3999975300772345 ch:0.06823007256220148 \n",
      " It:575 Obj:229.72454774566978 Vol:0.39999361505701037 ch:0.08046384181180954 \n",
      " It:576 Obj:229.69248015950706 Vol:0.399992629498475 ch:0.08866040387955904 \n",
      " It:577 Obj:229.65665918950813 Vol:0.3999935942064911 ch:0.09042398384384465 \n",
      " It:578 Obj:229.62400148123822 Vol:0.3999957583002001 ch:0.08717754993269655 \n",
      " It:579 Obj:229.5974206975714 Vol:0.399998494294803 ch:0.08193315087921693 \n",
      " It:580 Obj:229.57664859910824 Vol:0.4000005020799712 ch:0.07659902160111365 \n",
      " It:581 Obj:229.56067017205447 Vol:0.4000000266135348 ch:0.07184343040954266 \n",
      " It:582 Obj:229.5487469185519 Vol:0.39999633661234124 ch:0.03525166047985928 \n",
      " It:583 Obj:229.5438310717946 Vol:0.4000043840839485 ch:0.016983311945965474 \n",
      " It:584 Obj:229.53271867164986 Vol:0.39999476633215947 ch:0.016008290698884875 \n",
      " It:585 Obj:229.53568343245263 Vol:0.4000008159068237 ch:0.017023147594145693 \n",
      " It:586 Obj:229.52653729750241 Vol:0.4000047079066649 ch:0.017017433739267673 \n",
      " It:587 Obj:229.5194001659595 Vol:0.40000707972106875 ch:0.016963856665792365 \n",
      " It:588 Obj:229.51370930404164 Vol:0.39999391771580306 ch:0.015688658048906623 \n",
      " It:589 Obj:229.5202622970906 Vol:0.39999695342230684 ch:0.01666689529088139 \n",
      " It:590 Obj:229.51401718614613 Vol:0.3999983033023867 ch:0.01652379739356058 \n",
      " It:591 Obj:229.50925433713633 Vol:0.3999988649553773 ch:0.016350020746235705 \n",
      " It:592 Obj:229.5053148014454 Vol:0.3999988906204298 ch:0.016151113009501117 \n",
      " It:593 Obj:229.50197281317094 Vol:0.39999842412953235 ch:0.015931950699949793 \n",
      " It:594 Obj:229.4992046957442 Vol:0.3999976469115804 ch:0.015692868749745292 \n",
      " It:595 Obj:229.49683386678066 Vol:0.39999671622097555 ch:0.015439607394401422 \n",
      " It:596 Obj:229.4947047640121 Vol:0.3999957079575721 ch:0.015177572915086035 \n",
      " It:597 Obj:229.49274652537957 Vol:0.39999465742676504 ch:0.014909169857732163 \n",
      " It:598 Obj:229.49092389963783 Vol:0.3999935898225365 ch:0.01463643221173061 \n",
      " It:599 Obj:229.48921058829802 Vol:0.4000062641379883 ch:0.015857229893629476 \n",
      " It:600 Obj:229.4769959580458 Vol:0.4000025108754215 ch:0.014152602614852294 \n",
      " It:601 Obj:229.47772257119206 Vol:0.399999488539033 ch:0.013853621086778123 \n",
      " It:602 Obj:229.47787061766996 Vol:0.3999970070912132 ch:0.013561440626825405 \n",
      " It:603 Obj:229.47763114906743 Vol:0.3999946637528097 ch:0.01327542731427589 \n",
      " It:604 Obj:229.4772901811749 Vol:0.400005638584042 ch:0.014617236461677119 \n",
      " It:605 Obj:229.46662048516907 Vol:0.4000012839372773 ch:0.012790856295604724 \n",
      " It:606 Obj:229.46814677166634 Vol:0.39999781813582064 ch:0.01249739792543536 \n",
      " It:607 Obj:229.46896688770886 Vol:0.3999949607895577 ch:0.012215912547724916 \n",
      " It:608 Obj:229.4693180176933 Vol:0.40000568438544976 ch:0.013658988022349439 \n",
      " It:609 Obj:229.4591937119044 Vol:0.4000009706539788 ch:0.011754036981588944 \n",
      " It:610 Obj:229.4612316769331 Vol:0.3999971634575754 ch:0.011473288941591386 \n",
      " It:611 Obj:229.46253388066032 Vol:0.39999397843787105 ch:0.01120683528652 \n",
      " It:612 Obj:229.4633454651689 Vol:0.4000047002419306 ch:0.012752135894717687 \n",
      " It:613 Obj:229.4534973424803 Vol:0.39999927888330067 ch:0.0094450007424558 \n"
     ]
    },
    {
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      ]
     },
     "execution_count": 208,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function topologyOptimization(nelx,nely,volfrac,rmin,penal)\n",
    "    function lk()\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",
    "        KE = E/(1-nu^2)*[  k[0+1] k[1+1] k[2+1] k[3+1] k[4+1] k[5+1] k[6+1] k[7+1];\n",
    "                           k[1+1] k[0+1] k[7+1] k[6+1] k[5+1] k[4+1] k[3+1] k[2+1];\n",
    "                           k[2+1] k[7+1] k[0+1] k[5+1] k[6+1] k[3+1] k[4+1] k[1+1];\n",
    "                           k[3+1] k[6+1] k[5+1] k[0+1] k[7+1] k[2+1] k[1+1] k[4+1];\n",
    "                           k[4+1] k[5+1] k[6+1] k[7+1] k[0+1] k[1+1] k[2+1] k[3+1];\n",
    "                           k[5+1] k[4+1] k[3+1] k[2+1] k[1+1] k[0+1] k[7+1] k[6+1];\n",
    "                           k[6+1] k[3+1] k[4+1] k[1+1] k[2+1] k[7+1] k[0+1] k[5+1];\n",
    "                           k[7+1] k[2+1] k[1+1] k[4+1] k[3+1] k[6+1] k[5+1] k[0+1] ];\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",
    "    # 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",
    "    # 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",
    "    # 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: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(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",
    "            dc = -penal*(Emax-Emin)*xPhys.^(penal-1).*ce\n",
    "            dv = ones(nely,nelx)\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=180\n",
    "nely=60\n",
    "volfrac=0.4\n",
    "rmin=5.4\n",
    "penal=3.0\n",
    "\n",
    "xPhys=topologyOptimization(nelx,nely,volfrac,rmin,penal)\n",
    "Gray.(xPhys)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
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       " Gray{Float64}(1.0)              Gray{Float64}(3.25102e-53) \n",
       " Gray{Float64}(1.0)           …  Gray{Float64}(1.0)         \n",
       " Gray{Float64}(1.0)              Gray{Float64}(1.0)         \n",
       " Gray{Float64}(1.0)              Gray{Float64}(1.0)         \n",
       " Gray{Float64}(1.0)              Gray{Float64}(1.0)         \n",
       " Gray{Float64}(1.0)              Gray{Float64}(1.0)         \n",
       " Gray{Float64}(1.0)           …  Gray{Float64}(1.0)         \n",
       " Gray{Float64}(1.0)              Gray{Float64}(1.0)         \n",
       " Gray{Float64}(1.0)              Gray{Float64}(1.0)         \n",
       " Gray{Float64}(1.0)              Gray{Float64}(1.0)         \n",
       " Gray{Float64}(1.0)              Gray{Float64}(1.0)         "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Gray.(xPhys)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 209,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "CompliantTopologyOptimization (generic function with 1 method)"
      ]
     },
     "execution_count": 209,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function CompliantTopologyOptimization(nelx,nely,volfrac,rmin,penal,maxIter,Load,Support,Spring,DOut)\n",
    "    function lk()\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",
    "        KE = E/(1-nu^2)*[  k[0+1] k[1+1] k[2+1] k[3+1] k[4+1] k[5+1] k[6+1] k[7+1];\n",
    "                           k[1+1] k[0+1] k[7+1] k[6+1] k[5+1] k[4+1] k[3+1] k[2+1];\n",
    "                           k[2+1] k[7+1] k[0+1] k[5+1] k[6+1] k[3+1] k[4+1] k[1+1];\n",
    "                           k[3+1] k[6+1] k[5+1] k[0+1] k[7+1] k[2+1] k[1+1] k[4+1];\n",
    "                           k[4+1] k[5+1] k[6+1] k[7+1] k[0+1] k[1+1] k[2+1] k[3+1];\n",
    "                           k[5+1] k[4+1] k[3+1] k[2+1] k[1+1] k[0+1] k[7+1] k[6+1];\n",
    "                           k[6+1] k[3+1] k[4+1] k[1+1] k[2+1] k[7+1] k[0+1] k[5+1];\n",
    "                           k[7+1] k[2+1] k[1+1] k[4+1] k[3+1] k[6+1] k[5+1] k[0+1] ];\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",
    "    change = 1\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",
    "    \n",
    "    # DEFINE LOADS AND SUPPORTS \n",
    "    F = sparse(2 .*Load[:,1] .-2 .+ Load[:,2],ones(size(Load,1)),Load[:,3],2*(nely+1)*(nelx+1),2)\n",
    "    DofDOut = 2 * DOut[1] - 2 +DOut[2]; #only one\n",
    "    F=Array(F)\n",
    "    F[DofDOut,2]=-1\n",
    "    fixeddofs = 2 .*Support[:,1] .-2 .+ Support[:,2]\n",
    "    NSpring = size(Spring,1);\n",
    "    s = sparse(2 .*Spring[:,1] .-2 .+ Spring[:,2],ones(size(Spring,1)),Spring[:,3],2*(nely+1)*(nelx+1),2)\n",
    "    m=Array(s)[:,1]\n",
    "    S= sparse(diagm(m))\n",
    "    \n",
    "    U = zeros(2*(nely+1)*(nelx+1),2)\n",
    "\n",
    "    alldofs = 1:(2*(nely+1)*(nelx+1))\n",
    "    freedofs = setdiff(alldofs,fixeddofs)\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: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(vec(iH),vec(jH),vec(sH))\n",
    "    Hs = sum(H,dims=2)\n",
    "    \n",
    "    change= 1\n",
    "    loop = 0\n",
    "    changeStable=0\n",
    "    # Start iteration\n",
    "    for penal in 1.0:0.5:4\n",
    "        println(\" Penalty: $penal\")\n",
    "        loop = 0\n",
    "        for i =1:maxIter\n",
    "            if (change < 0.01)\n",
    "                changeStable+=1\n",