{
"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",
" It:118 Obj:230.55544485913543 Vol:0.39999964404393384 ch:0.0985676916848871 \n",
" 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",
" It:142 Obj:230.78420435144045 Vol:0.39999175812322846 ch:0.10157194937365721 \n",
" It:143 Obj:230.81703621414795 Vol:0.3999965930719082 ch:0.1148970660867098 \n",
" It:144 Obj:230.82118071974617 Vol:0.4000060181131577 ch:0.12806886012738328 \n",
" It:145 Obj:230.82961677532086 Vol:0.40000873685852334 ch:0.12546987578770585 \n",
" It:146 Obj:230.84067198805784 Vol:0.4000037625339007 ch:0.0921554359585911 \n",
" It:147 Obj:230.8514729181254 Vol:0.40000071686260763 ch:0.10354313587998498 \n",
" It:148 Obj:230.86143922947474 Vol:0.40000492914456637 ch:0.11580415289937462 \n",
" It:149 Obj:230.86760134371528 Vol:0.39999238455857855 ch:0.11029743382854407 \n",
" It:150 Obj:230.89868036614638 Vol:0.40000691256814846 ch:0.12571705737730876 \n",
" It:151 Obj:230.88554957491016 Vol:0.4000098992662701 ch:0.07444768699597948 \n",
" It:152 Obj:230.8940862492192 Vol:0.399997420810854 ch:0.08463996536804708 \n",
" It:153 Obj:230.92161374805983 Vol:0.399995799509448 ch:0.09709593539143535 \n",
" It:154 Obj:230.92985394614337 Vol:0.40000135392294295 ch:0.11043935695293716 \n",
" It:155 Obj:230.93639505538277 Vol:0.40000984691032315 ch:0.12450751243090019 \n",
" It:156 Obj:230.93983297732888 Vol:0.40000959226467053 ch:0.07409131925859652 \n",
" It:157 Obj:230.9454644366964 Vol:0.3999908716153634 ch:0.08419564422387771 \n",
" It:158 Obj:230.97316522681592 Vol:0.40000647277326057 ch:0.09805444535959451 \n",
" It:159 Obj:230.95113682866628 Vol:0.40000115308337203 ch:0.11036558999262047 \n",
" It:160 Obj:230.97026304685792 Vol:0.3999890817725564 ch:0.12279396375397611 \n",
" It:161 Obj:230.98619117153032 Vol:0.3999973251643885 ch:0.08655716953444337 \n",
" It:162 Obj:230.96154154950108 Vol:0.39999246391721105 ch:0.0942171335942309 \n",
" It:163 Obj:230.95792297837238 Vol:0.39999371585528637 ch:0.10795863296865504 \n",
" It:164 Obj:230.94899280785802 Vol:0.399999517391223 ch:0.1296387738520669 \n",
" It:165 Obj:230.94226760687297 Vol:0.40000835702141674 ch:0.1536076526809087 \n",
" It:166 Obj:230.94106107777304 Vol:0.4000023734287374 ch:0.10162894361197061 \n",
" It:167 Obj:230.95856872845152 Vol:0.39999103443670686 ch:0.09128460065898647 \n",
" It:168 Obj:230.97162773521904 Vol:0.4000083091895935 ch:0.10665424387418121 \n",
" It:169 Obj:230.95184427095012 Vol:0.4000041099178935 ch:0.12043181453961616 \n",
" It:170 Obj:230.97515632071367 Vol:0.4000105062875789 ch:0.1362109275419654 \n",
" It:171 Obj:230.97857674684894 Vol:0.40000650214960254 ch:0.09323376524579208 \n",
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" It:177 Obj:231.00693248932419 Vol:0.4000044858941082 ch:0.11182170380217726 \n",
" It:178 Obj:231.00781832727802 Vol:0.39999428438290335 ch:0.12658171422865128 \n",
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" It:180 Obj:231.01385422787445 Vol:0.4000080478765347 ch:0.09566934570640673 \n",
" It:181 Obj:231.0164134076793 Vol:0.39999580578746535 ch:0.10996301504763795 \n",
" It:182 Obj:231.0394784131991 Vol:0.39999337329214507 ch:0.12641299339540435 \n",
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" It:186 Obj:231.05346008154893 Vol:0.3999922926112615 ch:0.1268417084549589 \n",
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{
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" It:424 Obj:231.2428945725298 Vol:0.39999984558611856 ch:0.05149317482105409 \n"
]
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{
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"text": [
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" It:530 Obj:230.22794617074794 Vol:0.399999831081099 ch:0.13325885630719858 \n",
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" It:574 Obj:229.7467921544736 Vol:0.3999975300772345 ch:0.06823007256220148 \n",
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" 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"
]
},
{
"data": {
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"60×180 Array{Gray{Float64},2} with eltype Gray{Float64}:\n",
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" Gray{Float64}(1.0) Gray{Float64}(0.0) \n",
" Gray{Float64}(1.0) Gray{Float64}(0.0) \n",
" Gray{Float64}(1.0) Gray{Float64}(0.0) \n",
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" Gray{Float64}(1.0) Gray{Float64}(0.0) \n",
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" Gray{Float64}(1.63216e-173) Gray{Float64}(0.0) \n",
" Gray{Float64}(6.20198e-306) Gray{Float64}(0.0) \n",
" ⋮ ⋱ \n",
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" Gray{Float64}(1.0) Gray{Float64}(3.25102e-53) \n",
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" Gray{Float64}(1.0) Gray{Float64}(1.0) \n",
" Gray{Float64}(1.0) Gray{Float64}(1.0) "
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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": [
{
"data": {
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" Gray{Float64}(1.0) Gray{Float64}(0.0) \n",
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" Gray{Float64}(1.63216e-173) Gray{Float64}(0.0) \n",
" Gray{Float64}(6.20198e-306) Gray{Float64}(0.0) \n",
" ⋮ ⋱ \n",
" Gray{Float64}(1.0) Gray{Float64}(1.93162e-115)\n",
" Gray{Float64}(1.0) Gray{Float64}(3.25102e-53) \n",
" Gray{Float64}(1.0) … Gray{Float64}(1.0) \n",
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" 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",
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" Gray{Float64}(1.0) Gray{Float64}(1.0) \n",
" Gray{Float64}(1.0) Gray{Float64}(1.0) "
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},
"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",
" println(\" Change Stable for $changeStable iterations\")\n",
" else\n",
" changeStable=0\n",
" end\n",
" if (changeStable<10)\n",
" # Start iteration\n",
" loop += 1\n",
" # FE-ANALYSIS\n",
" sK = reshape(KE[:]*(Emin.+xPhys[:]'.^penal*(Emax-Emin)),64*nelx*nely,1)\n",
" K = sparse(vec(iK),vec(jK),vec(sK))+S;K = (K+K')/2\n",
" @timed U[freedofs,:] = K[freedofs,freedofs] \\ Array(F[freedofs,:])\n",
" U1=U[:,1]\n",
" U2=U[:,2]\n",
" # Objective function and sensitivity analysis\n",
" #ce = reshape(sum((U1[edofMat]*KE).*U2[edofMat],dims=2),nely,nelx)\n",
"\n",
" ce=reshape(-sum((U1[edofMat]*KE).*U2[edofMat],dims=2),nely,nelx)\n",
"\n",
" #c = sum((Emin.+xPhys[:].^penal*(Emax-Emin)).*ce)\n",
"\n",
" c=U[DofDOut,1]\n",
"\n",
" dc = -penal.*(Emax-Emin).*xPhys.^(penal-1).*ce\n",
" dv = ones(nely,nelx)\n",
" dc[:] = H*(dc[:]./Hs)\n",
" dv[:] = H*(dv[:]./Hs)\n",
"\n",
" # OPTIMALITY CRITERIA UPDATE OF DESIGN VARIABLES AND PHYSICAL DENSITIES\n",
" l1 = 0; l2 = 1e9; move = 0.05; xnew = 0 #move=0.2\n",
" while (l2-l1)/(l2+l1) > 1e-4 && l2>1e-40\n",
" #while (l2-l1)/(l1+l2) > 1e-3\n",
" lmid = 0.5*(l2+l1)\n",
" xnew = max.(0,max.(x.-move,min.(1,min.(x.+move,x.*sqrt.(max.(1e-10,-dc./dv./lmid))))))\n",
" #xnew = max.(0,max.(x.-move,min.(1,min.(x.+move,x.*sqrt.(-dc./dv./lmid)))))\n",
" xPhys[:] = (H*xnew[:])./Hs\n",
" if sum(xPhys[:]) > volfrac*nelx*nely\n",
" l1 = lmid\n",
" else\n",
" l2 = lmid\n",
" end\n",
" end\n",
" change = maximum(abs.(xnew[:].-x[:]))\n",
" x = xnew\n",
"\n",
" # print result\n",
" m=mean(xPhys[:])\n",
" println(\" It:$loop Obj:$c Vol:$m ch:$change \")\n",
"\n",
" xPhys = copy(x)\n",
" end\n",
" end\n",
" end\n",
" # heatmap(xPhys, legend=false, axis=nothing, foreground_color_subplot=colorant\"white\",fc=:grays,clims=(0.0, 1.0))\n",
" # heatmap(xPhys, legend=false,fc=:grays,clims=(0.0, 1.0))\n",
" return xPhys\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 210,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"2×3 Array{Float64,2}:\n",
" 1.0 1.0 1.0\n",
" 7321.0 1.0 1.0"
]
},
"execution_count": 210,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"nelx=120\n",
"nely=60\n",
"\n",
"function getIndex(i,j,nelx,nely)\n",
" return (i-1)*(nely+1)+(j-1)+1\n",
"end\n",
"\n",
"# DEFINE LOADS AND SUPPORTS \n",
"LeftUpperNode=getIndex(1,1,nelx,nely)\n",
"LeftEdgeNodes = 1:nely+1\n",
"RigthBottomNode=getIndex(nelx+1,nely+1,nelx,nely)\n",
"LeftBottomNode=getIndex(1,nely+1,nelx,nely)\n",
"UpperEdgeNodes= 1:nely+1:getIndex(nelx+1,1,nelx,nely)\n",
"LeftUpperNode= getIndex(1,1,nelx,nely)\n",
"RightUpperNode= getIndex(nelx+1,1,nelx,nely)\n",
"\n",
"\n",
"Index=[LeftUpperNode];Direction=[1];Value=[0.5]; #direction 1 if x and 2 if y\n",
"Load=[Index Direction Value]\n",
"\n",
"# Index=union(UpperEdgeNodes,LeftBottomNode,LeftBottomNode);\n",
"Index=vcat(Array(UpperEdgeNodes),LeftBottomNode,LeftBottomNode)\n",
"Direction=ones(Int,length(Index)).+1\n",
"Direction[length(Index)]=1\n",
"Direction[length(Index)-1]=1\n",
"Support=[Index Direction]\n",
"\n",
"DOut=[RightUpperNode,1] #Index,Direction 1 if x and 2 if y\n",
"\n",
"Index=union(LeftUpperNode,RightUpperNode);\n",
"Direction=ones(Int,length(Index))\n",
"Value=[1.0 ,1.0] # k values.. 1.0 for now\n",
"Spring=[Index Direction Value]\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 211,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Minimum compliance problem with OC\n",
"ndes: 120 x 60\n",
"volfrac: 0.3 rmin: 5.4 penal: 3.0\n",
" Penalty: 1.0\n",
" It:1 Obj:0.00724865568899182 Vol:0.28414411113183696 ch:0.04999999999999999 \n",
" It:2 Obj:0.005577169689665992 Vol:0.27226037328947356 ch:0.04999999999999999 \n",
" It:3 Obj:0.004015190620551415 Vol:0.26386838585823374 ch:0.04999999999999999 \n",
" It:4 Obj:0.0025962809792353637 Vol:0.25899471124996154 ch:0.05 \n",
" It:5 Obj:0.0013733154197931488 Vol:0.2576702933804316 ch:0.05 \n",
" It:6 Obj:0.0004416514831678389 Vol:0.2551778713119799 ch:0.050000000000000044 \n",
" It:7 Obj:1.6880032413706386e-9 Vol:0.2653530239539523 ch:0.050000000000000044 \n",
" It:8 Obj:5.160688096686572e-19 Vol:0.2954986712623933 ch:0.050000000000000044 \n",
" It:9 Obj:4.1325124678686526e-19 Vol:0.29999895731286996 ch:0.050000000000000044 \n",
" It:10 Obj:3.210150145410155e-19 Vol:0.30000059096025883 ch:0.050000000000000044 \n",
" It:11 Obj:1.6605007496275894e-19 Vol:0.2999988915327227 ch:0.050000000000000044 \n",
" It:12 Obj:1.0689917989226525e-20 Vol:0.30000000421569767 ch:0.050000000000000044 \n",
" It:13 Obj:-7.873292010239972e-19 Vol:0.2924252176758186 ch:0.050000000000000044 \n",
" It:14 Obj:-1.3742945266680687e-18 Vol:0.2832277378698141 ch:0.050000000000000044 \n",
" It:15 Obj:-5.114660848423582e-13 Vol:0.2668847611189359 ch:0.050000000000000044 \n",
" It:16 Obj:-0.0005357163278417841 Vol:0.26973705180360263 ch:0.050000000000000044 \n",
" It:17 Obj:-0.0005547613800468885 Vol:0.2829107498827742 ch:0.050000000000000044 \n",
" It:18 Obj:-0.0012707730105698358 Vol:0.29096259975144384 ch:0.050000000000000044 \n",
" It:19 Obj:-0.0006983097116753007 Vol:0.29999989659396964 ch:0.050000000000000044 \n",
" It:20 Obj:-0.0009691946636089665 Vol:0.3000002974767414 ch:0.050000000000000044 \n",
" It:21 Obj:-0.0008580332248741345 Vol:0.300000591208515 ch:0.050000000000000044 \n",
" It:22 Obj:-0.0013789850353710946 Vol:0.30000087693714916 ch:0.050000000000000044 \n",
" It:23 Obj:-0.001742201801465127 Vol:0.30000028830818615 ch:0.050000000000000044 \n",
" It:24 Obj:-0.0018685116335939156 Vol:0.299999475182089 ch:0.050000000000000044 \n",
" It:25 Obj:-0.0018581390694917355 Vol:0.3000010021650325 ch:0.050000000000000044 \n",
" It:26 Obj:-0.002033114627213097 Vol:0.3000000911406021 ch:0.050000000000000044 \n",
" It:27 Obj:-0.0020198531668903013 Vol:0.29999835659526425 ch:0.050000000000000044 \n",
" It:28 Obj:-0.0018259546799917737 Vol:0.2999990268498648 ch:0.050000000000000044 \n",
" It:29 Obj:-0.0018227686526821536 Vol:0.29999785473463203 ch:0.050000000000000044 \n",
" It:30 Obj:-0.0020110971037746463 Vol:0.2999974138226926 ch:0.050000000000000044 \n",
" It:31 Obj:-0.0019691004451147715 Vol:0.299997436368705 ch:0.050000000000000044 \n",
" It:32 Obj:-0.002022448374449018 Vol:0.3000022133658273 ch:0.050000000000000044 \n",
" It:33 Obj:-0.0017190942370086712 Vol:0.30000118901777134 ch:0.050000000000000044 \n",
" It:34 Obj:-0.0014235113450949603 Vol:0.30000129398978637 ch:0.050000000000000044 \n",
" It:35 Obj:-0.001953803503860813 Vol:0.2999993033798008 ch:0.050000000000000044 \n",
" It:36 Obj:-0.001470819108930642 Vol:0.2999999579798965 ch:0.050000000000000044 \n",
" It:37 Obj:-0.0019558980274770803 Vol:0.29999879950132796 ch:0.050000000000000044 \n",
" It:38 Obj:-0.0014616434137992847 Vol:0.3000009067945146 ch:0.050000000000000044 \n",
" It:39 Obj:-0.001936235750450506 Vol:0.3000000538121737 ch:0.050000000000000044 \n",
" It:40 Obj:-0.001453631754969432 Vol:0.3000003130119977 ch:0.050000000000000044 \n",
" It:41 Obj:-0.0019061636731031594 Vol:0.30000028194875283 ch:0.050000000000000044 \n",
" It:42 Obj:-0.0014414479075445254 Vol:0.3000003849312099 ch:0.050000000000000044 \n",
" It:43 Obj:-0.0018631415425843481 Vol:0.3000004146823153 ch:0.050000000000000044 \n",
" It:44 Obj:-0.0014085813772937907 Vol:0.2999994682049826 ch:0.050000000000000044 \n",
" It:45 Obj:-0.001825553159368587 Vol:0.29999910465832463 ch:0.050000000000000044 \n",
" It:46 Obj:-0.0013840532764661604 Vol:0.2999998133536182 ch:0.050000000000000044 \n",
" It:47 Obj:-0.0017325891322723592 Vol:0.29999964167786103 ch:0.050000000000000044 \n",
" It:48 Obj:-0.0013435980093728659 Vol:0.2999998724534713 ch:0.050000000000000044 \n",
" It:49 Obj:-0.0017013511767632787 Vol:0.30000005437963495 ch:0.050000000000000044 \n",
" It:50 Obj:-0.001312398025570331 Vol:0.2999997031746756 ch:0.050000000000000044 \n",
" It:51 Obj:-0.001648390484837648 Vol:0.3000000016965559 ch:0.050000000000000044 \n",
" It:52 Obj:-0.0012819067148071874 Vol:0.29999999969357394 ch:0.050000000000000044 \n",
" It:53 Obj:-0.0013475289219641187 Vol:0.30000003904559336 ch:0.050000000000000044 \n",
" It:54 Obj:-0.0012764957680772263 Vol:0.2999999987838839 ch:0.050000000000000044 \n",
" It:55 Obj:-0.001327743022011671 Vol:0.300000000026415 ch:0.050000000000000044 \n",
" It:56 Obj:-0.0013100226911368456 Vol:0.30000004186615065 ch:0.050000000000000044 \n",
" It:57 Obj:-0.00132073523316995 Vol:0.2994321242658948 ch:0.050000000000000044 \n",
" It:58 Obj:-0.0012957800051783153 Vol:0.29984718960614737 ch:0.050000000000000044 \n",
" It:59 Obj:-0.0012833065545167046 Vol:0.2995943798358368 ch:0.050000000000000044 \n",
" It:60 Obj:-0.0012697422936858045 Vol:0.2986744304528967 ch:0.050000000000000044 \n",
" It:61 Obj:-0.0015362108881567002 Vol:0.2975686541436958 ch:0.050000000000000044 \n",
" It:62 Obj:-0.0013287547567995578 Vol:0.2955802510502939 ch:0.050000000000000044 \n",
" It:63 Obj:-0.0015512275374638116 Vol:0.2939449353278186 ch:0.050000000000000044 \n",
" It:64 Obj:-0.0016693977506686394 Vol:0.2930036503694704 ch:0.050000000000000044 \n",
" It:65 Obj:-0.001183236539970163 Vol:0.2952139041132043 ch:0.050000000000000044 \n",
" It:66 Obj:-0.001327573718478943 Vol:0.2941448741296751 ch:0.050000000000000044 \n",
" It:67 Obj:-0.0010992868479182381 Vol:0.29690410631818065 ch:0.050000000000000044 \n",
" It:68 Obj:-0.0014021912946957024 Vol:0.2950892724345704 ch:0.050000000000000044 \n",
" It:69 Obj:-0.0012800047126479406 Vol:0.29308722283220656 ch:0.050000000000000044 \n",
" It:70 Obj:-0.0013951800378358334 Vol:0.2911118016482039 ch:0.050000000000000044 \n",
" It:71 Obj:-0.0012882112157517169 Vol:0.28797676856561893 ch:0.050000000000000044 \n",
" It:72 Obj:-0.0014414725236112308 Vol:0.28546454275068234 ch:0.050000000000000044 \n",
" It:73 Obj:-0.001287495472651417 Vol:0.2837597379500384 ch:0.050000000000000044 \n",
" It:74 Obj:-0.0014412755618518286 Vol:0.28147592827716916 ch:0.050000000000000044 \n",
" It:75 Obj:-0.0014027392231504082 Vol:0.28198567523197526 ch:0.050000000000000044 \n",
" It:76 Obj:-0.0014653003724419056 Vol:0.28101723644628807 ch:0.050000000000000044 \n",
" It:77 Obj:-0.0013896473519235744 Vol:0.28138727933908353 ch:0.050000000000000044 \n",
" It:78 Obj:-0.0014165690649422585 Vol:0.2814287323301939 ch:0.050000000000000044 \n",
" It:79 Obj:-0.0015009063995478481 Vol:0.2822983385390617 ch:0.050000000000000044 \n",
" It:80 Obj:-0.001426020637040477 Vol:0.2829048375532662 ch:0.050000000000000044 \n",
" It:81 Obj:-0.001391898791841554 Vol:0.2830001016692758 ch:0.050000000000000044 \n",
" It:82 Obj:-0.001229499750772157 Vol:0.2847141817830438 ch:0.050000000000000044 \n",
" It:83 Obj:-0.0013729715677859376 Vol:0.2847391000242437 ch:0.050000000000000044 \n",
" It:84 Obj:-0.001317426553689101 Vol:0.28496319255386443 ch:0.050000000000000044 \n",
" It:85 Obj:-0.0012913087552637644 Vol:0.2853928454466152 ch:0.050000000000000044 \n",
" It:86 Obj:-0.0010886910963276311 Vol:0.28611436882685454 ch:0.050000000000000044 \n",
" It:87 Obj:-0.001402681118106818 Vol:0.28682416855774123 ch:0.050000000000000044 \n",
" It:88 Obj:-0.0013844346421734302 Vol:0.28720090973690016 ch:0.050000000000000044 \n",
" It:89 Obj:-0.0014337850405349805 Vol:0.28842898338359374 ch:0.050000000000000044 \n",
" It:90 Obj:-0.0017128137541596571 Vol:0.28986434039110287 ch:0.050000000000000044 \n",
" It:91 Obj:-0.0015803114037223993 Vol:0.2916437172684146 ch:0.050000000000000044 \n",
" It:92 Obj:-0.00173364278801786 Vol:0.2929724176043912 ch:0.050000000000000044 \n",
" It:93 Obj:-0.0016757394331418833 Vol:0.2945222194550542 ch:0.050000000000000044 \n",
" It:94 Obj:-0.0016664362077244718 Vol:0.295199265521328 ch:0.050000000000000044 \n",
" It:95 Obj:-0.0016326933499954336 Vol:0.29716968169066277 ch:0.050000000000000044 \n",
" It:96 Obj:-0.0017658216640493063 Vol:0.29739849808206154 ch:0.050000000000000044 \n",
" It:97 Obj:-0.001611536837838809 Vol:0.29891644427589176 ch:0.050000000000000044 \n",
" It:98 Obj:-0.00182009762792397 Vol:0.297858637581634 ch:0.050000000000000044 \n",
" It:99 Obj:-0.0015259468905119066 Vol:0.2983013430037904 ch:0.050000000000000044 \n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
" It:100 Obj:-0.0012157621945690378 Vol:0.29549192974007954 ch:0.050000000000000044 \n",
" It:101 Obj:-0.0014953712855319394 Vol:0.2984639145567242 ch:0.050000000000000044 \n",
" It:102 Obj:-0.0017768473184934248 Vol:0.2986582769090124 ch:0.050000000000000044 \n",
" It:103 Obj:-0.0015860733126989823 Vol:0.2999999952011394 ch:0.050000000000000044 \n",
" It:104 Obj:-0.0016726566707796946 Vol:0.3000000271303147 ch:0.050000000000000044 \n",
" It:105 Obj:-0.0016882357670502984 Vol:0.30000010679536554 ch:0.050000000000000044 \n",
" It:106 Obj:-0.0016235980989781527 Vol:0.299999851345384 ch:0.050000000000000044 \n",
" It:107 Obj:-0.0016483308524467548 Vol:0.3000000912873617 ch:0.050000000000000044 \n",
" It:108 Obj:-0.0015189647524668573 Vol:0.3000002898444881 ch:0.050000000000000044 \n",
" It:109 Obj:-0.0013348233047333015 Vol:0.2999999565454052 ch:0.050000000000000044 \n",
" It:110 Obj:-0.0012786969944339447 Vol:0.2999998676300767 ch:0.050000000000000044 \n",
" It:111 Obj:-0.0013966972426780423 Vol:0.30000012170886886 ch:0.050000000000000044 \n",
" It:112 Obj:-0.0015433915694432808 Vol:0.29999986846398746 ch:0.050000000000000044 \n",
" It:113 Obj:-0.0015274114621395781 Vol:0.299999800464802 ch:0.050000000000000044 \n",
" It:114 Obj:-0.0013893870105992558 Vol:0.2999996781720371 ch:0.050000000000000044 \n",
" It:115 Obj:-0.0012150542991524306 Vol:0.29999970435490336 ch:0.050000000000000044 \n",
" It:116 Obj:-0.0012375832418498967 Vol:0.3000001266130067 ch:0.050000000000000044 \n",
" It:117 Obj:-0.0012179138894537124 Vol:0.3000000022512137 ch:0.050000000000000044 \n",
" It:118 Obj:-0.0013150167570500034 Vol:0.29929648459858654 ch:0.050000000000000044 \n",
" It:119 Obj:-0.0010936629690339915 Vol:0.298546747385337 ch:0.050000000000000044 \n",
" It:120 Obj:-8.627289154506408e-8 Vol:0.2970464035436409 ch:0.050000000000000044 \n",
" It:121 Obj:-0.0011126250759435534 Vol:0.29932324171365 ch:0.050000000000000044 \n",
" It:122 Obj:-8.236316540934388e-8 Vol:0.29785757162294657 ch:0.050000000000000044 \n",
" It:123 Obj:-0.0010662141796081114 Vol:0.2994580395649838 ch:0.050000000000000044 \n",
" It:124 Obj:-0.001161392720417068 Vol:0.3000000318111312 ch:0.050000000000000044 \n",
" It:125 Obj:-0.0011214330160958972 Vol:0.29968532990603386 ch:0.050000000000000044 \n",
" It:126 Obj:-0.0012257171688615442 Vol:0.2999998743409085 ch:0.050000000000000044 \n",
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" It:24 Obj:-0.002719612702050429 Vol:0.29999977865167493 ch:0.050000000000000044 \n",
" It:25 Obj:-0.0027599001585451584 Vol:0.2999997623162617 ch:0.050000000000000044 \n",
" It:26 Obj:-0.002799877082550653 Vol:0.2999993867946807 ch:0.050000000000000044 \n",
" It:27 Obj:-0.0028407955823897117 Vol:0.3000009020668353 ch:0.050000000000000044 \n",
" It:28 Obj:-0.002869513896961084 Vol:0.29999889207042646 ch:0.050000000000000044 \n",
" It:29 Obj:-0.0028878330192528404 Vol:0.29999929697297245 ch:0.050000000000000044 \n",
" It:30 Obj:-0.0029067861851776364 Vol:0.3000011564625649 ch:0.050000000000000044 \n",
" It:31 Obj:-0.0029233403167833565 Vol:0.29999899394311874 ch:0.050000000000000044 \n",
" It:32 Obj:-0.0029360818168740733 Vol:0.30000037471329183 ch:0.050000000000000044 \n",
" It:33 Obj:-0.0029537061996023407 Vol:0.2999991249190479 ch:0.050000000000000044 \n",
" It:34 Obj:-0.0029580008661003565 Vol:0.29999895025684764 ch:0.050000000000000044 \n",
" It:35 Obj:-0.002961587863354767 Vol:0.2999998086947669 ch:0.050000000000000044 \n",
" It:36 Obj:-0.002968128183361903 Vol:0.30000049401374423 ch:0.050000000000000044 \n",
" It:37 Obj:-0.002972071993680647 Vol:0.3000000302513733 ch:0.050000000000000044 \n",
" It:38 Obj:-0.0029834055391387408 Vol:0.300000091875189 ch:0.050000000000000044 \n",
" It:39 Obj:-0.0029888898998069024 Vol:0.2999989555043544 ch:0.050000000000000044 \n",
" It:40 Obj:-0.003000977310247962 Vol:0.30000083152145984 ch:0.050000000000000044 \n",
" It:41 Obj:-0.0030101459944996767 Vol:0.299999143709483 ch:0.050000000000000044 \n",
" It:42 Obj:-0.0030104819770236987 Vol:0.30000004096445093 ch:0.050000000000000044 \n",
" It:43 Obj:-0.0030115854171694797 Vol:0.3000004167221948 ch:0.050000000000000044 \n",
" It:44 Obj:-0.0030173964853148503 Vol:0.299999757227402 ch:0.050000000000000044 \n",
" It:45 Obj:-0.0030232031613742177 Vol:0.30000020669217853 ch:0.050000000000000044 \n",
" It:46 Obj:-0.0030290245603923228 Vol:0.2999990966951201 ch:0.050000000000000044 \n",
" It:47 Obj:-0.003033450197493283 Vol:0.30000104207936235 ch:0.050000000000000044 \n",
" It:48 Obj:-0.0030342394064318628 Vol:0.2999993521583482 ch:0.050000000000000044 \n",
" It:49 Obj:-0.0030351043934612803 Vol:0.30000058831914833 ch:0.050000000000000044 \n",
" It:50 Obj:-0.0030363223786318873 Vol:0.2999992292400217 ch:0.050000000000000044 \n",
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" It:52 Obj:-0.0030388591732141298 Vol:0.3000008019080327 ch:0.050000000000000044 \n",
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" It:54 Obj:-0.0030414114272671864 Vol:0.3000004836108745 ch:0.050000000000000044 \n",
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" It:58 Obj:-0.0030469697452426927 Vol:0.3000000931647004 ch:0.050000000000000044 \n",
" It:59 Obj:-0.003048432849054328 Vol:0.29999982992252244 ch:0.050000000000000044 \n",
" It:60 Obj:-0.003049891453463604 Vol:0.30000006203519947 ch:0.050000000000000044 \n",
" It:61 Obj:-0.0030512482139773635 Vol:0.3000006001733549 ch:0.050000000000000044 \n",
" It:62 Obj:-0.0030524747400144064 Vol:0.2999995012789525 ch:0.050000000000000044 \n",
" It:63 Obj:-0.0030536997795506267 Vol:0.3000000796306338 ch:0.050000000000000044 \n",
" It:64 Obj:-0.0030550351390995468 Vol:0.29999944249409366 ch:0.050000000000000044 \n",
" It:65 Obj:-0.003056418934260959 Vol:0.30000064958354605 ch:0.050000000000000044 \n",
" It:66 Obj:-0.0030578447081921903 Vol:0.3000003097425185 ch:0.050000000000000044 \n",
" It:67 Obj:-0.0030593645734356945 Vol:0.2999998304581575 ch:0.050000000000000044 \n",
" It:68 Obj:-0.003060935785412832 Vol:0.3000003922894368 ch:0.050000000000000044 \n",
" It:69 Obj:-0.003062589790209095 Vol:0.3000005406760159 ch:0.050000000000000044 \n",
" It:70 Obj:-0.0030643523370892643 Vol:0.30000042730334453 ch:0.050000000000000044 \n",
" It:71 Obj:-0.003066182792112461 Vol:0.30000019767728114 ch:0.050000000000000044 \n",
" It:72 Obj:-0.003068029042065628 Vol:0.3000003038717537 ch:0.050000000000000044 \n",
" It:73 Obj:-0.00306981898648954 Vol:0.29999962351683535 ch:0.050000000000000044 \n",
" It:74 Obj:-0.003070994442281453 Vol:0.3000000523322362 ch:0.050000000000000044 \n",
" It:75 Obj:-0.0030716607106402306 Vol:0.3000001166041756 ch:0.050000000000000044 \n",
" It:76 Obj:-0.0030721371514543733 Vol:0.3000001455091443 ch:0.050000000000000044 \n",
" It:77 Obj:-0.00307248497091673 Vol:0.30000009297830127 ch:0.050000000000000044 \n",
" It:78 Obj:-0.003072811795352044 Vol:0.30000002826239736 ch:0.050000000000000044 \n",
" It:79 Obj:-0.00307313639145496 Vol:0.29999985742645446 ch:0.050000000000000044 \n",
" It:80 Obj:-0.0030735025410681934 Vol:0.2999997760358454 ch:0.050000000000000044 \n",
" It:81 Obj:-0.003073973256838923 Vol:0.30000012070930526 ch:0.050000000000000044 \n",
" It:82 Obj:-0.0030745387191518318 Vol:0.30000007615076396 ch:0.050000000000000044 \n",
" It:83 Obj:-0.0030751620538359385 Vol:0.2999997861560461 ch:0.050000000000000044 \n",
" It:84 Obj:-0.0030757981261247073 Vol:0.3000001646995105 ch:0.050000000000000044 \n",
" It:85 Obj:-0.003076395413063132 Vol:0.299999925422432 ch:0.050000000000000044 \n",
" It:86 Obj:-0.0030768786076796418 Vol:0.29999974208294905 ch:0.050000000000000044 \n",
" It:87 Obj:-0.0030772220354788418 Vol:0.30000007422375347 ch:0.050000000000000044 \n",
" It:88 Obj:-0.0030774376176152594 Vol:0.299999724225195 ch:0.050000000000000044 \n",
" It:89 Obj:-0.003077563898225548 Vol:0.2999997826889268 ch:0.050000000000000044 \n",
" It:90 Obj:-0.0030776302567761334 Vol:0.2999998138816657 ch:0.050000000000000044 \n",
" It:91 Obj:-0.00307765502320817 Vol:0.3000000655837105 ch:0.050000000000000044 \n",
" It:92 Obj:-0.0030776569887133996 Vol:0.29999964860857276 ch:0.050000000000000044 \n",
" It:93 Obj:-0.003077637651504718 Vol:0.2999996751023599 ch:0.050000000000000044 \n",
" It:94 Obj:-0.003077605803858416 Vol:0.3000002412463228 ch:0.050000000000000044 \n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
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" It:120 Obj:-0.003076120656094327 Vol:0.3000001999532593 ch:0.050000000000000044 \n",
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" It:125 Obj:-0.0030763503901859385 Vol:0.29999995517970507 ch:0.050000000000000044 \n",
" It:126 Obj:-0.0030765268201852908 Vol:0.299999896104003 ch:0.050000000000000044 \n",
" It:127 Obj:-0.0030766900772892657 Vol:0.29999999649496994 ch:0.050000000000000044 \n",
" It:128 Obj:-0.0030768284003147087 Vol:0.2999998791685251 ch:0.050000000000000044 \n",
" It:129 Obj:-0.0030769409235641707 Vol:0.300000166614415 ch:0.050000000000000044 \n",
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" It:131 Obj:-0.0030770993666042966 Vol:0.30000006591326267 ch:0.050000000000000044 \n",
" It:132 Obj:-0.0030771530277931385 Vol:0.3000000914874426 ch:0.050000000000000044 \n",
" It:133 Obj:-0.003077194294603084 Vol:0.30000018896272207 ch:0.050000000000000044 \n",
" It:134 Obj:-0.003077245632888801 Vol:0.29999984128888213 ch:0.050000000000000044 \n",
" It:135 Obj:-0.0030772888910095024 Vol:0.2999998583895629 ch:0.050000000000000044 \n",
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" It:139 Obj:-0.0030773726871309312 Vol:0.29999995192261664 ch:0.050000000000000044 \n",
" It:140 Obj:-0.0030773799967530754 Vol:0.2999998245893696 ch:0.050000000000000044 \n",
" It:141 Obj:-0.003077377129829409 Vol:0.29999980262337306 ch:0.050000000000000044 \n",
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" It:147 Obj:-0.003077209394717277 Vol:0.3000000469139103 ch:0.04999999999999999 \n",
" It:148 Obj:-0.0030771838359403446 Vol:0.2999998663142222 ch:0.04999999999999999 \n",
" It:149 Obj:-0.0030771565821416107 Vol:0.30000006213882063 ch:0.04999999999999999 \n",
" It:150 Obj:-0.0030771288380503606 Vol:0.2999999616138735 ch:0.050000000000000044 \n",
" It:151 Obj:-0.003077098614105002 Vol:0.30000007731235434 ch:0.050000000000000044 \n",
" It:152 Obj:-0.0030770683126103253 Vol:0.30000003183517354 ch:0.050000000000000044 \n",
" It:153 Obj:-0.0030770369479557486 Vol:0.30000010241588054 ch:0.050000000000000044 \n",
" It:154 Obj:-0.003077007910741091 Vol:0.30000015050624773 ch:0.050000000000000044 \n",
" It:155 Obj:-0.003076997004594955 Vol:0.2999999789999136 ch:0.050000000000000044 \n",
" It:156 Obj:-0.003076986747648052 Vol:0.29999989640992186 ch:0.050000000000000044 \n",
" It:157 Obj:-0.0030769768513477934 Vol:0.2999999806801696 ch:0.050000000000000044 \n",
" It:158 Obj:-0.003076966970632988 Vol:0.29999990696919127 ch:0.050000000000000044 \n",
" It:159 Obj:-0.003076955861579197 Vol:0.30000015690511556 ch:0.050000000000000044 \n",
" It:160 Obj:-0.0030769448481764118 Vol:0.2999999934608023 ch:0.050000000000000044 \n",
" It:161 Obj:-0.0030769317726759967 Vol:0.3000001854966493 ch:0.017512381766340956 \n",
" It:162 Obj:-0.0030769298425234416 Vol:0.3000000651023012 ch:0.01667234864262196 \n",
" It:163 Obj:-0.0030769333276989036 Vol:0.3000000160858759 ch:0.01651020442812967 \n",
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" It:166 Obj:-0.0030769512151485735 Vol:0.300000098186401 ch:0.016164984493151513 \n",
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" It:168 Obj:-0.0030769938426125692 Vol:0.2999999177998898 ch:0.031446917037062073 \n",
" It:169 Obj:-0.0030770495869667223 Vol:0.30000008793391897 ch:0.05000000000000002 \n",
" It:170 Obj:-0.0030771541033245203 Vol:0.3000000526115831 ch:0.04999999999999999 \n",
" It:171 Obj:-0.00307725926733006 Vol:0.30000017239959736 ch:0.04999999999999999 \n",
" It:172 Obj:-0.0030773587107434754 Vol:0.29999990504145096 ch:0.04999999999999999 \n",
" It:173 Obj:-0.0030774475074989817 Vol:0.3000002022641494 ch:0.04999999999999999 \n",
" It:174 Obj:-0.0030775273431963776 Vol:0.30000006354406233 ch:0.04999999999999999 \n",
" It:175 Obj:-0.0030775952137337454 Vol:0.29999989485068596 ch:0.04999999999999999 \n",
" It:176 Obj:-0.003077652662344552 Vol:0.3000001400390099 ch:0.04999999999999999 \n",
" It:177 Obj:-0.003077706256960872 Vol:0.30000004522450024 ch:0.04999999999999999 \n",
" It:178 Obj:-0.0030777509317615535 Vol:0.29999981360125844 ch:0.050000000000000044 \n",
" It:179 Obj:-0.0030777875184466387 Vol:0.3000000050282173 ch:0.050000000000000044 \n",
" It:180 Obj:-0.003077818435109529 Vol:0.30000017208645824 ch:0.050000000000000044 \n",
" It:181 Obj:-0.0030778428863135637 Vol:0.29999993626290405 ch:0.050000000000000044 \n",
" It:182 Obj:-0.0030778600489879014 Vol:0.2999998671082464 ch:0.050000000000000044 \n",
" It:183 Obj:-0.0030778722019727746 Vol:0.30000001773662327 ch:0.050000000000000044 \n",
" It:184 Obj:-0.003077879991244268 Vol:0.3000001132374389 ch:0.050000000000000044 \n",
" It:185 Obj:-0.0030778868986575244 Vol:0.29999977294342506 ch:0.050000000000000044 \n",
" It:186 Obj:-0.0030778930703015744 Vol:0.30000013353360255 ch:0.050000000000000044 \n",
" It:187 Obj:-0.003077897363026379 Vol:0.29999995805091756 ch:0.022752628019923532 \n",
" It:188 Obj:-0.003077891362580865 Vol:0.29999981237196627 ch:0.025387609344886097 \n",
" It:189 Obj:-0.0030778821342201876 Vol:0.3000002084970069 ch:0.02818241017413442 \n",
" It:190 Obj:-0.00307787428061125 Vol:0.2999999251763357 ch:0.03116500000424055 \n",
" It:191 Obj:-0.003077863985392979 Vol:0.30000020505442737 ch:0.03455284146811255 \n",
" It:192 Obj:-0.0030778567344931836 Vol:0.2999997895453038 ch:0.03808050934256074 \n",
" It:193 Obj:-0.0030778510729702266 Vol:0.2999998941074342 ch:0.04205124344560762 \n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
" It:194 Obj:-0.0030778544122268517 Vol:0.30000018708384113 ch:0.04799752887619346 \n",
" It:195 Obj:-0.003077869306568557 Vol:0.3000002189677961 ch:0.050000000000000044 \n",
" It:196 Obj:-0.0030778809513936235 Vol:0.2999997532742924 ch:0.050000000000000044 \n",
" It:197 Obj:-0.0030778872413611356 Vol:0.29999985964457393 ch:0.050000000000000044 \n",
" It:198 Obj:-0.003077890892172017 Vol:0.2999999620791707 ch:0.050000000000000044 \n",
" It:199 Obj:-0.0030778902990715425 Vol:0.30000009216194123 ch:0.050000000000000044 \n",
" It:200 Obj:-0.00307788591728608 Vol:0.29999978787456577 ch:0.050000000000000044 \n",
" It:201 Obj:-0.003077876789637798 Vol:0.30000015569403965 ch:0.050000000000000044 \n",
" It:202 Obj:-0.0030778669820983695 Vol:0.30000016498885335 ch:0.050000000000000044 \n",
" It:203 Obj:-0.003077853857467055 Vol:0.29999994006602404 ch:0.050000000000000044 \n",
" It:204 Obj:-0.003077838142580014 Vol:0.30000006143885394 ch:0.050000000000000044 \n",
" It:205 Obj:-0.0030778254030929928 Vol:0.2999999239307067 ch:0.050000000000000044 \n",
" It:206 Obj:-0.0030778364255810344 Vol:0.30000018611906093 ch:0.050000000000000044 \n",
" It:207 Obj:-0.0030778495636837816 Vol:0.2999999796233068 ch:0.050000000000000044 \n",
" It:208 Obj:-0.003077859910180883 Vol:0.30000007960104047 ch:0.050000000000000044 \n",
" It:209 Obj:-0.0030778697992775764 Vol:0.30000008747074564 ch:0.050000000000000044 \n",
" It:210 Obj:-0.003077877517001641 Vol:0.3000000628538053 ch:0.050000000000000044 \n",
" It:211 Obj:-0.003077882895294789 Vol:0.29999992492441163 ch:0.050000000000000044 \n",
" It:212 Obj:-0.0030778879610465293 Vol:0.30000001768863466 ch:0.050000000000000044 \n",
" It:213 Obj:-0.0030779018567521333 Vol:0.2999998115275061 ch:0.050000000000000044 \n",
" It:214 Obj:-0.0030779145123471015 Vol:0.29999987903173464 ch:0.050000000000000044 \n",
" It:215 Obj:-0.003077926949022908 Vol:0.299999865872564 ch:0.050000000000000044 \n",
" It:216 Obj:-0.0030779377548510894 Vol:0.3000001599461752 ch:0.009588390665415392 \n",
" Change Stable for 1 iterations\n",
" It:217 Obj:-0.003077950442934854 Vol:0.3000000533310668 ch:0.009372044422398584 \n",
" Change Stable for 2 iterations\n",
" It:218 Obj:-0.0030779582315918017 Vol:0.29999985769588144 ch:0.009235962873130443 \n",
" Change Stable for 3 iterations\n",
" It:219 Obj:-0.0030779636272146166 Vol:0.3000000906981922 ch:0.008994440704987006 \n",
" Change Stable for 4 iterations\n",
" It:220 Obj:-0.0030779695680891433 Vol:0.3000000164276834 ch:0.00929643717487183 \n",
" Change Stable for 5 iterations\n",
" It:221 Obj:-0.0030779741087450666 Vol:0.3000001743902207 ch:0.010661278578249778 \n",
" It:222 Obj:-0.003077979441966654 Vol:0.3000000492812237 ch:0.012208214712954149 \n",
" It:223 Obj:-0.0030779868213570566 Vol:0.3000000846500106 ch:0.013908481089929897 \n",
" It:224 Obj:-0.0030779957946317662 Vol:0.300000017943337 ch:0.01576375877772733 \n",
" It:225 Obj:-0.0030780051541210002 Vol:0.3000000408422298 ch:0.017840300586527733 \n",
" It:226 Obj:-0.003078017077023672 Vol:0.30000004117164325 ch:0.0200447498253902 \n",
" It:227 Obj:-0.0030780293813384057 Vol:0.30000013043775986 ch:0.022437408137293252 \n",
" It:228 Obj:-0.0030780419852927537 Vol:0.3000000149097582 ch:0.024992221404045417 \n",
" It:229 Obj:-0.0030780534085990915 Vol:0.2999998122230998 ch:0.02775658735089981 \n",
" It:230 Obj:-0.0030780636714171613 Vol:0.30000000426958723 ch:0.03079039208625861 \n",
" It:231 Obj:-0.0030780742530314483 Vol:0.2999998941696213 ch:0.033976024554419004 \n",
" It:232 Obj:-0.003078082370664454 Vol:0.3000000007983587 ch:0.03749424895161213 \n",
" It:233 Obj:-0.0030780896337587195 Vol:0.30000003252935975 ch:0.04124393755523681 \n",
" It:234 Obj:-0.0030780948538308883 Vol:0.3000001141904872 ch:0.04531120525875082 \n",
" It:235 Obj:-0.0030780983301993583 Vol:0.2999998975069315 ch:0.049631649618980034 \n",
" It:236 Obj:-0.0030780985601174438 Vol:0.3000000638245957 ch:0.04999999999999999 \n",
" It:237 Obj:-0.003078098043764601 Vol:0.3000001447021031 ch:0.050000000000000044 \n",
" It:238 Obj:-0.0030780952077734455 Vol:0.30000015991595125 ch:0.050000000000000044 \n",
" It:239 Obj:-0.0030780902528825733 Vol:0.3000001266822087 ch:0.050000000000000044 \n",
" It:240 Obj:-0.003078083404959979 Vol:0.30000006174748056 ch:0.050000000000000044 \n",
" It:241 Obj:-0.0030780748676322947 Vol:0.2999999820377712 ch:0.050000000000000044 \n",
" It:242 Obj:-0.003078064814147738 Vol:0.2999999047810539 ch:0.050000000000000044 \n",
" It:243 Obj:-0.003078053390639543 Vol:0.2999998474592189 ch:0.050000000000000044 \n",
" It:244 Obj:-0.0030780407215889177 Vol:0.29999981110100005 ch:0.050000000000000044 \n",
" It:245 Obj:-0.0030780268508864383 Vol:0.3000000976791208 ch:0.050000000000000044 \n",
" It:246 Obj:-0.003078012973082538 Vol:0.2999999273051204 ch:0.028258903158283943 \n",
" It:247 Obj:-0.003078001701988989 Vol:0.299999981194345 ch:0.030632583319112228 \n",
" It:248 Obj:-0.0030779952339119072 Vol:0.3000001730714562 ch:0.032138858853471786 \n",
" It:249 Obj:-0.003077987668981196 Vol:0.3000001513524092 ch:0.033494593805852624 \n",
" It:250 Obj:-0.0030779778127068996 Vol:0.29999999967927793 ch:0.03488732253135385 \n",
" It:251 Obj:-0.003077966021590457 Vol:0.3000001872414662 ch:0.036450044063742304 \n",
" It:252 Obj:-0.0030779541595096307 Vol:0.2999999122293046 ch:0.037752805685402624 \n",
" It:253 Obj:-0.0030779393126757074 Vol:0.3000000560590373 ch:0.039429054601942015 \n",
" It:254 Obj:-0.0030779248810521957 Vol:0.30000019826616353 ch:0.040954856552850694 \n",
" It:255 Obj:-0.0030779094425552288 Vol:0.2999999683348829 ch:0.042380540559239566 \n",
" It:256 Obj:-0.003077891618027906 Vol:0.3000001371971689 ch:0.028662056281705706 \n",
" It:257 Obj:-0.0030778819940605637 Vol:0.30000003560235095 ch:0.012225978128077242 \n",
" It:258 Obj:-0.00307788558275521 Vol:0.3000001380710603 ch:0.012242780247639473 \n",
" It:259 Obj:-0.0030778895425220797 Vol:0.30000009266794414 ch:0.012344448413893483 \n",
" It:260 Obj:-0.003077892160607148 Vol:0.2999999748466251 ch:0.012416065555770683 \n",
" It:261 Obj:-0.0030778935632042653 Vol:0.29999984693748105 ch:0.012461482122069767 \n",
" It:262 Obj:-0.003077893963372191 Vol:0.3000001649409673 ch:0.012383692202811325 \n",
" It:263 Obj:-0.0030778951287170116 Vol:0.3000001353859231 ch:0.012492338817442938 \n",
" It:264 Obj:-0.0030778940577365723 Vol:0.30000017523337796 ch:0.012473584006470806 \n",
" It:265 Obj:-0.0030778924996110587 Vol:0.30000002994000385 ch:0.012343627712449234 \n",
" It:266 Obj:-0.00307789152100064 Vol:0.30000005911184174 ch:0.012299560263343778 \n",
" It:267 Obj:-0.0030778902744186655 Vol:0.29999993443283546 ch:0.012329953715747188 \n",
" It:268 Obj:-0.003077887340007316 Vol:0.3000001266613297 ch:0.012247441044498597 \n",
" It:269 Obj:-0.0030778844756831117 Vol:0.29999992635277883 ch:0.012324740039432514 \n",
" It:270 Obj:-0.0030778787735888324 Vol:0.29999984830079074 ch:0.012286169622579779 \n",
" It:271 Obj:-0.0030778720946189825 Vol:0.29999998837605935 ch:0.012228972337468669 \n",
" It:272 Obj:-0.0030778646898269985 Vol:0.30000002472986415 ch:0.012234600486346947 \n",
" It:273 Obj:-0.0030778552026094587 Vol:0.3000001581494263 ch:0.013860896695421045 \n",
" It:274 Obj:-0.0030778463712683884 Vol:0.2999998389143209 ch:0.01796488878040816 \n",
" It:275 Obj:-0.003077832898123752 Vol:0.30000008398878036 ch:0.023309399528078548 \n",
" It:276 Obj:-0.0030778182590392826 Vol:0.3000000774496354 ch:0.030174036263527354 \n",
" It:277 Obj:-0.0030777982806429786 Vol:0.29999988679385703 ch:0.03900859873031581 \n",
" It:278 Obj:-0.003077772080690549 Vol:0.2999999726455386 ch:0.05000000000000002 \n",
" It:279 Obj:-0.0030777404053489643 Vol:0.29999999021890067 ch:0.04999999999999999 \n",
" It:280 Obj:-0.0030777081539265744 Vol:0.2999999355391113 ch:0.04999999999999999 \n",
" It:281 Obj:-0.003077675589775181 Vol:0.30000015743604874 ch:0.04999999999999999 \n",
" It:282 Obj:-0.0030776443095453555 Vol:0.29999993322062724 ch:0.04999999999999999 \n",
" It:283 Obj:-0.0030776112839487986 Vol:0.3000000055593201 ch:0.04999999999999999 \n",
" It:284 Obj:-0.003077579618854915 Vol:0.299999987230852 ch:0.04999999999999999 \n",
" It:285 Obj:-0.0030775477744937 Vol:0.2999998609158217 ch:0.050000000000000044 \n",
" It:286 Obj:-0.003077515768008624 Vol:0.3000000155518841 ch:0.050000000000000044 \n",
" It:287 Obj:-0.0030774852092294164 Vol:0.30000008515783105 ch:0.050000000000000044 \n",
" It:288 Obj:-0.003077454670231062 Vol:0.3000000346261347 ch:0.050000000000000044 \n",
" It:289 Obj:-0.003077424376873776 Vol:0.2999998951189077 ch:0.050000000000000044 \n",
" It:290 Obj:-0.0030773948263263027 Vol:0.3000001549151736 ch:0.050000000000000044 \n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
" It:291 Obj:-0.003077368424323772 Vol:0.3000000971789634 ch:0.050000000000000044 \n",
" It:292 Obj:-0.0030773435095898974 Vol:0.29999993886861026 ch:0.050000000000000044 \n",
" It:293 Obj:-0.0030773227168042682 Vol:0.2999999673397761 ch:0.050000000000000044 \n",
" It:294 Obj:-0.003077310398515596 Vol:0.300000074348329 ch:0.02922488699392034 \n",
" It:295 Obj:-0.003077322392907143 Vol:0.2999998393467465 ch:0.03576314116626024 \n",
" It:296 Obj:-0.0030773691602752366 Vol:0.2999999997643156 ch:0.05 \n",
" It:297 Obj:-0.003077441846989483 Vol:0.29999996063412787 ch:0.04999999999999999 \n",
" It:298 Obj:-0.003077511978088433 Vol:0.300000133646935 ch:0.04999999999999999 \n",
" It:299 Obj:-0.0030775773246777974 Vol:0.30000010851933934 ch:0.04999999999999999 \n",
" It:300 Obj:-0.003077634798151736 Vol:0.2999999037738149 ch:0.04999999999999999 \n",
" Penalty: 2.0\n",
" It:1 Obj:-0.0030759270444538516 Vol:0.30000011505489144 ch:0.050000000000000044 \n",
" It:2 Obj:-0.003075599500124638 Vol:0.29999998532483313 ch:0.050000000000000044 \n",
" It:3 Obj:-0.0030748313702024664 Vol:0.30000016041105826 ch:0.050000000000000044 \n",
" It:4 Obj:-0.0030734899337824585 Vol:0.2999998054738852 ch:0.050000000000000044 \n",
" It:5 Obj:-0.003071606438431855 Vol:0.2999999109749293 ch:0.050000000000000044 \n",
" It:6 Obj:-0.003069877239125141 Vol:0.3000000197032239 ch:0.050000000000000044 \n",
" It:7 Obj:-0.003068646872783965 Vol:0.3000000076612225 ch:0.050000000000000044 \n",
" It:8 Obj:-0.0030679241104713023 Vol:0.2999998150025726 ch:0.050000000000000044 \n",
" It:9 Obj:-0.0030676595312687086 Vol:0.2999997898539019 ch:0.050000000000000044 \n",
" It:10 Obj:-0.003067631089288137 Vol:0.3000001615854265 ch:0.050000000000000044 \n",
" It:11 Obj:-0.0030676491355074303 Vol:0.299999971365321 ch:0.050000000000000044 \n",
" It:12 Obj:-0.0030676846703579365 Vol:0.299999865302206 ch:0.050000000000000044 \n",
" It:13 Obj:-0.0030677181885883724 Vol:0.3000001161660781 ch:0.037390974835829094 \n",
" It:14 Obj:-0.0030677451370605107 Vol:0.29999997923448884 ch:0.020139529008745494 \n",
" It:15 Obj:-0.003067754377519817 Vol:0.29999990537053767 ch:0.01895645445930172 \n",
" It:16 Obj:-0.003067786866266583 Vol:0.30000002688692823 ch:0.019929841534344295 \n",
" It:17 Obj:-0.0030678211482111604 Vol:0.29999996661541306 ch:0.02015024031538648 \n",
" It:18 Obj:-0.0030678685678615755 Vol:0.30000009866905514 ch:0.0204731240399445 \n",
" It:19 Obj:-0.0030679172801690384 Vol:0.30000013068880066 ch:0.021166449993354375 \n",
" It:20 Obj:-0.003067967417290077 Vol:0.300000122765418 ch:0.02150256448492871 \n",
" It:21 Obj:-0.003068023687820688 Vol:0.30000010597243265 ch:0.021748926759221576 \n",
" It:22 Obj:-0.0030680842565307463 Vol:0.3000000365220106 ch:0.022368958826939372 \n",
" It:23 Obj:-0.0030681525334603165 Vol:0.30000005803057306 ch:0.025636188337604532 \n",
" It:24 Obj:-0.003068227106821033 Vol:0.2999999961703312 ch:0.029196360241879604 \n",
" It:25 Obj:-0.003068309544757985 Vol:0.2999999493379682 ch:0.03302778049078198 \n",
" It:26 Obj:-0.0030683991952832777 Vol:0.29999996854508393 ch:0.037005340335399206 \n",
" It:27 Obj:-0.0030684957825910233 Vol:0.30000006751883385 ch:0.040991725918031685 \n",
" It:28 Obj:-0.0030685978903683023 Vol:0.2999999391130798 ch:0.04478463103391095 \n",
" It:29 Obj:-0.0030687033227443177 Vol:0.3000000362146218 ch:0.048436415494607366 \n",
" It:30 Obj:-0.003068806966490432 Vol:0.3000000224640701 ch:0.050000000000000044 \n",
" It:31 Obj:-0.0030689047271519254 Vol:0.29999994692629733 ch:0.050000000000000044 \n",
" It:32 Obj:-0.003068991921412257 Vol:0.29999991896106126 ch:0.050000000000000044 \n",
" It:33 Obj:-0.003069068084456242 Vol:0.2999999232642403 ch:0.050000000000000044 \n",
" It:34 Obj:-0.0030691257385845796 Vol:0.2999999651102615 ch:0.050000000000000044 \n",
" It:35 Obj:-0.003069191673335137 Vol:0.3000000438858879 ch:0.050000000000000044 \n",
" It:36 Obj:-0.0030692540276140456 Vol:0.2999999456261032 ch:0.050000000000000044 \n",
" It:37 Obj:-0.003069310486159426 Vol:0.2999999532339151 ch:0.050000000000000044 \n",
" It:38 Obj:-0.00306935935666993 Vol:0.30000007554307323 ch:0.050000000000000044 \n",
" It:39 Obj:-0.0030694025350046592 Vol:0.3000000977468864 ch:0.050000000000000044 \n",
" It:40 Obj:-0.00306944109970003 Vol:0.3000001171847543 ch:0.03993519809553869 \n",
" It:41 Obj:-0.0030694618297681187 Vol:0.2999999925439092 ch:0.01514989570915759 \n",
" It:42 Obj:-0.0030694391107908736 Vol:0.30000009651646287 ch:0.015594170360948456 \n",
" It:43 Obj:-0.003069446299657292 Vol:0.29999998600168687 ch:0.016269667463410298 \n",
" It:44 Obj:-0.0030694568906593903 Vol:0.30000005092456644 ch:0.016800621092357915 \n",
" It:45 Obj:-0.003069464939928314 Vol:0.2999999000273627 ch:0.018887026197729542 \n",
" It:46 Obj:-0.003069472608130001 Vol:0.29999993033846106 ch:0.02200393300217754 \n",
" It:47 Obj:-0.0030694766613455935 Vol:0.30000001556145045 ch:0.025615506718337983 \n",
" It:48 Obj:-0.003069479262328056 Vol:0.3000000746866586 ch:0.029797305496290588 \n",
" It:49 Obj:-0.0030694797755706875 Vol:0.30000004887428444 ch:0.03462814858733934 \n",
" It:50 Obj:-0.003069477606199279 Vol:0.2999999031053197 ch:0.040195597425672636 \n",
" It:51 Obj:-0.003069472188326142 Vol:0.30000011083825756 ch:0.04667782174186724 \n",
" It:52 Obj:-0.0030694619201417964 Vol:0.30000001891223066 ch:0.04999999999999999 \n",
" It:53 Obj:-0.0030694489725139546 Vol:0.29999991802459286 ch:0.04999999999999999 \n",
" It:54 Obj:-0.00306943037499544 Vol:0.29999993700880107 ch:0.04999999999999999 \n",
" It:55 Obj:-0.0030694093461304576 Vol:0.29999987825720614 ch:0.050000000000000044 \n",
" It:56 Obj:-0.003069386143875013 Vol:0.3000000494079764 ch:0.050000000000000044 \n",
" It:57 Obj:-0.0030693607546666024 Vol:0.29999994676778974 ch:0.050000000000000044 \n",
" It:58 Obj:-0.0030693354314862468 Vol:0.2999999271641762 ch:0.050000000000000044 \n",
" It:59 Obj:-0.0030693072574540397 Vol:0.30000002728982683 ch:0.050000000000000044 \n",
" It:60 Obj:-0.0030692777877520524 Vol:0.29999998160847113 ch:0.050000000000000044 \n",
" It:61 Obj:-0.0030692471520308872 Vol:0.3000000988754438 ch:0.050000000000000044 \n",
" It:62 Obj:-0.0030692115436780137 Vol:0.29999985715553 ch:0.050000000000000044 \n",
" It:63 Obj:-0.0030691746886760897 Vol:0.30000001221365147 ch:0.050000000000000044 \n",
" It:64 Obj:-0.0030691344358173816 Vol:0.30000000973786206 ch:0.050000000000000044 \n",
" It:65 Obj:-0.0030690942095981948 Vol:0.29999999249449766 ch:0.017444311808238355 \n",
" It:66 Obj:-0.0030690473863644713 Vol:0.2999999766812447 ch:0.017654013801502666 \n",
" It:67 Obj:-0.0030690160184072596 Vol:0.299999947845846 ch:0.018379530918839704 \n",
" It:68 Obj:-0.003068998185587826 Vol:0.299999862985067 ch:0.01906639866300841 \n",
" It:69 Obj:-0.0030689799537476797 Vol:0.3000001316523557 ch:0.01986407568826476 \n",
" It:70 Obj:-0.003068959780153244 Vol:0.299999977164786 ch:0.020445667616180607 \n",
" It:71 Obj:-0.0030689402026128853 Vol:0.30000011383179975 ch:0.021217815010911356 \n",
" It:72 Obj:-0.003068916977910824 Vol:0.30000001204139987 ch:0.021840864445341612 \n",
" It:73 Obj:-0.0030688939373573806 Vol:0.3000000590139595 ch:0.022573534895810154 \n",
" It:74 Obj:-0.003068868389592674 Vol:0.3000000076575289 ch:0.023234782559373612 \n",
" It:75 Obj:-0.003068842429446169 Vol:0.29999992578874585 ch:0.02391309136847808 \n",
" It:76 Obj:-0.00306881496502495 Vol:0.300000009529266 ch:0.0248118367610477 \n",
" It:77 Obj:-0.0030687836849859346 Vol:0.3000001293802255 ch:0.0256404159518282 \n",
" It:78 Obj:-0.003068752922966496 Vol:0.3000000256751063 ch:0.02628052945053605 \n",
" It:79 Obj:-0.0030687232926144337 Vol:0.30000002003812865 ch:0.027041877115595803 \n",
" It:80 Obj:-0.003068691641343203 Vol:0.30000012516410934 ch:0.027820685675844392 \n",
" It:81 Obj:-0.003068659607215711 Vol:0.30000008163272013 ch:0.028499008254588842 \n",
" It:82 Obj:-0.0030686275949143365 Vol:0.29999994153700754 ch:0.029185495679527773 \n",
" It:83 Obj:-0.0030685944580309916 Vol:0.30000001515060504 ch:0.030005457286557347 \n",
" It:84 Obj:-0.003068560184712077 Vol:0.3000000892033243 ch:0.008872092687224442 \n",
" Change Stable for 1 iterations\n",
" It:85 Obj:-0.0030685234366592275 Vol:0.30000001557187317 ch:0.008432917046483968 \n",
" Change Stable for 2 iterations\n",
" It:86 Obj:-0.0030685003429381658 Vol:0.2999999301643366 ch:0.008412296299960986 \n",
" Change Stable for 3 iterations\n",
" It:87 Obj:-0.0030684811151655343 Vol:0.29999991012260957 ch:0.008465826038815516 \n",
" Change Stable for 4 iterations\n",
" It:88 Obj:-0.0030684616367746046 Vol:0.3000000125593366 ch:0.0087429650757197 \n",
" Change Stable for 5 iterations\n",
" It:89 Obj:-0.0030684411566384373 Vol:0.29999992042973156 ch:0.008799496223780845 \n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
" Change Stable for 6 iterations\n",
" It:90 Obj:-0.003068422838174673 Vol:0.29999992836303946 ch:0.008858432284104323 \n",
" Change Stable for 7 iterations\n",
" It:91 Obj:-0.0030684041404703153 Vol:0.3000000719829836 ch:0.008918762060392438 \n",
" Change Stable for 8 iterations\n",
" It:92 Obj:-0.003068385261772839 Vol:0.30000011977251045 ch:0.009168132110249805 \n",
" Change Stable for 9 iterations\n",
" It:93 Obj:-0.0030683664895736562 Vol:0.29999987650856846 ch:0.010221180161329002 \n",
" It:94 Obj:-0.0030683468189756334 Vol:0.2999999546075946 ch:0.010900574017444264 \n",
" It:95 Obj:-0.0030683248686327724 Vol:0.3000000698190844 ch:0.011597019735249292 \n",
" It:96 Obj:-0.0030683037584408653 Vol:0.2999999760595167 ch:0.012290403895444113 \n",
" It:97 Obj:-0.0030682822379097976 Vol:0.30000001555896066 ch:0.012739077337439397 \n",
" It:98 Obj:-0.0030682590835466005 Vol:0.2999999164429975 ch:0.013195355698642053 \n",
" It:99 Obj:-0.003068235953456647 Vol:0.30000002397949743 ch:0.013422893143419046 \n",
" It:100 Obj:-0.003068211624589026 Vol:0.30000005268858115 ch:0.013668260264206533 \n",
" It:101 Obj:-0.0030681877247731018 Vol:0.30000005635890487 ch:0.013812035658081756 \n",
" It:102 Obj:-0.003068163045315936 Vol:0.30000006690198006 ch:0.013865330632640283 \n",
" It:103 Obj:-0.0030681378163369562 Vol:0.3000001096218415 ch:0.013838141294266304 \n",
" It:104 Obj:-0.0030681122129800203 Vol:0.3000000256625905 ch:0.013637148061439452 \n",
" It:105 Obj:-0.003068086027488708 Vol:0.2999999345711595 ch:0.013288566350939446 \n",
" It:106 Obj:-0.0030680605163069083 Vol:0.30000009162298696 ch:0.013013247751147872 \n",
" It:107 Obj:-0.003068037386139413 Vol:0.2999999810482413 ch:0.012895521949950473 \n",
" It:108 Obj:-0.0030680153677974053 Vol:0.29999995382875455 ch:0.012622871545307612 \n",
" It:109 Obj:-0.0030679918232664766 Vol:0.30000001103102614 ch:0.012320211652526392 \n",
" It:110 Obj:-0.0030679683063183877 Vol:0.29999990000438514 ch:0.012086339031124216 \n",
" It:111 Obj:-0.003067945002348548 Vol:0.29999992610106546 ch:0.012347986165856861 \n",
" It:112 Obj:-0.0030679190608848723 Vol:0.30000003495724203 ch:0.012594426271687664 \n",
" It:113 Obj:-0.0030678955509812404 Vol:0.29999993626598187 ch:0.01271330605179799 \n",
" It:114 Obj:-0.0030678737338339346 Vol:0.2999999359491935 ch:0.012871103721076638 \n",
" It:115 Obj:-0.003067850780763331 Vol:0.30000002170058987 ch:0.01301187928802644 \n",
" It:116 Obj:-0.0030678281282564795 Vol:0.2999999497843274 ch:0.0130725850018098 \n",
" It:117 Obj:-0.003067805932966832 Vol:0.30000000434790625 ch:0.013174068120252458 \n",
" It:118 Obj:-0.00306778280016193 Vol:0.2999999226203966 ch:0.013190231399475116 \n",
" It:119 Obj:-0.0030677603047463056 Vol:0.29999998429794 ch:0.013248186602312972 \n",
" It:120 Obj:-0.00306773701044637 Vol:0.29999992329806974 ch:0.01321497414475259 \n",
" It:121 Obj:-0.0030677144889239877 Vol:0.3000000166809119 ch:0.013224088086802754 \n",
" It:122 Obj:-0.0030676912860692807 Vol:0.2999999968769453 ch:0.013135726774380463 \n",
" It:123 Obj:-0.00306766896300645 Vol:0.29999988056278715 ch:0.01301656011173602 \n",
" It:124 Obj:-0.003067646198093168 Vol:0.29999991407666143 ch:0.012939991312883037 \n",
" It:125 Obj:-0.00306762294542186 Vol:0.3000000717236993 ch:0.012832132212923009 \n",
" It:126 Obj:-0.0030676005753691045 Vol:0.30000005140343455 ch:0.012612248527718584 \n",
" It:127 Obj:-0.0030675791681574077 Vol:0.29999985211394375 ch:0.012825449916987142 \n",
" It:128 Obj:-0.003067557390190289 Vol:0.2999999719099768 ch:0.013242377465742805 \n",
" It:129 Obj:-0.003067535027902989 Vol:0.30000005389903245 ch:0.013609781927474085 \n",
" It:130 Obj:-0.003067514880888903 Vol:0.30000011000847293 ch:0.013990582291528886 \n",
" It:131 Obj:-0.003067495575735712 Vol:0.30000014191234325 ch:0.014383181677509238 \n",
" It:132 Obj:-0.00306747717879564 Vol:0.2999998593649596 ch:0.014721572872205213 \n",
" It:133 Obj:-0.0030674598887504567 Vol:0.2999998984906607 ch:0.015206517965575483 \n",
" It:134 Obj:-0.0030674423324119973 Vol:0.2999999205582892 ch:0.01563547912639307 \n",
" It:135 Obj:-0.003067427508550923 Vol:0.2999999564142316 ch:0.016081025004749727 \n",
" It:136 Obj:-0.003067414266514907 Vol:0.30000002703583345 ch:0.016541368260214018 \n",
" It:137 Obj:-0.0030674029501029437 Vol:0.29999986383226945 ch:0.016940535647620436 \n",
" It:138 Obj:-0.0030673940966533496 Vol:0.30000012575788365 ch:0.017509746499970946 \n",
" It:139 Obj:-0.0030673867240020676 Vol:0.2999999099076288 ch:0.017853635188017303 \n",
" It:140 Obj:-0.003067384563714244 Vol:0.2999999406064072 ch:0.01837651127136375 \n",
" It:141 Obj:-0.003067384241201488 Vol:0.299999936012024 ch:0.018825910473543428 \n",
" It:142 Obj:-0.0030673896797306253 Vol:0.3000000579595044 ch:0.019377827245136037 \n",
" It:143 Obj:-0.0030674006175391965 Vol:0.2999999967337275 ch:0.02074301629904929 \n",
" It:144 Obj:-0.0030674198699450956 Vol:0.30000015450371165 ch:0.023731369328808927 \n",
" It:145 Obj:-0.0030674473971741218 Vol:0.29999994377325073 ch:0.027015665054897192 \n",
" It:146 Obj:-0.00306748601612647 Vol:0.30000011826741046 ch:0.03076556815854037 \n",
" It:147 Obj:-0.003067533896413567 Vol:0.3000000632134955 ch:0.03473360258375596 \n",
" It:148 Obj:-0.0030675941653987905 Vol:0.29999989932561005 ch:0.03905302035911612 \n",
" It:149 Obj:-0.00306766363244556 Vol:0.3000000088982237 ch:0.04363871853151935 \n",
" It:150 Obj:-0.003067740730491489 Vol:0.2999999571642724 ch:0.04835061552554387 \n",
" It:151 Obj:-0.0030678240047339526 Vol:0.29999992032197104 ch:0.04999999999999999 \n",
" It:152 Obj:-0.0030679027148518352 Vol:0.30000003533702485 ch:0.04999999999999999 \n",
" It:153 Obj:-0.003067974273278686 Vol:0.2999999619056319 ch:0.050000000000000044 \n",
" It:154 Obj:-0.0030680392663215337 Vol:0.30000011867887955 ch:0.050000000000000044 \n",
" It:155 Obj:-0.003068096232135168 Vol:0.29999991721986996 ch:0.050000000000000044 \n",
" It:156 Obj:-0.003068147194425349 Vol:0.299999939808733 ch:0.050000000000000044 \n",
" It:157 Obj:-0.0030681851719962586 Vol:0.29999995541390684 ch:0.050000000000000044 \n",
" It:158 Obj:-0.0030682302970340015 Vol:0.29999994429472243 ch:0.050000000000000044 \n",
" It:159 Obj:-0.0030682714248489963 Vol:0.3000001032538712 ch:0.050000000000000044 \n",
" It:160 Obj:-0.0030683069365266807 Vol:0.300000014503228 ch:0.050000000000000044 \n",
" It:161 Obj:-0.003068338253848506 Vol:0.299999923573116 ch:0.050000000000000044 \n",
" It:162 Obj:-0.0030683641973471725 Vol:0.30000001327058196 ch:0.02811723270478028 \n",
" It:163 Obj:-0.003068368365508361 Vol:0.2999998739793961 ch:0.03024422509358382 \n",
" It:164 Obj:-0.0030683652563005177 Vol:0.3000000094370826 ch:0.032663785556327485 \n",
" It:165 Obj:-0.0030683786082198634 Vol:0.2999999553169988 ch:0.0392766519727461 \n",
" It:166 Obj:-0.003068395890396711 Vol:0.30000010300596713 ch:0.047050282338781 \n",
" It:167 Obj:-0.003068414093124493 Vol:0.29999993068595143 ch:0.04999999999999999 \n",
" It:168 Obj:-0.00306843015528713 Vol:0.3000000076835838 ch:0.04999999999999999 \n",
" It:169 Obj:-0.003068440882533124 Vol:0.29999997300280157 ch:0.04999999999999999 \n",
" It:170 Obj:-0.003068449685448608 Vol:0.3000000896063348 ch:0.04999999999999999 \n",
" It:171 Obj:-0.003068454729743544 Vol:0.3000000291143548 ch:0.04999999999999999 \n",
" It:172 Obj:-0.0030684567983004334 Vol:0.29999998955017376 ch:0.050000000000000044 \n",
" It:173 Obj:-0.003068455352664632 Vol:0.2999999096014079 ch:0.050000000000000044 \n",
" It:174 Obj:-0.0030684678320409206 Vol:0.2999999306144001 ch:0.050000000000000044 \n",
" It:175 Obj:-0.0030684784119957547 Vol:0.2999998961351515 ch:0.050000000000000044 \n",
" It:176 Obj:-0.0030684872580772115 Vol:0.29999986357065267 ch:0.050000000000000044 \n",
" It:177 Obj:-0.003068493339967548 Vol:0.2999998665870285 ch:0.050000000000000044 \n",
" It:178 Obj:-0.0030684970604855162 Vol:0.29999993124387375 ch:0.050000000000000044 \n",
" It:179 Obj:-0.003068498791015747 Vol:0.30000007779678955 ch:0.050000000000000044 \n",
" It:180 Obj:-0.0030684988573657303 Vol:0.3000000249700368 ch:0.050000000000000044 \n",
" It:181 Obj:-0.0030684977028304933 Vol:0.2999998962937582 ch:0.024370136318857427 \n",
" It:182 Obj:-0.003068485291288097 Vol:0.2999999510279327 ch:0.011564537598714508 \n",
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" It:186 Obj:-0.00306850756151946 Vol:0.29999990044698305 ch:0.012504624129751396 \n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
" It:187 Obj:-0.0030685141638797323 Vol:0.30000008342823375 ch:0.01342863120302873 \n",
" It:188 Obj:-0.0030685196853991576 Vol:0.30000007414464447 ch:0.014325432707232522 \n",
" It:189 Obj:-0.0030685279526506556 Vol:0.2999999659318418 ch:0.015291289090418658 \n",
" It:190 Obj:-0.0030685350946078657 Vol:0.3000000657595946 ch:0.016338885703487793 \n",
" It:191 Obj:-0.003068541063580588 Vol:0.30000011794692377 ch:0.017399584511002042 \n",
" It:192 Obj:-0.003068547651627811 Vol:0.29999990860914105 ch:0.01847935417081864 \n",
" It:193 Obj:-0.003068553974523211 Vol:0.30000001800853093 ch:0.019684971754009906 \n",
" It:194 Obj:-0.0030685583611996295 Vol:0.29999990048487685 ch:0.020838896656848294 \n",
" It:195 Obj:-0.003068564117355116 Vol:0.2999998799942431 ch:0.022089706463214898 \n",
" It:196 Obj:-0.0030685684337863686 Vol:0.2999999568389111 ch:0.02336687001362825 \n",
" It:197 Obj:-0.003068572715492747 Vol:0.2999998818918599 ch:0.02462715309401975 \n",
" It:198 Obj:-0.003068577261386576 Vol:0.2999999568307161 ch:0.02597531886034765 \n",
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" It:201 Obj:-0.003068586474259349 Vol:0.3000000913726845 ch:0.0300184239493424 \n",
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" It:204 Obj:-0.0030685915437422455 Vol:0.29999993162492855 ch:0.03415499691063262 \n",
" It:205 Obj:-0.0030685912920856784 Vol:0.3000000937056965 ch:0.03563506183975451 \n",
" It:206 Obj:-0.003068589841991197 Vol:0.29999995129904766 ch:0.036943909988096824 \n",
" It:207 Obj:-0.0030685889870388046 Vol:0.3000000551025789 ch:0.038472923517226865 \n",
" It:208 Obj:-0.0030685855904689593 Vol:0.3000000871309289 ch:0.03988394200778045 \n",
" It:209 Obj:-0.0030685824895992572 Vol:0.30000004388152857 ch:0.0413275319933456 \n",
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" It:215 Obj:-0.0030685362848763852 Vol:0.30000005872885466 ch:0.005847402227461829 \n",
" Change Stable for 1 iterations\n",
" It:216 Obj:-0.003068528517254768 Vol:0.3000000581492314 ch:0.005623565180185308 \n",
" Change Stable for 2 iterations\n",
" It:217 Obj:-0.0030685312945810317 Vol:0.30000001399153586 ch:0.00546023520601957 \n",
" Change Stable for 3 iterations\n",
" It:218 Obj:-0.0030685353739252864 Vol:0.3000000850356714 ch:0.005306488503616702 \n",
" Change Stable for 4 iterations\n",
" It:219 Obj:-0.003068539268833824 Vol:0.3000000419603074 ch:0.005208684438260558 \n",
" Change Stable for 5 iterations\n",
" It:220 Obj:-0.003068543324276965 Vol:0.29999993994520824 ch:0.005118129114731584 \n",
" Change Stable for 6 iterations\n",
" It:221 Obj:-0.003068546400855745 Vol:0.30000007806152723 ch:0.004986653636631644 \n",
" Change Stable for 7 iterations\n",
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" Change Stable for 8 iterations\n",
" It:223 Obj:-0.0030685513353756614 Vol:0.299999891968266 ch:0.004876142958318563 \n",
" Change Stable for 9 iterations\n",
" It:224 Obj:-0.0030685524736437804 Vol:0.2999999539502484 ch:0.004803801696469989 \n",
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" Penalty: 2.5\n",
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" Change Stable for 184 iterations\n",
" Change Stable for 185 iterations\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
" Change Stable for 186 iterations\n",
" Change Stable for 187 iterations\n",
" Change Stable for 188 iterations\n",
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},
{
"name": "stdout",
"output_type": "stream",
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},
{
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"60×120 Array{Gray{Float64},2} with eltype Gray{Float64}:\n",
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" Gray{Float64}(1.0) Gray{Float64}(1.0) Gray{Float64}(1.0)\n",
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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",
" ⋮ ⋱ \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)\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": {
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"</svg>\n"
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"text/plain": [
"Gray{Float64}(1.0)"
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},
"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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]
},
"execution_count": 201,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# m= Matlab.meshgrid(1:nelx,1:nely,1:nelz)# Coordinates\n",
"# scatter(m[1],m[2],m[3])\n",
"ix=[]\n",
"iy=[]\n",
"iz=[]\n",
"for j in 1:nely\n",
" for i in 1:nelx\n",
" for k in 1:nelz\n",
" if(xPhys[j,i,k]>0.0)\n",
" append!(ix,i)\n",
" append!(iy,j)\n",
" append!(iz,k)\n",
" end\n",
" end\n",
" end\n",
"end\n",
"# r = 4.0\n",
"# lim = FRect3D((-4,-4,-4*r),(8,8,8*r))\n",
"scatter(ix,iz,iy,color=\"black\",label=\"\",markersize =4, aspect_ratio=:equal,markerstrokealpha = 0.2,markeralpha = 0.6,markershape = :square,camera = (30, 60))#,markershape = :square"
]
},
{
"cell_type": "code",
"execution_count": 265,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Minimum compliance problem with OC\n",
"ndes: 40 x 20\n",
"volfrac: 0.3 rmin: 1.5 penal: 3.0\n",
" It:1 Obj:0.09026852193011448 Vol:0.1999999999999997 ch:0.1 \n",
" It:2 Obj:0.027983195754231225 Vol:0.09999999999999984 ch:0.1 \n",
" It:3 Obj:0.003557660740646075 Vol:0.06000187456145997 ch:0.1 \n",
" It:4 Obj:8.460015090099223e-12 Vol:0.060001058279334794 ch:0.10000000000000003 \n",
" It:5 Obj:8.758662158398278e-14 Vol:0.05999965957320142 ch:0.10000000000000003 \n",
" It:6 Obj:-6.60152160752389e-15 Vol:0.05999932613042742 ch:0.10000000000000003 \n",
" It:7 Obj:2.1384782467078744e-13 Vol:0.06000049391942632 ch:0.10000000000000003 \n",
" It:8 Obj:1.8093546831861042e-14 Vol:0.06000007305778338 ch:0.10000000000000003 \n",
" It:9 Obj:-1.4294401820209172e-14 Vol:0.06000009916457487 ch:0.10000000000000003 \n",
" It:10 Obj:-1.6627209652942483e-13 Vol:0.05999998531001037 ch:0.10000000000000003 \n",
" It:11 Obj:-5.242071702169678e-12 Vol:0.05999999921803433 ch:0.10000000000000003 \n",
" It:12 Obj:4.569833426118347e-9 Vol:0.04973656419833696 ch:0.10000000000000003 \n",
" It:13 Obj:-6.286088375958999e-12 Vol:0.05138408890412637 ch:0.10000000000000002 \n",
" It:14 Obj:5.312124713597383e-9 Vol:0.03801196242189398 ch:0.10000000000000002 \n",
" It:15 Obj:-6.431989396881844e-12 Vol:0.044962795555469226 ch:0.10000000000000003 \n",
" It:16 Obj:1.2495718835863832e-6 Vol:0.02570312406734146 ch:0.1 \n",
" It:17 Obj:7.614319294406219e-11 Vol:0.053116010631054894 ch:0.10000000000000003 \n",
" It:18 Obj:-7.168201027516775e-13 Vol:0.051411546444320715 ch:0.10000000000000003 \n",
" It:19 Obj:0.0006335762548853362 Vol:0.06000008046314534 ch:0.10000000000000003 \n",
" It:20 Obj:-5.439129067379216e-14 Vol:0.057419894124181324 ch:0.10000000000000003 \n",
" It:21 Obj:0.0017548941000755719 Vol:0.05999998599763824 ch:0.10000000000000003 \n",
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{
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" It:459 Obj:-0.3427967195165015 Vol:0.059999918553365984 ch:0.013122217899545319 \n",
" It:460 Obj:-0.3428136774545058 Vol:0.06000013176240786 ch:0.012754105779273828 \n",
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" It:476 Obj:-0.3448689229244438 Vol:0.05999987528602334 ch:0.012630341361194869 \n",
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" It:479 Obj:-0.3450993671388836 Vol:0.05999987545277923 ch:0.00969290088768461 \n"
]
}
],
"source": [
"function compliantOptimization3d(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",
" # USER-DEFINED LOAD DOFs\n",
" il = [0 nelx]; jl = [nely nely]; kl = [0 0];\n",
" loadnid = kl .*(nelx+1) .*(nely+1) .+il .*(nely .+1) .+(nely+1 .-jl);\n",
" loaddof = 3 .*loadnid[:] .- 2;\n",
" din = loaddof[1]; dout = loaddof[2];\n",
" F = sparse(loaddof,[1;2],[1;-1],ndof,2);\n",
" \n",
" # USER-DEFINED SUPPORT FIXED DOFs\n",
" # Top face\n",
" m = Matlab.meshgrid(0:nelx,0:nelz)\n",
" iif=m[1]\n",
" kf=m[2]\n",
" fixednid = kf .*(nelx+1) .*(nely+1) .+iif .*(nely+1) .+1;\n",
" fixeddof_t = 3 .*fixednid[:] .-1;\n",
" # Side face\n",
" m = Matlab.meshgrid(0:nelx,0:nely)\n",
" iif=m[1]\n",
" jf=m[2]\n",
" fixednid = iif .*(nely+1) .+(nely+1 .-jf);\n",
" fixeddof_s = 3*fixednid[:];\n",
" # Two pins\n",
" iif = [0;0]; jf = [0;1]; kf = [nelz;nelz];\n",
" fixednid = kf .*(nelx+1) .*(nely .+1) .+iif .*(nely .+1) .+(nely+1 .-jf)\n",
" fixeddof_p = [3 .*fixednid[:]; 3 .*fixednid[:].-1; 3 .*fixednid[:].-2] # DOFs\n",
" # Fixed DOFs\n",
" fixeddof = union(fixeddof_t,fixeddof_s);\n",
" fixeddof = union(fixeddof, fixeddof_p);\n",
" fixeddof = sort(fixeddof);\n",
" \n",
" # Displacement vector\n",
" U = zeros(ndof,2);\n",
" freedofs = setdiff(1:ndof,fixeddof)\n",
" \n",
" \n",
" \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",
"\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)) \n",
" K[din,din] = K[din,din] + 0.1\n",
" K[dout,dout] = K[dout,dout] + 0.1\n",
" K = (K+K')/2\n",
" \n",
" \n",
"# @timed U[freedofs] = K[freedofs,freedofs] \\ Array(F[freedofs])\n",
" @timed U[freedofs,:] = K[freedofs,freedofs] \\ Array(F[freedofs,:])\n",
" U1 = U[:,1]\n",
" U2 = U[:,2]\n",
" \n",
" # Objective function and sensitivity analysis\n",
" \n",
" #ce = reshape(sum((U[edofMat]*KE).*U[edofMat],dims=2),nely,nelx,nelz)\n",
" ce = reshape(sum((U1[edofMat]*KE).*U2[edofMat],dims=2),nely,nelx,nelz);\n",
" \n",
" #c = sum(sum(sum((Emin.+xPhys.^penal*(Emax-Emin)).*ce)))\n",
" c = U[dout,1]\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",
" l1 = 0; l2 = 1e9; move = 0.1;xnew = 0\n",
" #while (l2-l1)/(l1+l2) > 1e-3\n",
" while (l2-l1)/(l1+l2) > 1e-4 && l2 > 1e-40\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",
" xnew = max.(0,max.(x.-move,min.(1,min.(x.+move,x.*(max.(1e-10,-dc./dv./lmid)).^0.3))));\n",
"\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=40\n",
"nely=20\n",
"nelz=5\n",
"volfrac=0.3\n",
"rmin=1.5\n",
"penal=3.0\n",
"\n",
"xPhysC=compliantOptimization3d(nelx,nely,nelz,volfrac,rmin,penal);\n"
]
},
{
"cell_type": "code",
"execution_count": 266,
"metadata": {},
"outputs": [
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},
"execution_count": 266,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# m= Matlab.meshgrid(1:nelx,1:nely,1:nelz)# Coordinates\n",
"# scatter(m[1],m[2],m[3])\n",
"ix=[]\n",
"iy=[]\n",
"iz=[]\n",
"for j in 1:nely\n",
" for i in 1:nelx\n",
" for k in 1:nelz\n",
" if(xPhysC[j,i,k]>0.0)\n",
" append!(ix,i)\n",
" append!(iy,j)\n",
" append!(iz,k)\n",
" end\n",
" end\n",
" end\n",
"end\n",
"# r = 4.0\n",
"# lim = FRect3D((-4,-4,-4*r),(8,8,8*r))\n",
"scatter(ix,iz,iy,color=\"black\",label=\"\",markersize =4, aspect_ratio=:equal,markerstrokealpha = 0.2,markeralpha = 0.6,markershape = :square,camera = (30, 60))#,markershape = :square"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
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