A computational study of symmetry and well-posedness of structural topology optimization
We are concerned with the computational topological optimization of elastic structures, in particular minimization of compliance subject to a constraint on the mass. Through computational experiments, it is discovered that even very simple optimization problems can exhibit complex behavior such as c...
Saved in:
| Published in | Structural and multidisciplinary optimization Vol. 59; no. 3; pp. 759 - 766 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.03.2019
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1615-147X 1615-1488 1615-1488 |
| DOI | 10.1007/s00158-018-2098-9 |
Cover
| Abstract | We are concerned with the computational topological optimization of elastic structures, in particular minimization of compliance subject to a constraint on the mass. Through computational experiments, it is discovered that even very simple optimization problems can exhibit complex behavior such as critical points and bifurcation. In the vicinity of critical points, structural topology optimization problems are not well-posed since infinitesimally small perturbations lead to distinct topologies. |
|---|---|
| AbstractList | We are concerned with the computational topological optimization of elastic structures, in particular minimization of compliance subject to a constraint on the mass. Through computational experiments, it is discovered that even very simple optimization problems can exhibit complex behavior such as critical points and bifurcation. In the vicinity of critical points, structural topology optimization problems are not well-posed since infinitesimally small perturbations lead to distinct topologies. |
| Author | Voronin, Alexey White, Daniel A. |
| Author_xml | – sequence: 1 givenname: Daniel A. orcidid: 0000-0001-8461-2829 surname: White fullname: White, Daniel A. email: white37@llnl.gov organization: Lawrence Livermore National Laboratory – sequence: 2 givenname: Alexey surname: Voronin fullname: Voronin, Alexey organization: Lawrence Livermore National Laboratory |
| BookMark | eNqNkF1LwzAUhoNMcJv-AO8KXldP0qZNLsfwCwbeKOwupGkyOtqmJimj_nqrHQqC4lUCOc-b8z4LNGttqxG6xHCNAfIbD4ApiwGzmABnMT9Bc5xhGuOUsdnXPd-eoYX3ewBgkPI52q4iZZuuDzJUtpV15ENfDpE1kR-aRgc3RLIto4Ou67izXpet9v7zObhehd6NSLCdre1upLpQNdXbZ9Q5OjWy9vrieC7Ry93t8_oh3jzdP65Xm1gllIc4yY3ExihqCFNFRoHnmKjEkCKXXLKElqTMirGipimAgoRBIVMlKRQZZKlMlohMuX3byeEg61p0rmqkGwQG8eFGTG7E6EZ8uBF8hK4mqHP2tdc-iL3t3VjfC8KSHHMChI5TeJpSznrvtPlXcv6DUdXkNjhZ1X-SxyJ-_KXdafe90-_QO4OFmAg |
| CitedBy_id | crossref_primary_10_1016_j_engstruct_2023_116978 crossref_primary_10_1007_s00158_019_02457_7 crossref_primary_10_3788_CJL221485 crossref_primary_10_1016_j_finel_2020_103399 crossref_primary_10_1007_s00158_019_02418_0 |
| Cites_doi | 10.1016/S0045-7949(98)00158-8 10.1002/nme.3072 10.1007/s001580050176 10.1007/s00158-012-0802-8 10.1007/s00158-009-0476-z 10.1007/BF01197436 10.1007/BF01742465 10.1007/s00158-012-0871-8 10.1007/s00158-011-0686-z 10.1007/s10107-004-0559-y 10.1007/s00158-010-0564-0 |
| ContentType | Journal Article |
| Copyright | This is a U.S. Government work and not under copyright protection in the US; foreign copyright protection may apply 2018 This is a U.S. Government work and not under copyright protection in the US; foreign copyright protection may apply 2018. |
| Copyright_xml | – notice: This is a U.S. Government work and not under copyright protection in the US; foreign copyright protection may apply 2018 – notice: This is a U.S. Government work and not under copyright protection in the US; foreign copyright protection may apply 2018. |
| DBID | AAYXX CITATION 8FE 8FG ABJCF AFKRA BENPR BGLVJ CCPQU DWQXO HCIFZ L6V M7S PHGZM PHGZT PKEHL PQEST PQGLB PQQKQ PQUKI PTHSS ADTOC UNPAY |
| DOI | 10.1007/s00158-018-2098-9 |
| DatabaseName | CrossRef ProQuest SciTech Collection ProQuest Technology Collection Materials Science & Engineering Collection ProQuest Central ProQuest Central ProQuest Technology Collection ProQuest One Community College ProQuest Central SciTech Premium Collection ProQuest Engineering Collection Engineering Database ProQuest Central Premium ProQuest One Academic (New) ProQuest One Academic Middle East (New) ProQuest One Academic Eastern Edition (DO NOT USE) ProQuest One Applied & Life Sciences ProQuest One Academic ProQuest One Academic UKI Edition Engineering Collection Unpaywall for CDI: Periodical Content Unpaywall |
| DatabaseTitle | CrossRef Engineering Database Technology Collection ProQuest One Academic Middle East (New) ProQuest One Academic Eastern Edition SciTech Premium Collection ProQuest One Community College ProQuest Technology Collection ProQuest SciTech Collection ProQuest Central ProQuest One Applied & Life Sciences ProQuest Engineering Collection ProQuest One Academic UKI Edition ProQuest Central Korea Materials Science & Engineering Collection ProQuest One Academic ProQuest Central (New) Engineering Collection ProQuest One Academic (New) |
| DatabaseTitleList | Engineering Database |
| Database_xml | – sequence: 1 dbid: UNPAY name: Unpaywall url: https://proxy.k.utb.cz/login?url=https://unpaywall.org/ sourceTypes: Open Access Repository – sequence: 2 dbid: 8FG name: ProQuest Technology Collection url: https://search.proquest.com/technologycollection1 sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering |
| EISSN | 1615-1488 |
| EndPage | 766 |
| ExternalDocumentID | oai:osti.gov:1557061 10_1007_s00158_018_2098_9 |
| GroupedDBID | -5B -5G -BR -EM -~C .86 .VR 06D 0R~ 0VY 123 199 1N0 203 29Q 29~ 2J2 2JN 2JY 2KG 2KM 2LR 2~H 30V 4.4 406 408 409 40D 40E 5VS 67Z 6NX 78A 8FE 8FG 8TC 8UJ 95- 95. 95~ 96X AAAVM AABHQ AACDK AAHNG AAIAL AAJBT AAJKR AANZL AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYZH ABAKF ABBBX ABBXA ABDZT ABECU ABFTD ABFTV ABHLI ABHQN ABJCF ABJNI ABJOX ABKCH ABKTR ABMNI ABMQK ABNWP ABQBU ABSXP ABTEG ABTHY ABTKH ABTMW ABWNU ABXPI ACAOD ACDTI ACGFS ACHSB ACHXU ACIWK ACKNC ACMDZ ACMLO ACOKC ACOMO ACPIV ACSNA ACZOJ ADHIR ADINQ ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADZKW AEFQL AEGAL AEGNC AEJHL AEJRE AEMSY AENEX AEOHA AEPYU AESKC AETLH AEVLU AEXYK AFBBN AFKRA AFLOW AFQWF AFWTZ AFZKB AGAYW AGDGC AGJBK AGMZJ AGQEE AGQMX AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHSBF AHYZX AIAKS AIGIU AIIXL AILAN AITGF AJRNO AJZVZ ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AOCGG ARMRJ ASPBG AVWKF AXYYD AYJHY AZFZN B-. BA0 BDATZ BENPR BGLVJ BGNMA BSONS CCPQU CS3 CSCUP DDRTE DL5 DNIVK DPUIP EBLON EBS EIOEI EJD ESBYG FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNWQR GQ6 GQ7 GQ8 GXS HCIFZ HF~ HG5 HG6 HMJXF HQYDN HRMNR HVGLF HZ~ I09 IHE IJ- IKXTQ IWAJR IXC IXD IXE IZIGR IZQ I~X I~Z J-C J0Z JBSCW JCJTX JZLTJ KDC KOV L6V LAS LLZTM M4Y M7S MA- N9A NB0 NPVJJ NQJWS NU0 O93 O9G O9I O9J OAM P19 P9P PF0 PT4 PT5 PTHSS QOK QOS R89 R9I RHV RNS ROL RPX RSV S16 S27 S3B SAP SDH SDM SEG SHX SISQX SJYHP SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 TSG TSK TSV TUC U2A UG4 UOJIU UTJUX UZXMN VC2 VFIZW W23 W48 WK8 YLTOR Z45 Z5O Z7R Z7S Z7V Z7X Z7Y Z7Z Z81 Z83 Z85 Z86 Z88 Z8M Z8N Z8P Z8R Z8S Z8T Z8U Z8W Z8Z Z92 ZMTXR _50 ~02 -Y2 2.D 2P1 2VQ 5QI AAPKM AARHV AAYTO AAYXX ABBRH ABDBE ABFSG ABQSL ABRTQ ABULA ACBXY ACSTC ADHKG ADPHR AEBTG AEFIE AEKMD AEZWR AFDZB AFEXP AFGCZ AFHIU AFOHR AGGDS AGQPQ AHPBZ AHWEU AIXLP AJBLW ARCEE ATHPR AYFIA CAG CITATION COF H13 N2Q NDZJH O9- PHGZM PHGZT PQGLB PUEGO RNI RZK S1Z S26 S28 SCLPG T16 DWQXO PKEHL PQEST PQQKQ PQUKI ADTOC UNPAY |
| ID | FETCH-LOGICAL-c359t-37fa1ffc5f28cb6509712c3f2b7a9a835d2d6b100e5400c0380ba4ca50b6064a3 |
| IEDL.DBID | BENPR |
| ISSN | 1615-147X 1615-1488 |
| IngestDate | Sun Oct 26 04:05:39 EDT 2025 Fri Jul 25 11:02:58 EDT 2025 Thu Apr 24 23:08:40 EDT 2025 Wed Oct 01 02:17:21 EDT 2025 Fri Feb 21 02:35:14 EST 2025 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 3 |
| Keywords | Bifurcation Well-posed Structures Topology Optimization |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c359t-37fa1ffc5f28cb6509712c3f2b7a9a835d2d6b100e5400c0380ba4ca50b6064a3 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ORCID | 0000-0001-8461-2829 |
| OpenAccessLink | https://proxy.k.utb.cz/login?url=https://www.osti.gov/biblio/1557061 |
| PQID | 2837192025 |
| PQPubID | 2043658 |
| PageCount | 8 |
| ParticipantIDs | unpaywall_primary_10_1007_s00158_018_2098_9 proquest_journals_2837192025 crossref_primary_10_1007_s00158_018_2098_9 crossref_citationtrail_10_1007_s00158_018_2098_9 springer_journals_10_1007_s00158_018_2098_9 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 2019-03-01 |
| PublicationDateYYYYMMDD | 2019-03-01 |
| PublicationDate_xml | – month: 03 year: 2019 text: 2019-03-01 day: 01 |
| PublicationDecade | 2010 |
| PublicationPlace | Berlin/Heidelberg |
| PublicationPlace_xml | – name: Berlin/Heidelberg – name: Heidelberg |
| PublicationTitle | Structural and multidisciplinary optimization |
| PublicationTitleAbbrev | Struct Multidisc Optim |
| PublicationYear | 2019 |
| Publisher | Springer Berlin Heidelberg Springer Nature B.V |
| Publisher_xml | – name: Springer Berlin Heidelberg – name: Springer Nature B.V |
| References | Sigmund (CR11) 2001; 21 Bendsoe, Sigmund (CR2) 2003 Wächter, Biegler (CR13) 2006; 106 Rozvany (CR9) 1998; 15 Blanchard, Devaney, Hall (CR3) 2006 Rozvany (CR10) 2011; 43 Guo, Ni, Cheng, Du (CR5) 2012; 46 Lazarov, Sigmund (CR7) 2011; 86 Richardson, Adriaenssens, Bouillard, Coelho (CR8) 2013; 47 Stolpe (CR12) 2010; 41 Kosakam, Swan (CR6) 1999; 70 Baier (CR1) 1994; 7 Cheng, Lui (CR4) 2011; 44 JN Richardson (2098_CR8) 2013; 47 GIN Rozvany (2098_CR10) 2011; 43 G Cheng (2098_CR4) 2011; 44 H Baier (2098_CR1) 1994; 7 B Lazarov (2098_CR7) 2011; 86 G Rozvany (2098_CR9) 1998; 15 X Guo (2098_CR5) 2012; 46 P Blanchard (2098_CR3) 2006 M Stolpe (2098_CR12) 2010; 41 I Kosakam (2098_CR6) 1999; 70 MP Bendsoe (2098_CR2) 2003 A Wächter (2098_CR13) 2006; 106 O Sigmund (2098_CR11) 2001; 21 |
| References_xml | – volume: 70 start-page: 47 year: 1999 end-page: 61 ident: CR6 article-title: A symmetry reduction method for continuum structural topology optimization publication-title: Comp Struct doi: 10.1016/S0045-7949(98)00158-8 – volume: 86 start-page: 765 year: 2011 end-page: 781 ident: CR7 article-title: Filters in topology optimization based on Helmholtz-type differential equations publication-title: Int J Numer Meth Eng doi: 10.1002/nme.3072 – volume: 21 start-page: 120 year: 2001 end-page: 127 ident: CR11 article-title: A 99 line topology optimization code written in matlab publication-title: Struct Multidis Optimiz doi: 10.1007/s001580050176 – year: 2006 ident: CR3 publication-title: Differential Equations – volume: 46 start-page: 631 year: 2012 end-page: 645 ident: CR5 article-title: Some symmetry results for optimal solutions in structural optimization publication-title: Struct Multidisc Optim doi: 10.1007/s00158-012-0802-8 – volume: 41 start-page: 661 year: 2010 end-page: 670 ident: CR12 article-title: On some fundamental properties of structural topology optimization problems publication-title: Struct Multidisp Optim doi: 10.1007/s00158-009-0476-z – year: 2003 ident: CR2 publication-title: Topology Optimization Theory, Methods, and Applications – volume: 15 start-page: 42 year: 1998 end-page: 48 ident: CR9 article-title: Exact analytical solutions for some popular benchmark problems in topology optimization publication-title: Struct Optim doi: 10.1007/BF01197436 – volume: 7 start-page: 184 year: 1994 end-page: 190 ident: CR1 article-title: Ill posed problems in structural optimization and their practical consequences publication-title: Struct Optim doi: 10.1007/BF01742465 – volume: 47 start-page: 631 year: 2013 end-page: 643 ident: CR8 article-title: Symmetry and asymmetry of solutions in discrete variable structural optimization publication-title: Struct Multidisc Optim doi: 10.1007/s00158-012-0871-8 – volume: 44 start-page: 713 year: 2011 end-page: 717 ident: CR4 article-title: Discussion on symmetry of optimum topology design publication-title: Struct Multidisc Optim doi: 10.1007/s00158-011-0686-z – volume: 106 start-page: 5 issue: 1 year: 2006 end-page: 57 ident: CR13 article-title: On the implementation of a primal-dual interior point filter line search algorithm for large-scale nonlinear programming publication-title: Math Program doi: 10.1007/s10107-004-0559-y – volume: 43 start-page: 297 year: 2011 end-page: 317 ident: CR10 article-title: On symmetry and non-uniqueness in exact topology optimization publication-title: Struct Multidisc Optim doi: 10.1007/s00158-010-0564-0 – volume-title: Differential Equations year: 2006 ident: 2098_CR3 – volume: 15 start-page: 42 year: 1998 ident: 2098_CR9 publication-title: Struct Optim doi: 10.1007/BF01197436 – volume: 7 start-page: 184 year: 1994 ident: 2098_CR1 publication-title: Struct Optim doi: 10.1007/BF01742465 – volume: 106 start-page: 5 issue: 1 year: 2006 ident: 2098_CR13 publication-title: Math Program doi: 10.1007/s10107-004-0559-y – volume: 44 start-page: 713 year: 2011 ident: 2098_CR4 publication-title: Struct Multidisc Optim doi: 10.1007/s00158-011-0686-z – volume: 70 start-page: 47 year: 1999 ident: 2098_CR6 publication-title: Comp Struct doi: 10.1016/S0045-7949(98)00158-8 – volume: 21 start-page: 120 year: 2001 ident: 2098_CR11 publication-title: Struct Multidis Optimiz doi: 10.1007/s001580050176 – volume: 41 start-page: 661 year: 2010 ident: 2098_CR12 publication-title: Struct Multidisp Optim doi: 10.1007/s00158-009-0476-z – volume: 46 start-page: 631 year: 2012 ident: 2098_CR5 publication-title: Struct Multidisc Optim doi: 10.1007/s00158-012-0802-8 – volume: 86 start-page: 765 year: 2011 ident: 2098_CR7 publication-title: Int J Numer Meth Eng doi: 10.1002/nme.3072 – volume: 43 start-page: 297 year: 2011 ident: 2098_CR10 publication-title: Struct Multidisc Optim doi: 10.1007/s00158-010-0564-0 – volume-title: Topology Optimization Theory, Methods, and Applications year: 2003 ident: 2098_CR2 – volume: 47 start-page: 631 year: 2013 ident: 2098_CR8 publication-title: Struct Multidisc Optim doi: 10.1007/s00158-012-0871-8 |
| SSID | ssj0008049 |
| Score | 2.2946646 |
| Snippet | We are concerned with the computational topological optimization of elastic structures, in particular minimization of compliance subject to a constraint on the... |
| SourceID | unpaywall proquest crossref springer |
| SourceType | Open Access Repository Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 759 |
| SubjectTerms | Additive manufacturing Advanced manufacturing technologies Boundary conditions Compliance Computational Mathematics and Numerical Analysis Critical point Design optimization Engineering Engineering Design Engineers Modulus of elasticity Partial differential equations Perturbation Research Paper Software Symmetry Theoretical and Applied Mechanics Topology optimization Well posed problems |
| SummonAdditionalLinks | – databaseName: SpringerLINK - Czech Republic Consortium dbid: AGYKE link: http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1LT8JAEJ4oHJSDbyOKZg-eJCV9P47EgESjJ0jqqdlXL0IhtsTgr3e2L9AYjOftTrs7szNfd2e_AbgVtsPQyTma59qxZlvS0Xzu25ohKDM9T_FBqv2O5xd3NLEfQycs73GnVbZ7dSSZe-r6spsK7yrxSmk2wFW6C82cbqsBzf7D69OgdsB-gXoVltEM2wurw8zfhHwPR2uMWR-LtmBvmSzo6oNOpxuRZ3gI4-qbi4STt94yYz3--YPO8Z-DOoKDEomSfmE6x7AjkxNobfATnkLYJzyv-lDuGJKcjJbMY5KuZjOZva8ITQRR-3_aYp5Kofxm3pyz0ipGD5IVVRiwFzqnWXnr8wwmw8H4fqSVpRg0bjlBhm4opkYccyc2fc4U655nmNyKTebRgCKKE6ZwGQ5JIgLUuW75OqO2KrfA8A_JptY5NJJ5Ii-ACC5wpJIqXn4MhsKnjiGMAKVIF83aa4NeaSTiJU-5KpcxjWqG5XzSIpy0SE1aFLThru6yKEg6tj3cqdQcles1jRQHEGJdBIBt6FaaWjdvEdatrePvV1_-S_YV7CM6C4qEtw40UHPyGhFQxm5Ki_8Cvhj64g priority: 102 providerName: Springer Nature – databaseName: Unpaywall dbid: UNPAY link: http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1ZS8NAEB5KfVAfvMV6saBPSjTX5ngsHhRB8cFCfQp7BcQ2KTZF6q93JkerPii-BfZIsjM78-3u7DcAp9rnEo0ct8LATy3fM9yKVORbjhbSDUPig6T9jvuHoNf37wZ80IKT5i4MhVXmqNxlTKV8kcOX_NIhmiha4iwFHAF3G5b6D4_dZ1pKoT-2HD8cLJ6jqDm7tEuqUIdTsBZpQ4wz-7v3WUDK-SnoKixPs7GYvYvh8IujuV2H6-YTq_iS14tpIS_Uxw_2xj_-YQPWaqDJupVmbELLZFuw-oV-cBsGXabKpA71hiAruWZZnrLJbDQyxduMiUwz2t6zxvnEaDKLZXFJOkuEHayokixgK7Q9o_pS5w70b2-ernpWnWnBUh6PC7QyqXDSVPHUjZQkUr3QcZWXujIUsUCQpl0dSBxSgwDPVrYX2VL4lE1B4gLIF94utLM8M3vAtNI40kYQ7T76Oh0J7mgnxl5MgFobdsBuJJComoacsmEMkzmBcim0BIWWkNCSuANn8ybjioPjt8qHjViTejpOEqL4QSiL-K4D542oF8W_dHY-14a_X73_r9oHsILgK67i2Q6hjZIzRwhwCnlcK_gnA7r0Fw priority: 102 providerName: Unpaywall |
| Title | A computational study of symmetry and well-posedness of structural topology optimization |
| URI | https://link.springer.com/article/10.1007/s00158-018-2098-9 https://www.proquest.com/docview/2837192025 https://www.osti.gov/biblio/1557061 |
| UnpaywallVersion | submittedVersion |
| Volume | 59 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVLSH databaseName: SpringerLink Journals customDbUrl: mediaType: online eissn: 1615-1488 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0008049 issn: 1615-147X databaseCode: AFBBN dateStart: 19890301 isFulltext: true providerName: Library Specific Holdings – providerCode: PRVPQU databaseName: ProQuest Central customDbUrl: http://www.proquest.com/pqcentral?accountid=15518 eissn: 1615-1488 dateEnd: 20241105 omitProxy: true ssIdentifier: ssj0008049 issn: 1615-147X databaseCode: BENPR dateStart: 19970201 isFulltext: true titleUrlDefault: https://www.proquest.com/central providerName: ProQuest – providerCode: PRVPQU databaseName: ProQuest Technology Collection customDbUrl: eissn: 1615-1488 dateEnd: 20241105 omitProxy: true ssIdentifier: ssj0008049 issn: 1615-147X databaseCode: 8FG dateStart: 19970201 isFulltext: true titleUrlDefault: https://search.proquest.com/technologycollection1 providerName: ProQuest – providerCode: PRVAVX databaseName: SpringerLINK - Czech Republic Consortium customDbUrl: eissn: 1615-1488 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0008049 issn: 1615-147X databaseCode: AGYKE dateStart: 19970101 isFulltext: true titleUrlDefault: http://link.springer.com providerName: Springer Nature – providerCode: PRVAVX databaseName: SpringerLink Journals (ICM) customDbUrl: eissn: 1615-1488 dateEnd: 99991231 omitProxy: true ssIdentifier: ssj0008049 issn: 1615-147X databaseCode: U2A dateStart: 19970101 isFulltext: true titleUrlDefault: http://www.springerlink.com/journals/ providerName: Springer Nature |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwhV1LS8NAEB60PWgP4hPro-zBk7KYZ5McRFJpFcUgYqGewmZ3c2rTaivSf-9MXtVLPYWw2Q3MTGa_zO5-H8CFctwEk5zLva6TcsfWLvel73BTicTyPOKDpHrHc9R9GDqPI3e0AVF1Foa2VVY5MU_UaiqpRn5NLC2IRnCKvp19cFKNotXVSkJDlNIK6ianGNuEpkXMWA1o9vrRy2udm_0CEBPM4abjjap1TiOnFTVd2thFkRNgFvg7U63gZ71i2oKtr2wmlt9iPP41KQ12YadEkyws3L8HGzrbh9YvjsEDGIVM5soNZdWP5YSybJqy-XIy0YvPJROZYlTD47PpXCvKfXlzzixLrBxsUSgpYC9MMJPy5OYhDAf9t7sHXsopcGm7wQJTSSrMNJVuavkyIeY8z7SknVqJJwKBSExZqpugLTSiOEMatm8kwiHJhAT_chxhH0Ejm2b6GJiSCk2kBXHr44SmfOGaygxwFN3F0PTaYFSmi2XJNU6SF-O4ZknOrR2jtWOydhy04bLuMiuINtY9fFb5Iy6_uXm8ipA2XFU-WjWvGeyqduP_rz5Z_-pT2EZIFRS71M6gga7S5whbFkkHNv3BfQea4aDXi-h6__7U75QRiq1DK8S7YfQSvv8A2Nfuhg |
| linkProvider | ProQuest |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1JT-swEB6xHIADggeIsvrAu4AssjhNckCIVWWrnp5A6i04tnNq00KLUP8cv42ZxEnhUk6cndjSrJ_H9jcAB1oEKQa5gIdNkXHhm4BHKhLc1TL1wpD4IKne8dButp7EbSfozMBH9RaGrlVWMbEI1LqvqEZ-TCwtiEYwRZ8OXjh1jaLT1aqFhrStFfRJQTFmH3bcmfE7buGGJzeXqO-_nnd99XjR4rbLAFd-EI_QwzLpZpkKMi9SKRHKha6n_MxLQxlLBCja083UdRyD4MZRjh85qRTUSSBF8C-kj_POwrzwRYybv_nzq_a__3UuiEoATrCKuyLsVOeqTkFj6gZ0kYwsNcao8z0zTuBufUK7BAtv-UCO32W3-yUJXq_AskWv7Kw0t1WYMfkfWPrCabgGnTOmik4RtsrICgJb1s_YcNzrmdHrmMlcM6oZ8kF_aDTF2mK4YLIlFhA2Kjs34F8Y0Hr2peg6PP2KYDdgLu_nZhOYVhpFZCRx-WMC1ZEMXO3GOItpoiuEDXAq0SXKcptTi41uUrMyF9JOUNoJSTuJG3BY_zIoiT2mfbxT6SOxPj5MJhbZgKNKR5PhKZMd1Wr8eemt6Uvvw0Lr8eE-ub9p323DIsK5uLwhtwNzqDazi5BplO5Zu2Tw_Nuu8AmXCyR- |
| linkToPdf | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1LT8MwDLZgSMAOiKcYDMiBE1PF2qav4wRM4zVxYFJvVZqkp62bWBHav8fua0NCQ5zTOJKd2F-d-DPAteJOjE7OMTyXJwa3tWP40ueGqURseR7xQVK-43XoDkb8KXTCss_pvHrtXl1JFjUNxNKUZrczldzWhW8U6ukRFlk5wBO7CVuceBJwQ4-sXu2K_QL_EqoxTO6F1bXmbyJ-BqYl2qwvSJuw85nOxOJLjMcrMai_D3sleGS9wtoHsKHTQ2iuUAoeQdhjMm_UUCb5WM4fy6YJmy8mE519LJhIFaOUnTGbzrUiV5cP50SyRMLBsqJxAs5CfzIpCzWPYdR_eL8bGGX3BEPaTpCh50iEmSTSSSxfxkSU55mWtBMr9kQgEHgpS7kx6kIjaOvKru13Y8GpQ0KMPzVc2CfQSKepPgWmpEIVaUFU-hi_lC8cU5kBStEu7kSvBd1KdZEsqcWpw8U4qkmRc21HqO2ItB0FLbipp8wKXo11H7cre0TlEZtHRNuD8BQxWws6lY2Ww2uEdWoz_r302b9kX8H2230_enkcPp_DLmKroHiu1oYGGlFfIH7J4st8j34DFqblMw |
| linkToUnpaywall | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1ZS8NAEB5KfVAfvMV6saBPSjTX5ngsHhRB8cFCfQp7BcQ2KTZF6q93JkerPii-BfZIsjM78-3u7DcAp9rnEo0ct8LATy3fM9yKVORbjhbSDUPig6T9jvuHoNf37wZ80IKT5i4MhVXmqNxlTKV8kcOX_NIhmiha4iwFHAF3G5b6D4_dZ1pKoT-2HD8cLJ6jqDm7tEuqUIdTsBZpQ4wz-7v3WUDK-SnoKixPs7GYvYvh8IujuV2H6-YTq_iS14tpIS_Uxw_2xj_-YQPWaqDJupVmbELLZFuw-oV-cBsGXabKpA71hiAruWZZnrLJbDQyxduMiUwz2t6zxvnEaDKLZXFJOkuEHayokixgK7Q9o_pS5w70b2-ernpWnWnBUh6PC7QyqXDSVPHUjZQkUr3QcZWXujIUsUCQpl0dSBxSgwDPVrYX2VL4lE1B4gLIF94utLM8M3vAtNI40kYQ7T76Oh0J7mgnxl5MgFobdsBuJJComoacsmEMkzmBcim0BIWWkNCSuANn8ybjioPjt8qHjViTejpOEqL4QSiL-K4D542oF8W_dHY-14a_X73_r9oHsILgK67i2Q6hjZIzRwhwCnlcK_gnA7r0Fw |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=A+computational+study+of+symmetry+and+well-posedness+of+structural+topology+optimization&rft.jtitle=Structural+and+multidisciplinary+optimization&rft.au=White%2C+Daniel+A.&rft.au=Voronin%2C+Alexey&rft.date=2019-03-01&rft.issn=1615-147X&rft.eissn=1615-1488&rft.volume=59&rft.issue=3&rft.spage=759&rft.epage=766&rft_id=info:doi/10.1007%2Fs00158-018-2098-9&rft.externalDBID=n%2Fa&rft.externalDocID=10_1007_s00158_018_2098_9 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1615-147X&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1615-147X&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1615-147X&client=summon |