An 88-line MATLAB code for the parameterized level set method based topology optimization using radial basis functions

This paper presents a compact and efficient 88-line MATLAB code for the parameterized level set method based topology optimization using radial basis functions (RBFs), which is applied to minimize the compliance of a two-dimensional linear elastic structure. This parameterized level set method using...

Ausführliche Beschreibung

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	Structural and multidisciplinary optimization Jg. 58; H. 2; S. 831 - 849
Hauptverfasser:	Wei, Peng, Li, Zuyu, Li, Xueping, Wang, Michael Yu
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2018 Springer Nature B.V
Schlagworte:	Basis functions Computational Mathematics and Numerical Analysis Dependence Educational Article Engineering Engineering Design Matlab Modulus of elasticity Neural networks Nucleation Parameterization Radial basis function Theoretical and Applied Mechanics Topology optimization Topology optimization Radial basis functions MATLAB code Level set method
ISSN:	1615-147X, 1615-1488
Online-Zugang:	Volltext
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

Abstract	This paper presents a compact and efficient 88-line MATLAB code for the parameterized level set method based topology optimization using radial basis functions (RBFs), which is applied to minimize the compliance of a two-dimensional linear elastic structure. This parameterized level set method using radial basis functions can maintain a relatively smooth level set function with an approximate re-initialization scheme during the optimization process. It also has less dependency on initial designs due to its capability in nucleation of new holes inside the material domain. The MATLAB code and simple modifications are explained in detail with numerical examples. The 88-line code included in the appendix is intended for educational purposes.
AbstractList	This paper presents a compact and efficient 88-line MATLAB code for the parameterized level set method based topology optimization using radial basis functions (RBFs), which is applied to minimize the compliance of a two-dimensional linear elastic structure. This parameterized level set method using radial basis functions can maintain a relatively smooth level set function with an approximate re-initialization scheme during the optimization process. It also has less dependency on initial designs due to its capability in nucleation of new holes inside the material domain. The MATLAB code and simple modifications are explained in detail with numerical examples. The 88-line code included in the appendix is intended for educational purposes. This paper presents a compact and efficient 88-line MATLAB code for the parameterized level set method based topology optimization using radial basis functions (RBFs), which is applied to minimize the compliance of a two-dimensional linear elastic structure. This parameterized level set method using radial basis functions can maintain a relatively smooth level set function with an approximate re-initialization scheme during the optimization process. It also has less dependency on initial designs due to its capability in nucleation of new holes inside the material domain. The MATLAB code and simple modifications are explained in detail with numerical examples. The 88-line code included in the appendix is intended for educational purposes.
Author	Wang, Michael Yu Wei, Peng Li, Zuyu Li, Xueping
Author_xml	– sequence: 1 givenname: Peng orcidid: 0000-0001-5826-1527 surname: Wei fullname: Wei, Peng email: ctpwei@scut.edu.cn organization: State Key Laboratory of Subtropical Building Science, School of Civil Engineering and Transportation, South China University of Technology – sequence: 2 givenname: Zuyu surname: Li fullname: Li, Zuyu organization: Architecture and Civil Engineering Institute, Guangdong University of Petrochemical Technology – sequence: 3 givenname: Xueping surname: Li fullname: Li, Xueping organization: State Key Laboratory of Subtropical Building Science, School of Civil Engineering and Transportation, South China University of Technology – sequence: 4 givenname: Michael Yu surname: Wang fullname: Wang, Michael Yu organization: Department of Mechanical and Aerospace Engineering, Hong Kong University of Science and Technology
BookMark	eNp9kU1LAzEQhoNUsH78AG8Bz6uTbHaTPdbiF1S8KHgL6e5sjWyTNUkF--vdWlEQ7CnDzPMkGd5DMnLeISGnDM4ZgLyIAKxQGTCVsQpEpvbImJWsyJhQavRTy-cDchjjKwAoENWYvE8cVSrrrEN6P3mcTS5p7RukrQ80vSDtTTBLTBjsGhva4Tt2NGKiQ-_FN3Ru4tBOvvedX3xQ3ye7tGuTrHd0Fa1b0GAaa7oNaCNtV67ezOIx2W9NF_Hk-zwiT9dXj9PbbPZwczedzLJaMEiZaKqi4KouGUMuCmmEZEbUHAyft2U-r4YRlGUuWuSlyE0jBRe5QNUwFKqs8yNytr23D_5thTHpV78KbnhSc17yQgoQfCcFUhZM5hUMlNxSdfAxBmx1bdPXqikY22kGehOF3kahhyj0JgqtBpP9MftglyZ87HT41okD6xYYfv_0v_QJqo6cDA
CitedBy_id	crossref_primary_10_3390_ma14195726 crossref_primary_10_1016_j_cma_2022_115444 crossref_primary_10_1016_j_ijmecsci_2025_110500 crossref_primary_10_1007_s00158_018_2138_5 crossref_primary_10_1016_j_mtcomm_2025_113250 crossref_primary_10_32604_cmes_2023_027603 crossref_primary_10_1080_15397734_2025_2458101 crossref_primary_10_1007_s00158_022_03291_0 crossref_primary_10_1007_s00158_019_02444_y crossref_primary_10_1016_j_compstruct_2023_117455 crossref_primary_10_1109_TMECH_2023_3333523 crossref_primary_10_1016_j_compstruct_2021_114065 crossref_primary_10_1016_j_jobe_2025_113254 crossref_primary_10_1016_j_compstruc_2024_107364 crossref_primary_10_1016_j_compstruc_2025_107882 crossref_primary_10_1016_j_mtcomm_2025_112965 crossref_primary_10_32604_cmes_2023_031538 crossref_primary_10_1007_s00366_019_00860_8 crossref_primary_10_1016_j_mser_2021_100648 crossref_primary_10_1016_j_cma_2025_118326 crossref_primary_10_1016_j_enganabound_2020_01_008 crossref_primary_10_1007_s40430_022_03382_5 crossref_primary_10_1016_j_apm_2024_115787 crossref_primary_10_1016_j_applthermaleng_2021_117159 crossref_primary_10_1007_s00158_020_02504_8 crossref_primary_10_1016_j_cma_2024_117292 crossref_primary_10_1007_s40430_025_05439_7 crossref_primary_10_1007_s00158_019_02209_7 crossref_primary_10_1007_s00158_020_02816_9 crossref_primary_10_1007_s10338_024_00542_z crossref_primary_10_1007_s12206_022_0928_6 crossref_primary_10_3390_su13063435 crossref_primary_10_1007_s00158_022_03239_4 crossref_primary_10_1016_j_ress_2025_111075 crossref_primary_10_3390_app132413005 crossref_primary_10_1007_s40314_022_01831_4 crossref_primary_10_1016_j_compscitech_2025_111227 crossref_primary_10_1007_s00158_022_03313_x crossref_primary_10_1007_s00158_025_04081_0 crossref_primary_10_1016_j_engstruct_2022_115338 crossref_primary_10_1016_j_compstruct_2022_116067 crossref_primary_10_1016_j_cma_2020_113235 crossref_primary_10_1016_j_jbiomech_2021_110233 crossref_primary_10_1007_s11433_024_2576_7 crossref_primary_10_1016_j_advengsoft_2022_103389 crossref_primary_10_1016_j_aca_2023_341127 crossref_primary_10_1007_s00158_020_02733_x crossref_primary_10_1007_s00158_022_03168_2 crossref_primary_10_1016_j_enganabound_2024_105853 crossref_primary_10_1007_s11465_021_0637_3 crossref_primary_10_1002_nme_7250 crossref_primary_10_3390_app11052112 crossref_primary_10_3390_ma12071152 crossref_primary_10_1007_s00158_021_02858_7 crossref_primary_10_1016_j_advengsoft_2020_102942 crossref_primary_10_1007_s11081_022_09752_1 crossref_primary_10_1007_s00158_022_03420_9 crossref_primary_10_1080_0305215X_2020_1759579 crossref_primary_10_1016_j_cma_2020_113187 crossref_primary_10_1007_s00158_021_03045_4 crossref_primary_10_1016_j_matdes_2022_110727 crossref_primary_10_1016_j_cma_2023_116052 crossref_primary_10_1007_s00158_024_03927_3 crossref_primary_10_1108_WJE_03_2021_0191 crossref_primary_10_1007_s00158_019_02396_3 crossref_primary_10_1007_s00158_024_03953_1 crossref_primary_10_1016_j_istruc_2020_12_090 crossref_primary_10_1016_j_compstruc_2021_106515 crossref_primary_10_1016_j_mtcomm_2024_110900 crossref_primary_10_1016_j_cma_2022_115350 crossref_primary_10_1016_j_cma_2019_05_029 crossref_primary_10_1016_j_cma_2024_116962 crossref_primary_10_1016_j_engstruct_2025_121025 crossref_primary_10_3390_app15179242 crossref_primary_10_1016_j_cma_2024_116963 crossref_primary_10_1080_0305215X_2020_1843162 crossref_primary_10_1007_s00158_022_03184_2 crossref_primary_10_32604_cmes_2024_054059 crossref_primary_10_1016_j_cma_2022_115112 crossref_primary_10_3390_ma14092119 crossref_primary_10_1016_j_cma_2022_115114 crossref_primary_10_1007_s11465_020_0614_2 crossref_primary_10_1016_j_cma_2024_117374 crossref_primary_10_1016_j_cma_2025_118087 crossref_primary_10_1121_10_0002965 crossref_primary_10_1016_j_cma_2025_118086 crossref_primary_10_1007_s10999_025_09768_2 crossref_primary_10_1007_s10338_023_00379_y crossref_primary_10_1007_s11465_020_0588_0 crossref_primary_10_1016_j_istruc_2023_06_140 crossref_primary_10_1007_s00158_019_02226_6 crossref_primary_10_1016_j_ijmecsci_2024_108967 crossref_primary_10_1016_j_cma_2024_116839 crossref_primary_10_1016_j_cma_2024_117009 crossref_primary_10_1016_j_cma_2019_112778 crossref_primary_10_1007_s00158_021_02917_z crossref_primary_10_3390_ma12193225 crossref_primary_10_1016_j_cma_2021_113674 crossref_primary_10_1007_s11081_022_09715_6 crossref_primary_10_1016_j_cad_2022_103407 crossref_primary_10_1016_j_cma_2024_116948 crossref_primary_10_1007_s00158_020_02544_0 crossref_primary_10_1007_s12206_025_0525_6 crossref_primary_10_1007_s12289_023_01768_x crossref_primary_10_1080_15376494_2021_1938302 crossref_primary_10_3390_app14135695 crossref_primary_10_1016_j_cma_2022_115252 crossref_primary_10_1016_j_cma_2025_117892 crossref_primary_10_1016_j_tws_2025_112907 crossref_primary_10_1103_PhysRevApplied_21_024055 crossref_primary_10_1007_s11081_023_09808_w crossref_primary_10_1080_10407782_2022_2079332 crossref_primary_10_1016_j_compstruct_2022_116546 crossref_primary_10_32604_cmes_2023_023978 crossref_primary_10_1016_j_mechmachtheory_2022_104750 crossref_primary_10_1002_adem_202402567 crossref_primary_10_1007_s10846_022_01731_z crossref_primary_10_1016_j_asoc_2021_108031 crossref_primary_10_1007_s12206_024_1123_8 crossref_primary_10_1007_s00158_022_03355_1 crossref_primary_10_1016_j_compstruct_2018_10_034 crossref_primary_10_3390_ma15144972 crossref_primary_10_1016_j_tws_2025_113680 crossref_primary_10_1109_ACCESS_2022_3206368 crossref_primary_10_1002_nme_70044 crossref_primary_10_1016_j_cma_2019_02_026 crossref_primary_10_1016_j_apm_2022_06_026 crossref_primary_10_1016_j_cma_2025_118032 crossref_primary_10_1016_j_cma_2018_04_034 crossref_primary_10_1007_s00158_024_03798_8 crossref_primary_10_3390_app13074627 crossref_primary_10_3390_ma16114061 crossref_primary_10_1007_s10409_020_01045_z crossref_primary_10_1051_smdo_2019019 crossref_primary_10_3390_app11167409 crossref_primary_10_1016_j_tws_2025_113013 crossref_primary_10_1007_s00158_023_03603_y crossref_primary_10_1016_j_cma_2020_113658 crossref_primary_10_1016_j_ress_2025_111440 crossref_primary_10_3390_app10217449 crossref_primary_10_1016_j_cma_2024_117698 crossref_primary_10_1016_j_cma_2025_117995 crossref_primary_10_1016_j_cma_2024_117697 crossref_primary_10_1016_j_matdes_2022_111448 crossref_primary_10_1007_s00158_021_03050_7 crossref_primary_10_1007_s00158_023_03539_3 crossref_primary_10_1016_j_apm_2022_09_005 crossref_primary_10_1007_s00158_022_03306_w crossref_primary_10_1007_s10999_025_09747_7 crossref_primary_10_1007_s00158_022_03339_1 crossref_primary_10_3390_app14020657 crossref_primary_10_1016_j_enganabound_2023_01_026 crossref_primary_10_1007_s00158_021_03009_8 crossref_primary_10_1016_j_ijheatmasstransfer_2022_122526 crossref_primary_10_1016_j_cma_2021_113829 crossref_primary_10_1016_j_cma_2021_114236 crossref_primary_10_1016_j_compstruc_2020_106324 crossref_primary_10_1016_j_advengsoft_2024_103778 crossref_primary_10_1007_s00158_020_02726_w crossref_primary_10_1016_j_finel_2024_104167 crossref_primary_10_1080_0305215X_2024_2350648 crossref_primary_10_1007_s00158_022_03464_x crossref_primary_10_1007_s00158_020_02682_5 crossref_primary_10_32604_cmes_2021_016894 crossref_primary_10_1007_s11709_023_0963_0 crossref_primary_10_1016_j_apm_2022_02_032 crossref_primary_10_1016_j_tws_2025_112942 crossref_primary_10_3390_app122110902 crossref_primary_10_1093_jcde_qwaf048 crossref_primary_10_12688_f1000research_150945_2 crossref_primary_10_12688_f1000research_150945_1 crossref_primary_10_1016_j_advengsoft_2022_103303 crossref_primary_10_1007_s00158_023_03517_9 crossref_primary_10_1007_s00158_019_02355_y crossref_primary_10_1016_j_cma_2025_118028 crossref_primary_10_1142_S0219876225500197 crossref_primary_10_1007_s00158_020_02610_7 crossref_primary_10_1007_s00158_025_03997_x crossref_primary_10_1007_s10409_023_23185_x crossref_primary_10_1016_j_euromechsol_2024_105499 crossref_primary_10_1155_2021_6839627 crossref_primary_10_1007_s11465_024_0798_y crossref_primary_10_1007_s10409_024_24119_x crossref_primary_10_1016_j_mechmachtheory_2019_103622 crossref_primary_10_3390_app14020878 crossref_primary_10_1007_s10338_025_00587_8 crossref_primary_10_1016_j_compstruct_2022_115385 crossref_primary_10_1007_s00158_019_02268_w crossref_primary_10_1007_s00158_022_03403_w crossref_primary_10_1007_s12273_024_1197_3 crossref_primary_10_1080_15376494_2025_2526015 crossref_primary_10_1007_s11081_021_09675_3 crossref_primary_10_1088_1361_665X_ab8b2d crossref_primary_10_1155_2023_7939516 crossref_primary_10_1016_j_addma_2021_101952 crossref_primary_10_1007_s00158_022_03236_7 crossref_primary_10_1016_j_amf_2024_200143 crossref_primary_10_1016_j_cma_2025_118114 crossref_primary_10_1016_j_compstruc_2019_05_010 crossref_primary_10_3934_math_2025648 crossref_primary_10_1007_s10409_023_22445_x crossref_primary_10_1080_15397734_2024_2411275 crossref_primary_10_1007_s10409_020_00942_7 crossref_primary_10_1088_1757_899X_671_1_012011 crossref_primary_10_1016_j_compstruct_2023_117532 crossref_primary_10_3390_ma17143591 crossref_primary_10_1016_j_cma_2020_113574 crossref_primary_10_1016_j_apm_2022_03_008 crossref_primary_10_1007_s00158_025_04083_y crossref_primary_10_1016_j_advengsoft_2024_103688 crossref_primary_10_1007_s00158_023_03702_w crossref_primary_10_1016_j_cma_2023_116589 crossref_primary_10_1016_j_engstruct_2025_120692 crossref_primary_10_1016_j_cma_2023_116587 crossref_primary_10_1002_nme_6976 crossref_primary_10_1007_s00158_021_03052_5 crossref_primary_10_1007_s00158_021_03098_5 crossref_primary_10_1016_j_cma_2024_117096 crossref_primary_10_1155_2020_5084167 crossref_primary_10_1007_s00158_021_02972_6 crossref_primary_10_1016_j_applthermaleng_2022_118707 crossref_primary_10_1016_j_advengsoft_2025_104001 crossref_primary_10_1016_j_cma_2021_114159 crossref_primary_10_1016_j_cja_2023_02_012 crossref_primary_10_1002_nme_6185 crossref_primary_10_1007_s00158_021_02958_4 crossref_primary_10_1016_j_cma_2025_118214 crossref_primary_10_1007_s00158_021_03086_9 crossref_primary_10_1016_j_ijmecsci_2024_109735 crossref_primary_10_3390_axioms11060294 crossref_primary_10_1016_j_engappai_2024_109732 crossref_primary_10_1016_j_jmapro_2021_02_050 crossref_primary_10_1016_j_compstruct_2023_117310 crossref_primary_10_1007_s00158_024_03877_w crossref_primary_10_32604_cmes_2024_045411 crossref_primary_10_1080_0305215X_2018_1562550 crossref_primary_10_1007_s00158_020_02540_4 crossref_primary_10_1016_j_cma_2022_115658 crossref_primary_10_1007_s00158_023_03590_0 crossref_primary_10_1007_s00158_019_02318_3 crossref_primary_10_1007_s00158_023_03701_x crossref_primary_10_1007_s00158_024_03891_y crossref_primary_10_1016_j_apm_2025_116119 crossref_primary_10_1007_s00158_021_03097_6 crossref_primary_10_1007_s11465_023_0780_0 crossref_primary_10_1002_ceat_202000555 crossref_primary_10_1007_s12206_024_0625_8 crossref_primary_10_1007_s00158_020_02719_9 crossref_primary_10_1089_soro_2021_0169 crossref_primary_10_1155_2022_2752678 crossref_primary_10_1002_nme_6642 crossref_primary_10_1007_s00158_020_02722_0 crossref_primary_10_1007_s00158_025_04095_8 crossref_primary_10_32604_cmes_2023_026043
Cites_doi	10.1016/j.ijheatmasstransfer.2012.08.028 10.1016/j.jcp.2003.09.033 10.1006/jcph.2001.6789 10.1017/S0956792505006182 10.1007/s00158-015-1372-3 10.1002/nme.1536 10.1016/S0045-7825(02)00559-5 10.1007/s00158-014-1107-x 10.1007/s00158-014-1190-z 10.1006/jcph.1996.0167 10.1137/S0363012997323230 10.1007/s00158-013-0999-1 10.1007/BF02123482 10.1007/s00158-015-1284-2 10.1007/s00158-013-0956-z 10.1007/s00158-013-0912-y 10.1016/j.imavis.2010.08.011 10.1002/nme.2478 10.1016/j.jcp.2003.09.032 10.1007/s00158-003-0322-7 10.1016/j.cma.2010.05.013 10.1016/0021-9991(88)90002-2 10.1007/s00791-012-0180-1 10.1007/s00158-011-0696-x 10.1016/j.advengsoft.2004.06.004 10.1007/s00158-010-0534-6 10.1006/jcph.2000.6581 10.1115/DETC2006-99294 10.1007/s00158-013-0978-6 10.1016/j.enganabound.2004.01.004 10.1109/83.902291 10.1007/s00158-013-0935-4 10.1007/s00158-010-0594-7 10.1007/BF00934777 10.1016/j.advengsoft.2015.02.006 10.1007/s00158-009-0430-0 10.1002/9780470689486 10.1371/journal.pone.0145041 10.1002/nme.1468 10.1006/jcph.1999.6345 10.1016/j.jcp.2006.06.029 10.1109/SMA.2001.923379 10.1007/s00158-015-1294-0 10.1016/j.jcp.2003.11.010 10.1007/s001580050176
ContentType	Journal Article
Copyright	Springer-Verlag GmbH Germany, part of Springer Nature 2018 Copyright Springer Science & Business Media 2018 Structural and Multidisciplinary Optimization is a copyright of Springer, (2018). All Rights Reserved.
Copyright_xml	– notice: Springer-Verlag GmbH Germany, part of Springer Nature 2018 – notice: Copyright Springer Science & Business Media 2018 – notice: Structural and Multidisciplinary Optimization is a copyright of Springer, (2018). All Rights Reserved.
DBID	AAYXX CITATION 8FE 8FG ABJCF AFKRA BENPR BGLVJ CCPQU DWQXO HCIFZ L6V M7S PHGZM PHGZT PKEHL PQEST PQGLB PQQKQ PQUKI PRINS PTHSS
DOI	10.1007/s00158-018-1904-8
DatabaseName	CrossRef ProQuest SciTech Collection ProQuest Technology Collection Materials Science & Engineering Collection ProQuest Central UK/Ireland ProQuest Central 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 (retired) ProQuest One Academic UKI Edition ProQuest Central China Engineering Collection
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 China 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: BENPR name: ProQuest Central url: https://www.proquest.com/central sourceTypes: Aggregation Database
DeliveryMethod	fulltext_linktorsrc
Discipline	Engineering
EISSN	1615-1488
EndPage	849
ExternalDocumentID	10_1007_s00158_018_1904_8
GrantInformation_xml	– fundername: State Key Laboratory of Subtropical Building Science, South China University of Technology grantid: 2016KB13 – fundername: National Natural Science Foundation of China grantid: 11002058; 11002056 funderid: http://dx.doi.org/10.13039/501100001809 – fundername: National Natural Science Foundation of China (CN) grantid: 11372004
GroupedDBID	-5B -5G -BR -EM -Y2 -~C .86 .VR 06D 0R~ 0VY 123 199 1N0 2.D 203 29Q 29~ 2J2 2JN 2JY 2KG 2KM 2LR 2P1 2VQ 2~H 30V 4.4 406 408 409 40D 40E 5QI 5VS 67Z 6NX 78A 8FE 8FG 8TC 8UJ 95- 95. 95~ 96X AAAVM AABHQ AACDK AAHNG AAIAL AAJBT AAJKR AANZL AARHV AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYTO AAYZH ABAKF ABBBX ABBXA ABDZT ABECU ABFTD ABFTV ABHLI ABHQN ABJCF ABJNI ABJOX ABKCH ABKTR ABMNI ABMQK ABNWP ABQBU ABQSL ABSXP ABTEG ABTHY ABTKH ABTMW ABULA ABWNU ABXPI ACAOD ACBXY ACDTI ACGFS ACHSB ACHXU ACIWK ACKNC ACMDZ ACMLO ACOKC ACOMO ACPIV ACSNA ACZOJ ADHIR ADINQ ADKNI ADKPE ADPHR ADRFC ADTPH ADURQ ADYFF ADZKW AEBTG AEFIE AEFQL AEGAL AEGNC AEJHL AEJRE AEKMD AEMSY AENEX AEOHA AEPYU AESKC AETLH AEVLU AEXYK AFBBN AFEXP AFGCZ AFKRA AFLOW AFQWF AFWTZ AFZKB AGAYW AGDGC AGGDS AGJBK AGMZJ AGQEE AGQMX AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHSBF AHYZX AIAKS AIGIU AIIXL AILAN AITGF AJBLW AJRNO AJZVZ ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AOCGG ARCEE ARMRJ ASPBG AVWKF AXYYD AYJHY AZFZN B-. BA0 BDATZ BENPR BGLVJ BGNMA BSONS CAG CCPQU COF 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 H13 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- N2Q N9A NB0 NDZJH NPVJJ NQJWS NU0 O9- O93 O9G O9I O9J OAM P19 P9P PF0 PT4 PT5 PTHSS QOK QOS R89 R9I RHV RIG RNI RNS ROL RPX RSV RZK S16 S1Z S26 S27 S28 S3B SAP SCLPG SDH SDM SEG SHX SISQX SJYHP SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 T16 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 AAPKM AAYXX ABBRH ABDBE ABFSG ABRTQ ACSTC ADHKG AEZWR AFDZB AFFHD AFHIU AFOHR AGQPQ AHPBZ AHWEU AIXLP ATHPR AYFIA CITATION PHGZM PHGZT PQGLB DWQXO PKEHL PQEST PQQKQ PQUKI PRINS
ID	FETCH-LOGICAL-c410t-4d95528c611e2457a471a4c20a2bf63b98c606634fe2643ad742434e8d1e486c3
IEDL.DBID	M7S
ISICitedReferencesCount	291
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000440107200030&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN	1615-147X
IngestDate	Tue Nov 04 23:18:06 EST 2025 Tue Nov 04 16:25:49 EST 2025 Sat Nov 29 02:50:11 EST 2025 Tue Nov 18 21:18:11 EST 2025 Fri Feb 21 02:35:13 EST 2025
IsPeerReviewed	true
IsScholarly	true
Issue	2
Keywords	Topology optimization Radial basis functions MATLAB code Level set method
Language	English
LinkModel	DirectLink
MergedId	FETCHMERGED-LOGICAL-c410t-4d95528c611e2457a471a4c20a2bf63b98c606634fe2643ad742434e8d1e486c3
Notes	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ORCID	0000-0001-5826-1527
PQID	2262574042
PQPubID	2043658
PageCount	19
ParticipantIDs	proquest_journals_2262574042 proquest_journals_2077517390 crossref_citationtrail_10_1007_s00158_018_1904_8 crossref_primary_10_1007_s00158_018_1904_8 springer_journals_10_1007_s00158_018_1904_8
PublicationCentury	2000
PublicationDate	2018-08-01
PublicationDateYYYYMMDD	2018-08-01
PublicationDate_xml	– month: 08 year: 2018 text: 2018-08-01 day: 01
PublicationDecade	2010
PublicationPlace	Berlin/Heidelberg
PublicationPlace_xml	– name: Berlin/Heidelberg – name: Heidelberg
PublicationTitle	Structural and multidisciplinary optimization
PublicationTitleAbbrev	Struct Multidisc Optim
PublicationYear	2018
Publisher	Springer Berlin Heidelberg Springer Nature B.V
Publisher_xml	– name: Springer Berlin Heidelberg – name: Springer Nature B.V
References	SethianJALevel set methods and fast marching methods: evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science1999CambridgeCambridge University Press0973.76003 Van DijkNPMauteKLangelaarMVan KeulenFLevel-set methods for structural topology optimization: a reviewStruct Multidiscip Optim2013483437472310758310.1007/s00158-013-0912-y TavakoliRMohseniSMAlternating active-phase algorithm for multimaterial topology optimization problems: a 115-line MATLAB implementationStruct Multidiscip Optim2014494621642318339710.1007/s00158-013-0999-1 OtomoriMYamadaTIzuiKNishiwakiSMATLAB code for a level set-based topology optimization method using a reaction diffusion equationStruct Multidiscip Optim201451511591172335386810.1007/s00158-014-1190-z Wei P, Wang MY (2006) The augmented Lagrangian method in structural shape and topology optimization with RBF based level set method, The 4th China-Japan-Korea Joint Symposium on Optimization of Structural and Mechanical Systems, Kunming, China OsherSFedkiwRLevel set methods and dynamic implicit surfaces2002New YorkSpringer1026.76001 DeatonJDGrandhiRVA survey of structural and multidisciplinary continuum topology optimization: post 2000Struct Multidiscip Optim2014491138318245010.1007/s00158-013-0956-z OlesenLHOkkelsFBruusHA high-level programming-language implementation of topology optimization applied to steady-state navier-stokes flowInt J Numer Methods Eng20066579751001220169110.1002/nme.14681111.76017 GainALPaulinoGHA critical comparative assessment of differential equation-driven methods for structural topology optimizationStruct Multidiscip Optim2013484685710310759710.1007/s00158-013-0935-4 SigmundOA 99 line topology optimization code written in MATLABStruct Multidiscip Optim2001212112012710.1007/s001580050176 XieXMirmehdiMRadial basis function based level set interpolation and evolution for deformable modellingImage Vis Comput2011292–316717710.1016/j.imavis.2010.08.011 MeiYWangXA level set method for structural topology optimization and its applicationsAdv Eng Softw200435741544110.1016/j.advengsoft.2004.06.0041067.90153 EmreBToACProportional topology optimization: a new non-sensitivity method for solving stress constrained and minimum compliance problems and its implementation in MATLABPLoS One20151012e014504110.1371/journal.pone.0145041 ZuoZHXieYMA simple and compact python code for complex 3D topology optimizationAdv Eng Softw20158511110.1016/j.advengsoft.2015.02.006 SokołowskiJZolésioJPIntroduction to shape optimization: shape Sensitity analysis. Introduction to shape optimization : shape sensitivity analysis1992BerlinSpringer-Verlag0761.73003 BurgerMOsherSJA survey on level set methods for inverse problems and optimal designEur J Appl Math2005162263301215529310.1017/S09567925050061821091.49001 KharmandaGOlhoffNMohamedALemaireMReliability-based topology optimizationStruct Multidiscip Optim200426529530710.1007/s00158-003-0322-7 WangSYLimKMKhooBCWangMYAn extended level set method for shape and topology optimizationJ Comput Phys20072211395421229057710.1016/j.jcp.2006.06.0291110.65058 ZhaoHKChanTMerrimanBOsherSA variational level set approach to multiphase motionJ Comput Phys1996127179195140806910.1006/jcph.1996.01670860.65050 Wang MY, Chen SK, Xia Q (2004) TOPLSM, 199-line version. http://ihome.ust.hk/~mywang/download/TOPLSM_199.m XiaLBreitkopfPDesign of materials using topology optimization and energy-based homogenization approach in MATLABStruct Multidiscip Optim201552612291241343333110.1007/s00158-015-1294-0 AndreassenEClausenASchevenelsMLazarovBSSigmundOEfficient topology optimization in MATLAB using 88 lines of codeStruct Multidiscip Optim201143111610.1007/s00158-010-0594-71274.74310 WeiPWangMYPiecewise constant level set method for structural topology optimizationInt J Numer Methods Eng2009784379402250947110.1002/nme.24781183.74222 CecilTQianJOsherSNumerical methods for high dimensional Hamilton-Jacobi equations using radial basis functionsJ Comput Phys20041961327347205434610.1016/j.jcp.2003.11.0101053.65086 ChanTFVeseLAActive contours without edgesIEEE Trans Image Process200110226627710.1109/83.9022911039.68779 HuangXXieYMEvolutionary Topology Optimization of Continuum Structures: Methods and Applications2010New YorkWiley10.1002/97804706894861279.90001 WangSYWangMYRadial basis functions and level set method for structural topology optimizationInt J Numer Meth Engng20066520602090220894010.1002/nme.15361174.74331 RochafellarRTThe multiplier method of Hestenes and Powell applied to convex programmingJ Optim Theory Appl19731255556233495310.1007/BF00934777 SethianJAWiegmannAStructural boundary design via level set and immersed interface methodsJ Comput Phys20001632489528178355910.1006/jcph.2000.65810994.74082 TalischiCPaulinoGHPereiraAMenezesIFMPolytop: a MATLAB implementation of a general topology optimization framework using unstructured polygonal finite element meshesStruct Multidiscip Optim2012453329357289711610.1007/s00158-011-0696-x1274.74402 AllaireGJouveFToaderAMStructural optimization using sensitivity analysis and a level-set methodJ Comput Phys20041941363393203339010.1016/j.jcp.2003.09.0321136.74368 ChoiKKKimNHStructural sensitivity analysis and optimization 12005BerlinSpringer SchmidtSSchulzVA 2589 line topology optimization code written for the graphics cardComput Vis Sci2011146249256297225010.1007/s00791-012-0180-11380.74100 WendlandHPiecewise polynomial, positive definite and compactly supported radial functions of minimal degreeAdv Comput Math199541389396136651010.1007/BF021234820838.41014 WangSYWangMYStructural shape and topology optimization using an implicit free boundary parameterization methodComput Model Eng Sci200613211914722261351232.74084 ZhangWYuanJZhangJGuoXA new topology optimization approach based on moving Morphable components (MMC) and the ersatz material modelStruct Multidiscip Optim201653612431260349888510.1007/s00158-015-1372-3 WangMYWangXGuoDA level set method for structural topology optimizationComput Methods Appl Mech Eng20031921–2227246195140810.1016/S0045-7825(02)00559-51083.74573 SureshKA 199-line MATLAB code for Pareto-optimal tracing in topology optimizationStruct Multidiscip Optim2010425665679272027410.1007/s00158-010-0534-61274.74005 OsherSSantosaFLevel set methods for optimization problems involving geometry and constraints: i. Frequencies of a two-density inhomogeneous drumJ Comput Phys20011711272288184364810.1006/jcph.2001.67891056.74061 ZegardTPaulinoGHGRAND3 - ground structure based topology optimization for arbitrary 3D domains using MATLABStruct Multidiscip Optim20155261161118410.1007/s00158-015-1284-2 DijkNPVMauteKLangelaarMvan KeulenFLevel-set methods for structural topology optimization: a reviewStruct Multidiscip Optim2013483437472310758310.1007/s00158-013-0912-y BendsøeMSigmundOTopology optimization. Theory, methods and applications2003BerlinSpringer1059.74001 MorseBSYooTSChenDTRheingansPSubramanianKRInterpolating implicit surfaces from scattered surface data using compactly supported radial basis functionsInt Conf Shape Model Appl2001152899810.1109/SMA.2001.923379 OsherSSethianJAFronts propagating with curvature-dependent speed: algorithms based on HamiltonJacobi formulationsJ Comput Phys1988791124996586010.1016/0021-9991(88)90002-20659.65132 Allaire G (2009) A 2-d Scilab Code for shape and topology optimization by the level set method. http://www.cmap.polytechnique.fr/∼allaire/levelset_en.html YamadaTIzuiKNishiwakiSTakezawaAA topology optimization method based on the level set method incorporating a fictitious interface energyComput Methods Appl Mech Eng201019945–4828762891274076510.1016/j.cma.2010.05.0131231.74365 ZhouSCadmanJChenYLiWXieYMHuangXDesign and fabrication of biphasic cellular materials with transport properties – a modified bidirectional evolutionary structural optimization procedure and MATLAB programInt J Heat Mass Transf20125525–268149816210.1016/j.ijheatmasstransfer.2012.08.028 KansaEJPowerHFasshauerGELingLA volumetric integral radial basis function method for time-dependent partial differential equations. I. FormulationEng Anal Bound Elem200428101191120610.1016/j.enganabound.2004.01.0041159.76363 LiuKTovarAAn efficient 3d topology optimization code written in MATLABStruct Multidiscip Optim201450611751196331242510.1007/s00158-014-1107-x PengDMerrimanBOsherSZhao H.& Kang M.A PDE-based fast local level set methodJ Comput Phys19991552410438172332110.1006/jcph.1999.63450964.76069 SigmundOMauteKTopology optimization approachesStruct Multidiscip Optim201348610311055313812410.1007/s00158-013-0978-6 AllaireGDe GournayFJouveFToaderAMStructural optimization using topological and shape sensitivity via a level set methodControl Cybern2005341598022110631167.49324 Wang MY, Wei P (2005) Topology optimization with level set method incorporating topological derivative. 6th World Congress on Structural & Multidisciplinary Optimization, Rio de Janeiro, Brazil BurgerMHacklBRingWIncorporating topological derivatives into level set methodsJ Comput Phys20041941344362203338910.1016/j.jcp.2003.09.0331044.65053 ChallisVJA discrete level-set topology optimization code written in MATLABStruct Multidiscip Optim2010413453464260213610.1007/s00158-009-0430-01274.74322 SokołowskiJŻochowskiAOn the topological derivative in shape optimizationSIAM J Control Optim199937412511272169194010.1137/S03630129973232300940.49026 X Huang (1904_CR16) 2010 JA Sethian (1904_CR30) 1999 ZH Zuo (1904_CR56) 2015; 85 C Talischi (1904_CR37) 2012; 45 NP Dijk Van (1904_CR39) 2013; 48 BS Morse (1904_CR21) 2001; 15 1904_CR46 S Osher (1904_CR24) 2001; 171 1904_CR42 X Xie (1904_CR50) 2011; 29 1904_CR44 M Burger (1904_CR6) 2005; 16 O Sigmund (1904_CR32) 2001; 21 G Allaire (1904_CR3) 2005; 34 MY Wang (1904_CR43) 2003; 192 E Andreassen (1904_CR4) 2011; 43 EJ Kansa (1904_CR17) 2004; 28 J Sokołowski (1904_CR35) 1992 H Wendland (1904_CR48) 1995; 4 S Osher (1904_CR25) 1988; 79 RT Rochafellar (1904_CR28) 1973; 12 R Tavakoli (1904_CR38) 2014; 49 M Burger (1904_CR7) 2004; 194 NPV Dijk (1904_CR13) 2013; 48 T Cecil (1904_CR8) 2004; 196 L Xia (1904_CR49) 2015; 52 TF Chan (1904_CR10) 2001; 10 1904_CR1 M Bendsøe (1904_CR5) 2003 SY Wang (1904_CR45) 2007; 221 D Peng (1904_CR27) 1999; 155 T Yamada (1904_CR51) 2010; 199 O Sigmund (1904_CR33) 2013; 48 AL Gain (1904_CR15) 2013; 48 K Liu (1904_CR19) 2014; 50 LH Olesen (1904_CR22) 2006; 65 K Suresh (1904_CR36) 2010; 42 M Otomori (1904_CR26) 2014; 51 JD Deaton (1904_CR12) 2014; 49 J Sokołowski (1904_CR34) 1999; 37 W Zhang (1904_CR53) 2016; 53 G Allaire (1904_CR2) 2004; 194 SY Wang (1904_CR41) 2006; 13 T Zegard (1904_CR52) 2015; 52 KK Choi (1904_CR11) 2005 SY Wang (1904_CR40) 2006; 65 P Wei (1904_CR47) 2009; 78 B Emre (1904_CR14) 2015; 10 S Osher (1904_CR23) 2002 JA Sethian (1904_CR31) 2000; 163 G Kharmanda (1904_CR18) 2004; 26 VJ Challis (1904_CR9) 2010; 41 S Schmidt (1904_CR29) 2011; 14 Y Mei (1904_CR20) 2004; 35 HK Zhao (1904_CR54) 1996; 127 S Zhou (1904_CR55) 2012; 55
References_xml	– reference: GainALPaulinoGHA critical comparative assessment of differential equation-driven methods for structural topology optimizationStruct Multidiscip Optim2013484685710310759710.1007/s00158-013-0935-4 – reference: LiuKTovarAAn efficient 3d topology optimization code written in MATLABStruct Multidiscip Optim201450611751196331242510.1007/s00158-014-1107-x – reference: OlesenLHOkkelsFBruusHA high-level programming-language implementation of topology optimization applied to steady-state navier-stokes flowInt J Numer Methods Eng20066579751001220169110.1002/nme.14681111.76017 – reference: DeatonJDGrandhiRVA survey of structural and multidisciplinary continuum topology optimization: post 2000Struct Multidiscip Optim2014491138318245010.1007/s00158-013-0956-z – reference: BurgerMOsherSJA survey on level set methods for inverse problems and optimal designEur J Appl Math2005162263301215529310.1017/S09567925050061821091.49001 – reference: MorseBSYooTSChenDTRheingansPSubramanianKRInterpolating implicit surfaces from scattered surface data using compactly supported radial basis functionsInt Conf Shape Model Appl2001152899810.1109/SMA.2001.923379 – reference: BurgerMHacklBRingWIncorporating topological derivatives into level set methodsJ Comput Phys20041941344362203338910.1016/j.jcp.2003.09.0331044.65053 – reference: ZhangWYuanJZhangJGuoXA new topology optimization approach based on moving Morphable components (MMC) and the ersatz material modelStruct Multidiscip Optim201653612431260349888510.1007/s00158-015-1372-3 – reference: SigmundOA 99 line topology optimization code written in MATLABStruct Multidiscip Optim2001212112012710.1007/s001580050176 – reference: TalischiCPaulinoGHPereiraAMenezesIFMPolytop: a MATLAB implementation of a general topology optimization framework using unstructured polygonal finite element meshesStruct Multidiscip Optim2012453329357289711610.1007/s00158-011-0696-x1274.74402 – reference: OtomoriMYamadaTIzuiKNishiwakiSMATLAB code for a level set-based topology optimization method using a reaction diffusion equationStruct Multidiscip Optim201451511591172335386810.1007/s00158-014-1190-z – reference: ZhouSCadmanJChenYLiWXieYMHuangXDesign and fabrication of biphasic cellular materials with transport properties – a modified bidirectional evolutionary structural optimization procedure and MATLAB programInt J Heat Mass Transf20125525–268149816210.1016/j.ijheatmasstransfer.2012.08.028 – reference: SethianJAWiegmannAStructural boundary design via level set and immersed interface methodsJ Comput Phys20001632489528178355910.1006/jcph.2000.65810994.74082 – reference: OsherSSantosaFLevel set methods for optimization problems involving geometry and constraints: i. Frequencies of a two-density inhomogeneous drumJ Comput Phys20011711272288184364810.1006/jcph.2001.67891056.74061 – reference: RochafellarRTThe multiplier method of Hestenes and Powell applied to convex programmingJ Optim Theory Appl19731255556233495310.1007/BF00934777 – reference: AndreassenEClausenASchevenelsMLazarovBSSigmundOEfficient topology optimization in MATLAB using 88 lines of codeStruct Multidiscip Optim201143111610.1007/s00158-010-0594-71274.74310 – reference: Wang MY, Chen SK, Xia Q (2004) TOPLSM, 199-line version. http://ihome.ust.hk/~mywang/download/TOPLSM_199.m – reference: XiaLBreitkopfPDesign of materials using topology optimization and energy-based homogenization approach in MATLABStruct Multidiscip Optim201552612291241343333110.1007/s00158-015-1294-0 – reference: WangSYLimKMKhooBCWangMYAn extended level set method for shape and topology optimizationJ Comput Phys20072211395421229057710.1016/j.jcp.2006.06.0291110.65058 – reference: WangSYWangMYStructural shape and topology optimization using an implicit free boundary parameterization methodComput Model Eng Sci200613211914722261351232.74084 – reference: AllaireGDe GournayFJouveFToaderAMStructural optimization using topological and shape sensitivity via a level set methodControl Cybern2005341598022110631167.49324 – reference: Wang MY, Wei P (2005) Topology optimization with level set method incorporating topological derivative. 6th World Congress on Structural & Multidisciplinary Optimization, Rio de Janeiro, Brazil – reference: HuangXXieYMEvolutionary Topology Optimization of Continuum Structures: Methods and Applications2010New YorkWiley10.1002/97804706894861279.90001 – reference: MeiYWangXA level set method for structural topology optimization and its applicationsAdv Eng Softw200435741544110.1016/j.advengsoft.2004.06.0041067.90153 – reference: ZhaoHKChanTMerrimanBOsherSA variational level set approach to multiphase motionJ Comput Phys1996127179195140806910.1006/jcph.1996.01670860.65050 – reference: SokołowskiJŻochowskiAOn the topological derivative in shape optimizationSIAM J Control Optim199937412511272169194010.1137/S03630129973232300940.49026 – reference: OsherSSethianJAFronts propagating with curvature-dependent speed: algorithms based on HamiltonJacobi formulationsJ Comput Phys1988791124996586010.1016/0021-9991(88)90002-20659.65132 – reference: SchmidtSSchulzVA 2589 line topology optimization code written for the graphics cardComput Vis Sci2011146249256297225010.1007/s00791-012-0180-11380.74100 – reference: SigmundOMauteKTopology optimization approachesStruct Multidiscip Optim201348610311055313812410.1007/s00158-013-0978-6 – reference: ZegardTPaulinoGHGRAND3 - ground structure based topology optimization for arbitrary 3D domains using MATLABStruct Multidiscip Optim20155261161118410.1007/s00158-015-1284-2 – reference: CecilTQianJOsherSNumerical methods for high dimensional Hamilton-Jacobi equations using radial basis functionsJ Comput Phys20041961327347205434610.1016/j.jcp.2003.11.0101053.65086 – reference: WeiPWangMYPiecewise constant level set method for structural topology optimizationInt J Numer Methods Eng2009784379402250947110.1002/nme.24781183.74222 – reference: DijkNPVMauteKLangelaarMvan KeulenFLevel-set methods for structural topology optimization: a reviewStruct Multidiscip Optim2013483437472310758310.1007/s00158-013-0912-y – reference: ChallisVJA discrete level-set topology optimization code written in MATLABStruct Multidiscip Optim2010413453464260213610.1007/s00158-009-0430-01274.74322 – reference: SethianJALevel set methods and fast marching methods: evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science1999CambridgeCambridge University Press0973.76003 – reference: SureshKA 199-line MATLAB code for Pareto-optimal tracing in topology optimizationStruct Multidiscip Optim2010425665679272027410.1007/s00158-010-0534-61274.74005 – reference: KansaEJPowerHFasshauerGELingLA volumetric integral radial basis function method for time-dependent partial differential equations. I. FormulationEng Anal Bound Elem200428101191120610.1016/j.enganabound.2004.01.0041159.76363 – reference: TavakoliRMohseniSMAlternating active-phase algorithm for multimaterial topology optimization problems: a 115-line MATLAB implementationStruct Multidiscip Optim2014494621642318339710.1007/s00158-013-0999-1 – reference: Allaire G (2009) A 2-d Scilab Code for shape and topology optimization by the level set method. http://www.cmap.polytechnique.fr/∼allaire/levelset_en.html – reference: XieXMirmehdiMRadial basis function based level set interpolation and evolution for deformable modellingImage Vis Comput2011292–316717710.1016/j.imavis.2010.08.011 – reference: ChoiKKKimNHStructural sensitivity analysis and optimization 12005BerlinSpringer – reference: ChanTFVeseLAActive contours without edgesIEEE Trans Image Process200110226627710.1109/83.9022911039.68779 – reference: AllaireGJouveFToaderAMStructural optimization using sensitivity analysis and a level-set methodJ Comput Phys20041941363393203339010.1016/j.jcp.2003.09.0321136.74368 – reference: WangMYWangXGuoDA level set method for structural topology optimizationComput Methods Appl Mech Eng20031921–2227246195140810.1016/S0045-7825(02)00559-51083.74573 – reference: WendlandHPiecewise polynomial, positive definite and compactly supported radial functions of minimal degreeAdv Comput Math199541389396136651010.1007/BF021234820838.41014 – reference: ZuoZHXieYMA simple and compact python code for complex 3D topology optimizationAdv Eng Softw20158511110.1016/j.advengsoft.2015.02.006 – reference: KharmandaGOlhoffNMohamedALemaireMReliability-based topology optimizationStruct Multidiscip Optim200426529530710.1007/s00158-003-0322-7 – reference: YamadaTIzuiKNishiwakiSTakezawaAA topology optimization method based on the level set method incorporating a fictitious interface energyComput Methods Appl Mech Eng201019945–4828762891274076510.1016/j.cma.2010.05.0131231.74365 – reference: BendsøeMSigmundOTopology optimization. Theory, methods and applications2003BerlinSpringer1059.74001 – reference: WangSYWangMYRadial basis functions and level set method for structural topology optimizationInt J Numer Meth Engng20066520602090220894010.1002/nme.15361174.74331 – reference: OsherSFedkiwRLevel set methods and dynamic implicit surfaces2002New YorkSpringer1026.76001 – reference: PengDMerrimanBOsherSZhao H.& Kang M.A PDE-based fast local level set methodJ Comput Phys19991552410438172332110.1006/jcph.1999.63450964.76069 – reference: Van DijkNPMauteKLangelaarMVan KeulenFLevel-set methods for structural topology optimization: a reviewStruct Multidiscip Optim2013483437472310758310.1007/s00158-013-0912-y – reference: EmreBToACProportional topology optimization: a new non-sensitivity method for solving stress constrained and minimum compliance problems and its implementation in MATLABPLoS One20151012e014504110.1371/journal.pone.0145041 – reference: SokołowskiJZolésioJPIntroduction to shape optimization: shape Sensitity analysis. Introduction to shape optimization : shape sensitivity analysis1992BerlinSpringer-Verlag0761.73003 – reference: Wei P, Wang MY (2006) The augmented Lagrangian method in structural shape and topology optimization with RBF based level set method, The 4th China-Japan-Korea Joint Symposium on Optimization of Structural and Mechanical Systems, Kunming, China – ident: 1904_CR44 – volume: 55 start-page: 8149 issue: 25–26 year: 2012 ident: 1904_CR55 publication-title: Int J Heat Mass Transf doi: 10.1016/j.ijheatmasstransfer.2012.08.028 – volume: 194 start-page: 344 issue: 1 year: 2004 ident: 1904_CR7 publication-title: J Comput Phys doi: 10.1016/j.jcp.2003.09.033 – volume-title: Level set methods and dynamic implicit surfaces year: 2002 ident: 1904_CR23 – volume: 171 start-page: 272 issue: 1 year: 2001 ident: 1904_CR24 publication-title: J Comput Phys doi: 10.1006/jcph.2001.6789 – volume: 16 start-page: 263 issue: 2 year: 2005 ident: 1904_CR6 publication-title: Eur J Appl Math doi: 10.1017/S0956792505006182 – volume: 53 start-page: 1243 issue: 6 year: 2016 ident: 1904_CR53 publication-title: Struct Multidiscip Optim doi: 10.1007/s00158-015-1372-3 – volume: 65 start-page: 2060 year: 2006 ident: 1904_CR40 publication-title: Int J Numer Meth Engng doi: 10.1002/nme.1536 – volume: 192 start-page: 227 issue: 1–2 year: 2003 ident: 1904_CR43 publication-title: Comput Methods Appl Mech Eng doi: 10.1016/S0045-7825(02)00559-5 – volume: 50 start-page: 1175 issue: 6 year: 2014 ident: 1904_CR19 publication-title: Struct Multidiscip Optim doi: 10.1007/s00158-014-1107-x – volume: 51 start-page: 1159 issue: 5 year: 2014 ident: 1904_CR26 publication-title: Struct Multidiscip Optim doi: 10.1007/s00158-014-1190-z – volume: 127 start-page: 179 year: 1996 ident: 1904_CR54 publication-title: J Comput Phys doi: 10.1006/jcph.1996.0167 – volume: 37 start-page: 1251 issue: 4 year: 1999 ident: 1904_CR34 publication-title: SIAM J Control Optim doi: 10.1137/S0363012997323230 – volume-title: Introduction to shape optimization: shape Sensitity analysis. Introduction to shape optimization : shape sensitivity analysis year: 1992 ident: 1904_CR35 – volume: 49 start-page: 621 issue: 4 year: 2014 ident: 1904_CR38 publication-title: Struct Multidiscip Optim doi: 10.1007/s00158-013-0999-1 – volume: 4 start-page: 389 issue: 1 year: 1995 ident: 1904_CR48 publication-title: Adv Comput Math doi: 10.1007/BF02123482 – volume: 52 start-page: 1161 issue: 6 year: 2015 ident: 1904_CR52 publication-title: Struct Multidiscip Optim doi: 10.1007/s00158-015-1284-2 – volume: 49 start-page: 1 issue: 1 year: 2014 ident: 1904_CR12 publication-title: Struct Multidiscip Optim doi: 10.1007/s00158-013-0956-z – volume: 48 start-page: 437 issue: 3 year: 2013 ident: 1904_CR13 publication-title: Struct Multidiscip Optim doi: 10.1007/s00158-013-0912-y – volume: 29 start-page: 167 issue: 2–3 year: 2011 ident: 1904_CR50 publication-title: Image Vis Comput doi: 10.1016/j.imavis.2010.08.011 – volume: 78 start-page: 379 issue: 4 year: 2009 ident: 1904_CR47 publication-title: Int J Numer Methods Eng doi: 10.1002/nme.2478 – volume: 194 start-page: 363 issue: 1 year: 2004 ident: 1904_CR2 publication-title: J Comput Phys doi: 10.1016/j.jcp.2003.09.032 – volume: 26 start-page: 295 issue: 5 year: 2004 ident: 1904_CR18 publication-title: Struct Multidiscip Optim doi: 10.1007/s00158-003-0322-7 – volume: 199 start-page: 2876 issue: 45–48 year: 2010 ident: 1904_CR51 publication-title: Comput Methods Appl Mech Eng doi: 10.1016/j.cma.2010.05.013 – volume: 79 start-page: 12 issue: 1 year: 1988 ident: 1904_CR25 publication-title: J Comput Phys doi: 10.1016/0021-9991(88)90002-2 – volume: 14 start-page: 249 issue: 6 year: 2011 ident: 1904_CR29 publication-title: Comput Vis Sci doi: 10.1007/s00791-012-0180-1 – volume: 45 start-page: 329 issue: 3 year: 2012 ident: 1904_CR37 publication-title: Struct Multidiscip Optim doi: 10.1007/s00158-011-0696-x – volume: 35 start-page: 415 issue: 7 year: 2004 ident: 1904_CR20 publication-title: Adv Eng Softw doi: 10.1016/j.advengsoft.2004.06.004 – volume: 13 start-page: 119 issue: 2 year: 2006 ident: 1904_CR41 publication-title: Comput Model Eng Sci – volume-title: Topology optimization. Theory, methods and applications year: 2003 ident: 1904_CR5 – volume: 42 start-page: 665 issue: 5 year: 2010 ident: 1904_CR36 publication-title: Struct Multidiscip Optim doi: 10.1007/s00158-010-0534-6 – volume: 163 start-page: 489 issue: 2 year: 2000 ident: 1904_CR31 publication-title: J Comput Phys doi: 10.1006/jcph.2000.6581 – ident: 1904_CR46 doi: 10.1115/DETC2006-99294 – volume: 48 start-page: 1031 issue: 6 year: 2013 ident: 1904_CR33 publication-title: Struct Multidiscip Optim doi: 10.1007/s00158-013-0978-6 – volume: 28 start-page: 1191 issue: 10 year: 2004 ident: 1904_CR17 publication-title: Eng Anal Bound Elem doi: 10.1016/j.enganabound.2004.01.004 – volume: 48 start-page: 437 issue: 3 year: 2013 ident: 1904_CR39 publication-title: Struct Multidiscip Optim doi: 10.1007/s00158-013-0912-y – volume: 10 start-page: 266 issue: 2 year: 2001 ident: 1904_CR10 publication-title: IEEE Trans Image Process doi: 10.1109/83.902291 – volume: 48 start-page: 685 issue: 4 year: 2013 ident: 1904_CR15 publication-title: Struct Multidiscip Optim doi: 10.1007/s00158-013-0935-4 – volume: 43 start-page: 1 issue: 1 year: 2011 ident: 1904_CR4 publication-title: Struct Multidiscip Optim doi: 10.1007/s00158-010-0594-7 – volume: 12 start-page: 555 year: 1973 ident: 1904_CR28 publication-title: J Optim Theory Appl doi: 10.1007/BF00934777 – volume-title: Structural sensitivity analysis and optimization 1 year: 2005 ident: 1904_CR11 – volume: 85 start-page: 1 year: 2015 ident: 1904_CR56 publication-title: Adv Eng Softw doi: 10.1016/j.advengsoft.2015.02.006 – volume: 34 start-page: 59 issue: 1 year: 2005 ident: 1904_CR3 publication-title: Control Cybern – volume: 41 start-page: 453 issue: 3 year: 2010 ident: 1904_CR9 publication-title: Struct Multidiscip Optim doi: 10.1007/s00158-009-0430-0 – ident: 1904_CR42 – volume-title: Evolutionary Topology Optimization of Continuum Structures: Methods and Applications year: 2010 ident: 1904_CR16 doi: 10.1002/9780470689486 – ident: 1904_CR1 – volume: 10 start-page: e0145041 issue: 12 year: 2015 ident: 1904_CR14 publication-title: PLoS One doi: 10.1371/journal.pone.0145041 – volume: 65 start-page: 975 issue: 7 year: 2006 ident: 1904_CR22 publication-title: Int J Numer Methods Eng doi: 10.1002/nme.1468 – volume: 155 start-page: 410 issue: 2 year: 1999 ident: 1904_CR27 publication-title: J Comput Phys doi: 10.1006/jcph.1999.6345 – volume: 221 start-page: 395 issue: 1 year: 2007 ident: 1904_CR45 publication-title: J Comput Phys doi: 10.1016/j.jcp.2006.06.029 – volume-title: Level set methods and fast marching methods: evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science year: 1999 ident: 1904_CR30 – volume: 15 start-page: 89 issue: 2 year: 2001 ident: 1904_CR21 publication-title: Int Conf Shape Model Appl doi: 10.1109/SMA.2001.923379 – volume: 52 start-page: 1229 issue: 6 year: 2015 ident: 1904_CR49 publication-title: Struct Multidiscip Optim doi: 10.1007/s00158-015-1294-0 – volume: 196 start-page: 327 issue: 1 year: 2004 ident: 1904_CR8 publication-title: J Comput Phys doi: 10.1016/j.jcp.2003.11.010 – volume: 21 start-page: 120 issue: 21 year: 2001 ident: 1904_CR32 publication-title: Struct Multidiscip Optim doi: 10.1007/s001580050176
SSID	ssj0008049
Score	2.6423442
Snippet	This paper presents a compact and efficient 88-line MATLAB code for the parameterized level set method based topology optimization using radial basis functions...
SourceID	proquest crossref springer
SourceType	Aggregation Database Enrichment Source Index Database Publisher
StartPage	831
SubjectTerms	Basis functions Computational Mathematics and Numerical Analysis Dependence Educational Article Engineering Engineering Design Matlab Modulus of elasticity Neural networks Nucleation Parameterization Radial basis function Theoretical and Applied Mechanics Topology optimization
SummonAdditionalLinks	– databaseName: SpringerLINK Contemporary 1997-Present dbid: RSV link: http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3JTsMwELXYDnBgR5RNc-AEihQvSexjQSAOBSGWqrcoi4MqlYKagARfz0yWFlBBgrOdRZ7xvGd55g1jh1GkrG-ldTxtEkfJ2MM9F_lOxqW1sWuyoOw81-0EV1e61zPXdR133mS7N1eSZaQeF7sRvFPiFZ56jKscPcvmEe007cab2-44_OqK8xKTcbgKes1V5rRXfAWjCcP8dilaYs35yr_-cpUt19QS2pUvrLEZO1xnS58EBzfYa3sI6LNELeGyfddpnwDVtAMyV0AmCCQE_kgJMv13m8KAEoogtwVUfaaBIC-Fouqr8AZPGG4e6zpOoAT6BxiR1MGAJvZzIMws3XqT3Z-f3Z1eOHXnBSdR3C0clRrPEzrxObdCeUGEEBapRLiRiDNfxgaHiKuozCKhklGKB2wlldUpt0r7idxic8Onod1mgJTEz9IUWWQslXB9wxWPhckwQqdITUSLuY0JwqSWJafuGINwLKhcLmmISxrSkoa6xY7GjzxXmhy_Td5r7BrW2zMPBQn_8UAad_qwwFNhoDCetdhxY-bJ8I_f2vnT7F22KMhPymzCPTZXjF7sPltIXot-PjoonfoDyUfumQ priority: 102 providerName: Springer Nature
Title	An 88-line MATLAB code for the parameterized level set method based topology optimization using radial basis functions
URI	https://link.springer.com/article/10.1007/s00158-018-1904-8 https://www.proquest.com/docview/2077517390 https://www.proquest.com/docview/2262574042
Volume	58
WOSCitedRecordID	wos000440107200030&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText	1
inHoldings	1
isFullTextHit
isPrint
journalDatabaseRights	– providerCode: PRVPQU databaseName: Engineering Database customDbUrl: eissn: 1615-1488 dateEnd: 20241207 omitProxy: false ssIdentifier: ssj0008049 issn: 1615-147X databaseCode: M7S dateStart: 19970201 isFulltext: true titleUrlDefault: http://search.proquest.com providerName: ProQuest – providerCode: PRVPQU databaseName: ProQuest Central customDbUrl: eissn: 1615-1488 dateEnd: 20241207 omitProxy: false ssIdentifier: ssj0008049 issn: 1615-147X databaseCode: BENPR dateStart: 19970201 isFulltext: true titleUrlDefault: https://www.proquest.com/central providerName: ProQuest – providerCode: PRVAVX databaseName: SpringerLINK Contemporary 1997-Present customDbUrl: eissn: 1615-1488 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0008049 issn: 1615-147X databaseCode: RSV dateStart: 20000301 isFulltext: true titleUrlDefault: https://link.springer.com/search?facet-content-type=%22Journal%22 providerName: Springer Nature
link	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1Lb9QwEB5BywEOvFGXPjQHTiCL-JGHT2hbteJQVlVbqr1FSeyglba77SZUgl_PjJNsAZVeuORiO4k0n2c-2-NvAN4VhfGJ117Ema2E0WVMc65IRC2192Vk6zRUnrs4TieTbDq1J_2GW9OnVQ4-MThqt6x4j_wj0QRClyGMfbq6Flw1ik9X-xIaD2GTVRJUSN07W3virKO_TGqENOl0ONWMgoiojDmNi9ZQNjIi-zMu3ZLNv85HQ9g5eva_P_wcnvaEE8cdQl7AA794CU9-kyF8BTfjBRKSmXDil_H58Xgf-aY7Ep9F4ofI8uCXnDYz--kdzjnNCBvfYld9GjkQOmy7ags_cElO6LK_3YmcVv8NVyyAMOeOswY5kgawv4avR4fnB59FX49BVEZGrTDOxrHKqkRKr0ycFhTYClOpqFBlnejSUhMzGFN7olm6cLTsNtr4zElvsqTSb2BjsVz4LUAiKkntHHHLUhsVJVYaWSpbk992RFjUCKLBGnnVi5VzzYx5vpZZDgbMyYA5GzDPRvB-PeSqU-q4r_POYLS8n7RNrlgOUKbaRnc3rw06gg8DKm6b__mtt_e_bBseK4ZhSCrcgY129d3vwqPqpp01qz3Y3D-cnJzuBWDT8_Ts4hdeo_vR
linkProvider	ProQuest
linkToHtml	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1Lb9NAEB6VggQceCMCBeYAF9AK78OPPSAUHlWrphESAeXm-rFGkdKkxKao_Ch-IzNrOwUEvfXAee217P1m5lvvzDcAT7LMuMhpJ8LEFsLoPCSbyyJRSe1cHtgq9p3nPo3i8TiZTu37DfjR18JwWmXvE72jLpcF_yN_QTSB0GUIY6-OvgjuGsWnq30LjRYWe-7kG23Z6pe7b2l9nyq1_W7yZkd0XQVEYWTQCFPaMFRJEUnplAnjjNxzZgoVZCqvIp1bGuI4bCpHZEFnJW0ejTYuKaUzSVRomvcCXDTs_X2q4Ie1509aus0kSkgTT_tT1MCLlsqQ08Zoz2YDI5Lf4-Apuf3jPNaHue3r_9sHugHXOkKNw9YCbsKGW9yCq7_ILN6G4-ECyVKZUOP-cDIavkau5Efi60j8F1n-_JDTgmbfXYlzTqPC2jXYdtdGDvQlNm03iRNckpM97KpXkcsGPuOKBR7mfOGsRmYK3pjvwMdzefG7sLlYLtw9QCJiUVWWxJ1zbVQQWWlkrmxFcakkQqYGEPSrnxadGDv3BJmnaxlpD5iUAJMyYNJkAM_Wtxy1SiRnXbzVgyTtnFKdKpY7lLG2wd-H1wAawPMehafD_3zW_bMnewyXdyb7o3S0O957AFcUm4BPoNyCzWb11T2ES8VxM6tXj7wxIRycNzh_AkQPUtw
linkToPdf	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LT9xADLZgqapyKBRasRSKDz21ikhmJo85Lm1XVCwrpFK0tyjJTKqVlrDaBCT49dh5LG1FkSrOM3nI9tifNfZngI9JomxgpXX8SGeOkqlPZy4JnNyT1qauzsN68tzFKByPo8lEn7VzTsuu2r27kmx6GpilqagO5yY_XDa-cajnIizKgLSrnGgV1hTPDOJ0_cfF0hVHDf5lVON4Kpx015qPveLPwPSANv-6IK3jznDj2X-8Ca9byImDxkbewIottmD9NyLCbbgZFEi2zJATTwfno8ERcq87EqJFQojIBOGXXDgzvbMGZ1xohKWtsJk_jRwKDVbNvIVbvCI3dNn2dyIX1v_CBVMgzHjjtESOpbW5v4Wfw2_nX46ddiKDk5F4K0cZ7fsiygLPs0L5YUKhLVGZcBOR5oFMNS0xhlG5JaAlE0OJt5LKRsazKgoy-Q56xVVhdwAJqgS5MYQuU6mEG2hPeanQOXluQ5BF9MHt1BFnLV05T82YxUui5VqkMYk0ZpHGUR8-LR-ZN1wdT23e63Qct8e2jAUTAnqh1O7jy4KyxVCRn-vD507lD8v__Nbuf-0-gJdnX4fx6Pv45D28EmwydcHhHvSqxbXdhxfZTTUtFx9qW78Hc-r6YQ
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=An+88-line+MATLAB+code+for+the+parameterized+level+set+method+based+topology+optimization+using+radial+basis+functions&rft.jtitle=Structural+and+multidisciplinary+optimization&rft.au=Peng%2C+Wei&rft.au=Li%2C+Zuyu&rft.au=Li%2C+Xueping&rft.au=Michael+Yu+Wang&rft.date=2018-08-01&rft.pub=Springer+Nature+B.V&rft.issn=1615-147X&rft.eissn=1615-1488&rft.volume=58&rft.issue=2&rft.spage=831&rft.epage=849&rft_id=info:doi/10.1007%2Fs00158-018-1904-8&rft.externalDBID=NO_FULL_TEXT
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