{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T17:28:04Z","timestamp":1780507684874,"version":"3.54.1"},"reference-count":73,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2023,5,12]],"date-time":"2023-05-12T00:00:00Z","timestamp":1683849600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,5,12]],"date-time":"2023-05-12T00:00:00Z","timestamp":1683849600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"name":"National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT","award":["2022R1A2C1003776"],"award-info":[{"award-number":["2022R1A2C1003776"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Engineering with Computers"],"published-print":{"date-parts":[[2024,4]]},"DOI":"10.1007\/s00366-023-01829-4","type":"journal-article","created":{"date-parts":[[2023,5,12]],"date-time":"2023-05-12T09:02:26Z","timestamp":1683882146000},"page":"677-713","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":26,"title":["A novel robust stress-based multimaterial topology optimization model for structural stability framework using refined adaptive continuation method"],"prefix":"10.1007","volume":"40","author":[{"given":"Thanh T.","family":"Banh","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qui X.","family":"Lieu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Joowon","family":"Kang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Youngkyu","family":"Ju","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Soomi","family":"Shin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dongkyu","family":"Lee","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2023,5,12]]},"reference":[{"key":"1829_CR1","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1016\/0045-7825(88)90086-2","volume":"71","author":"MP Bends\u00f8e","year":"1988","unstructured":"Bends\u00f8e MP, Kikuchi N (1988) Generating optimal topologies in structural design using a homogenization method. Comput Methods Appl Mech Eng 71:197\u2013224","journal-title":"Comput Methods Appl Mech Eng"},{"key":"1829_CR2","doi-asserted-by":"crossref","first-page":"1045","DOI":"10.1007\/s00158-016-1433-2","volume":"54","author":"M Zhou","year":"2016","unstructured":"Zhou M, Alexandersen J, Sigmund O, Pedersen CBW (2016) Industrial application of topology optimization for combined conductive and convective heat transfer problems. Struct Multidiscip Optim 54:1045\u20131060","journal-title":"Struct Multidiscip Optim"},{"key":"1829_CR3","doi-asserted-by":"crossref","first-page":"562","DOI":"10.1016\/j.cma.2018.04.035","volume":"338","author":"F Regazzoni","year":"2018","unstructured":"Regazzoni F, Parolini N, Verani M (2018) Topology optimization of multiple anisotropic materials, with application to self-assembling diblock copolymers. Comput Methods Appl Mech Eng 338:562\u2013596","journal-title":"Comput Methods Appl Mech Eng"},{"key":"1829_CR4","doi-asserted-by":"crossref","first-page":"855","DOI":"10.1007\/s00366-019-00860-8","volume":"37","author":"M Cui","year":"2021","unstructured":"Cui M, Luo C, Li G (2021) The parameterized level set method for structural topology optimization with shape sensitivity constraint factor. Eng Comput 37:855\u2013872","journal-title":"Eng Comput"},{"key":"1829_CR5","doi-asserted-by":"crossref","first-page":"1585","DOI":"10.1007\/s00366-021-01293-y","volume":"38","author":"W Li","year":"2022","unstructured":"Li W, Wang GG (2022) Elephant herding optimization using dynamic topology and biogeography-based optimization based on learning for numerical optimization. Eng Comput 38:1585\u20131613","journal-title":"Eng Comput"},{"key":"1829_CR6","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1007\/s11831-016-9203-2","volume":"25","author":"L Xia","year":"2016","unstructured":"Xia L, Huang X, Xie YM (2016) Bi-directional evolutionary structural optimization on advanced structures and materials: a comprehensive review. Arch Comput Methods Eng 25:437\u2013478","journal-title":"Arch Comput Methods Eng"},{"key":"1829_CR7","doi-asserted-by":"crossref","first-page":"2571","DOI":"10.1007\/s00158-019-02334-3","volume":"60","author":"YS Han","year":"2019","unstructured":"Han YS, Xu B, Zhao L, Xie YM (2019) Topology optimization of continuum structures under hybrid additive-subtractive manufacturing constraints. Struct Multidiscip Optim 60:2571\u20132595","journal-title":"Struct Multidiscip Optim"},{"key":"1829_CR8","doi-asserted-by":"crossref","first-page":"963","DOI":"10.1007\/s00158-019-02398-1","volume":"61","author":"Y Gai","year":"2020","unstructured":"Gai Y, Zhu X, Zhang YJ (2020) Explicit isogeometric topology optimization based on moving morphable voids with closed B-spline boundary curves. Struct Multidiscip Optim 61:963\u2013982","journal-title":"Struct Multidiscip Optim"},{"key":"1829_CR9","doi-asserted-by":"crossref","first-page":"605","DOI":"10.1016\/0020-7683(77)90043-9","volume":"13","author":"N Olhoff","year":"1977","unstructured":"Olhoff N, Rasmussen SH (1977) On single and bimodal optimum buckling loads of clamped columns. Int J Solids Struct 13:605\u2013614","journal-title":"Int J Solids Struct"},{"key":"1829_CR10","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1137\/0523015","volume":"23","author":"S Cox","year":"1992","unstructured":"Cox S, Overton M (1992) On the optimal design of columns against buckling. SIAM J Math Anal 23:287\u2013325","journal-title":"SIAM J Math Anal"},{"key":"1829_CR11","first-page":"62","volume":"15","author":"PG Cox","year":"1995","unstructured":"Cox PG, Hu KK (1995) The shape of the ideal column reconsidered. Math Intell 15:62\u201367","journal-title":"Math Intell"},{"key":"1829_CR12","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1007\/BF01197036","volume":"11","author":"G Rozvany","year":"1996","unstructured":"Rozvany G (1996) Difficulties in topology optimization with stress, local buckling and system stability constraints. Struct Optim 11:213\u2013217","journal-title":"Struct Optim"},{"key":"1829_CR13","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-68184-9","volume-title":"Stability and optimization of structures: generalized sensitivity analysis. Mechanical Engineering Series","author":"M Ohsaki","year":"2007","unstructured":"Ohsaki M, Ikeda K (2007) Stability and optimization of structures: generalized sensitivity analysis. Mechanical Engineering Series. Springer, Berlin"},{"key":"1829_CR14","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1007\/BF01743533","volume":"10","author":"MM Neves","year":"1995","unstructured":"Neves MM, Rodrigues H, Guedes JM (1995) Generalized topology design of structures with a buckling load criterion. Struct Optim 10:71\u201378","journal-title":"Struct Optim"},{"key":"1829_CR15","doi-asserted-by":"crossref","first-page":"565","DOI":"10.12989\/sem.1997.5.5.565","volume":"105","author":"SJ Min","year":"1997","unstructured":"Min SJ, Kikuchi N (1997) Optimal reinforcement design of structures under the buckling load using the homogenization design method. Struct Eng Mech 105:565\u201376","journal-title":"Struct Eng Mech"},{"key":"1829_CR16","doi-asserted-by":"crossref","first-page":"809","DOI":"10.1002\/nme.449","volume":"54","author":"MM Neves","year":"2002","unstructured":"Neves MM, Sigmund O, Bends\u00f8e MP (2002) Topology optimization of periodic microstructures with a penalization of highly localized buckling modes. Int J Numer Method Eng 54:809\u2013834","journal-title":"Int J Numer Method Eng"},{"key":"1829_CR17","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s00158-002-0209-z","volume":"24","author":"H Rodrigues","year":"2002","unstructured":"Rodrigues H, Guedes H, Bendsoe MP (2002) Hierarchical optimization of material and structure. Struct Multidiscip Optim 24:1\u201310","journal-title":"Struct Multidiscip Optim"},{"key":"1829_CR18","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1007\/s00158-007-0141-3","volume":"35","author":"PG Coelho","year":"2008","unstructured":"Coelho PG, Guedes PR, Guedes JM (2008) A hierarchical model for concurrent material and topology optimisation of three-dimensional structures. Struct Multidiscip Optim 35:107\u2013115","journal-title":"Struct Multidiscip Optim"},{"key":"1829_CR19","doi-asserted-by":"crossref","first-page":"1180","DOI":"10.2514\/2.2062","volume":"41","author":"S Rahmatalla","year":"2003","unstructured":"Rahmatalla S, Swan C (2003) Continuum topology optimization of buckling-sensitive structures. AIAA J 41:1180\u20131189","journal-title":"AIAA J"},{"key":"1829_CR20","doi-asserted-by":"crossref","first-page":"1026","DOI":"10.1002\/nme.4367","volume":"41","author":"PA Browne","year":"2012","unstructured":"Browne PA, Budd C, Gould NIM, Kim HA, Scott JA (2012) A fast method for binary programming using first-order derivatives, with application to topology optimization with buckling constraints. Int J Numer Methods Eng 41:1026\u20131043","journal-title":"Int J Numer Methods Eng"},{"key":"1829_CR21","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/j.cma.2018.04.031","volume":"339","author":"CR Thomsen","year":"2018","unstructured":"Thomsen CR, Wang F, Sigmund O (2018) Buckling strength topology optimization of 2D periodic materials based on linearized bifurcation analysis. Comput Methods Appl Mech Eng 339:115\u2013136","journal-title":"Comput Methods Appl Mech Eng"},{"key":"1829_CR22","doi-asserted-by":"crossref","first-page":"1401","DOI":"10.1007\/s00158-019-02253-3","volume":"59","author":"F Ferrari","year":"2019","unstructured":"Ferrari F, Sigmund O (2019) Revisiting topology optimization with buckling constraints. Struct Multidiscip Optim 59:1401\u20131415","journal-title":"Struct Multidiscip Optim"},{"key":"1829_CR23","doi-asserted-by":"crossref","first-page":"3045","DOI":"10.1007\/s00158-021-02854-x","volume":"63","author":"F Ferrari","year":"2021","unstructured":"Ferrari F, Sigmund O, Guest JK (2021) Topology optimization with linearized buckling criteria in 250 lines of Matlab. Struct Multidiscip Optim 63:3045\u20133066","journal-title":"Struct Multidiscip Optim"},{"key":"1829_CR24","doi-asserted-by":"crossref","first-page":"5635","DOI":"10.1007\/s00366-022-01718-2","volume":"38","author":"MN Nguyen","year":"2022","unstructured":"Nguyen MN, Hoang VN, Lee D (2022) Concurrent topology optimization of coated structure for non-homogeneous materials under buckling criteria. Eng Comput 38:5635\u20135656","journal-title":"Eng Comput"},{"key":"1829_CR25","doi-asserted-by":"crossref","first-page":"110405","DOI":"10.1016\/j.tws.2022.110405","volume":"183","author":"MN Nguyen","year":"2023","unstructured":"Nguyen MN, Hoang VN, Lee D (2023) Multiscale topology optimization with stress, buckling and dynamic constraints using adaptive geometric components. Thin-Walled Struct 183:110405","journal-title":"Thin-Walled Struct"},{"key":"1829_CR26","volume-title":"Topology optimization: theory, methods, and applications","author":"MP Bendsoe","year":"2003","unstructured":"Bendsoe MP, Sigmund O (2003) Topology optimization: theory, methods, and applications. Springer, New York"},{"key":"1829_CR27","doi-asserted-by":"crossref","first-page":"110","DOI":"10.1016\/j.advengsoft.2017.06.002","volume":"114","author":"QH Doan","year":"2017","unstructured":"Doan QH, Lee D (2017) Optimum topology design of multimaterial structures with non-spurious buckling constraints. Adv Eng Softw 114:110\u2013120","journal-title":"Adv Eng Softw"},{"key":"1829_CR28","doi-asserted-by":"crossref","first-page":"1179","DOI":"10.1007\/s11012-019-01009-z","volume":"54","author":"QH Doan","year":"2019","unstructured":"Doan QH, Lee D, Lee J (2019) Design of buckling constrained multiphase material structures using continuum topology optimization. Meccanica 54:1179\u20131201","journal-title":"Meccanica"},{"key":"1829_CR29","unstructured":"Zhou M (2004) Topology optimization for shell structures with linear buckling responses. In: Proceedings of WCCM VI in conjunction with APCOM\u201904, Beijing, China, pp 795\u2013800"},{"key":"1829_CR30","doi-asserted-by":"crossref","first-page":"142","DOI":"10.1016\/j.compstruc.2015.05.020","volume":"157","author":"X Gao","year":"2015","unstructured":"Gao X, Ma H (2015) Topology optimization of continuum structures under buckling constraints. Comput Struct 157:142\u2013152","journal-title":"Comput Struct"},{"key":"1829_CR31","doi-asserted-by":"crossref","first-page":"1333","DOI":"10.2514\/3.2546","volume":"2","author":"THH Pian","year":"1964","unstructured":"Pian THH (1964) Derivation of element stiffness matrices by assumed stress distributions. AIAA J 2:1333\u20131336","journal-title":"AIAA J"},{"key":"1829_CR32","doi-asserted-by":"crossref","first-page":"1685","DOI":"10.1002\/nme.1620200911","volume":"20","author":"THH Pian","year":"1984","unstructured":"Pian THH, Sumihara K (1984) Rational approach for assumed stress finite elements. Int J Numer Methods Eng 20:1685\u20131695","journal-title":"Int J Numer Methods Eng"},{"key":"1829_CR33","doi-asserted-by":"crossref","first-page":"1750092","DOI":"10.1142\/S1758825117500922","volume":"9","author":"X Gao","year":"2017","unstructured":"Gao X, Li L (2017) An adaptive continuation method for topology optimization of continuum structures considering buckling constraints. Int J Appl Mech 9:1750092","journal-title":"Int J Appl Mech"},{"key":"1829_CR34","doi-asserted-by":"crossref","first-page":"1453","DOI":"10.1002\/(SICI)1097-0207(19981230)43:8<1453::AID-NME480>3.0.CO;2-2","volume":"43","author":"P Duysinx","year":"1998","unstructured":"Duysinx P, Bends\u00f8e MP (1998) Topology optimization of continuum structures with local stress constraints. Int J Numer Methods Eng 43:1453\u20131478","journal-title":"Int J Numer Methods Eng"},{"key":"1829_CR35","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1007\/BF01836562","volume":"2","author":"U Kirsch","year":"1990","unstructured":"Kirsch U (1990) On singular topologies in optimum structural design. Struct Optim 2:133\u2013142","journal-title":"Struct Optim"},{"key":"1829_CR36","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1080\/03052159208941276","volume":"20","author":"G Cheng","year":"1992","unstructured":"Cheng G, Jiang Z (1992) Study on topology optimization with stress constraints. Eng Optim 20:129\u2013148","journal-title":"Eng Optim"},{"key":"1829_CR37","doi-asserted-by":"crossref","first-page":"98","DOI":"10.1007\/BF01196941","volume":"12","author":"RJ Yang","year":"1996","unstructured":"Yang RJ, Chen CJ (1996) Stress-based topology optimization. Struct Optim 12:98\u2013105","journal-title":"Struct Optim"},{"key":"1829_CR38","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1016\/j.cma.2012.10.019","volume":"254","author":"Y Luo","year":"2013","unstructured":"Luo Y, Wang M, Kang Z (2013) An enhanced aggregation method for topology optimization with local stress constraints. Comput Methods Appl Mech Eng 254:31\u201341","journal-title":"Comput Methods Appl Mech Eng"},{"key":"1829_CR39","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1016\/j.compstruct.2016.05.058","volume":"156","author":"CY Kiyono","year":"2016","unstructured":"Kiyono CY, Vatanabe SL, Reddy JN (2016) A new multi-p-norm formulation approach for stress-based topology optimization design. Compos Struct 156:10\u201319","journal-title":"Compos Struct"},{"key":"1829_CR40","doi-asserted-by":"crossref","first-page":"258","DOI":"10.1007\/BF01197454","volume":"13","author":"G Cheng","year":"1997","unstructured":"Cheng G, Guo X (1997) epsilon-relaxed approach in structural topology optimization. Struct Multidiscip Optim 13:258\u2013266","journal-title":"Struct Multidiscip Optim"},{"key":"1829_CR41","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1007\/s00158-007-0203-6","volume":"36","author":"M Bruggi","year":"2008","unstructured":"Bruggi M (2008) On an alternative approach to stress constraints relaxation in topology optimization. Struct Multidiscip Optim 36:125\u2013141","journal-title":"Struct Multidiscip Optim"},{"key":"1829_CR42","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1007\/s00158-012-0759-7","volume":"46","author":"M Bruggi","year":"2012","unstructured":"Bruggi M, Duysinx P (2012) Topology optimization for minimum weight with compliance and stress constraints. Struct Multidiscip Optim 46:369\u2013384","journal-title":"Struct Multidiscip Optim"},{"key":"1829_CR43","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1007\/s00158-008-0336-2","volume":"39","author":"J Paris","year":"2009","unstructured":"Paris J, Navarrina F, Casteleiro M (2009) Topology optimization of continuum structures with local and global stress constraints. Struct Multidiscip Optim 39:419\u2013437","journal-title":"Struct Multidiscip Optim"},{"key":"1829_CR44","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1007\/s00158-012-0880-7","volume":"48","author":"E Holmberg","year":"2013","unstructured":"Holmberg E, Torstenfelt B, Klarbring A (2013) Stress constrained topology optimization. Struct Multidiscip Optim 48:33\u201347","journal-title":"Struct Multidiscip Optim"},{"key":"1829_CR45","doi-asserted-by":"crossref","first-page":"113061","DOI":"10.1016\/j.cma.2020.113061","volume":"366","author":"HS Nguyen","year":"2020","unstructured":"Nguyen HS, Kim HG (2020) Stress-constrained shape and topology optimization with the level set method using trimmed hexahedral meshes. Comput Methods Appl Mech Eng 366:113061","journal-title":"Comput Methods Appl Mech Eng"},{"key":"1829_CR46","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1016\/j.camwa.2022.04.001","volume":"115","author":"HS Nguyen","year":"2022","unstructured":"Nguyen HS, Nguyen TN, Nguyen TT (2022) A finite element level-set method for stress-based topology optimization of plate structures. Comput Math Appl 115:26\u201340","journal-title":"Comput Math Appl"},{"key":"1829_CR47","doi-asserted-by":"crossref","first-page":"605","DOI":"10.1007\/s00158-009-0440-y","volume":"41","author":"C Le","year":"2010","unstructured":"Le C, Norato J, Bruns T, Ha C, Tortorelli D (2010) Stress-based topology optimization for continua. Struct Multidiscip Optim 41:605\u2013620","journal-title":"Struct Multidiscip Optim"},{"key":"1829_CR48","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1016\/j.compstruct.2017.11.088","volume":"186","author":"TT Banh","year":"2018","unstructured":"Banh TT, Lee D (2018) Multimaterial topology optimization design for continuum structures with crack patterns. Compos Struct 186:193\u2013209","journal-title":"Compos Struct"},{"issue":"3","key":"1829_CR49","first-page":"385","volume":"41","author":"TT Banh","year":"2021","unstructured":"Banh TT, Luu GN, Lieu XQ, Lee JH, Kang J, Lee DK (2021) Multiple bi-directional FGMs topology optimization approach with a preconditioned conjugate gradient multigrid. Steel Compos Struct 41(3):385\u2013402","journal-title":"Steel Compos Struct"},{"key":"1829_CR50","doi-asserted-by":"crossref","first-page":"1570","DOI":"10.1016\/j.cma.2014.11.002","volume":"283","author":"Y Wang","year":"2015","unstructured":"Wang Y, Luo Z, Kang Z, Zhang N (2015) A multi-material level set-based topology and shape optimization method. Comput Methods Appl Mech Eng 283:1570\u20131586","journal-title":"Comput Methods Appl Mech Eng"},{"key":"1829_CR51","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1016\/j.cma.2016.05.016","volume":"308","author":"P Liu","year":"2016","unstructured":"Liu P, Luo Y, Kang Z (2016) Multi-material topology optimization considering interface behavior via XFEM and level set method. Comput Methods Appl Mech Eng 308:113\u2013133","journal-title":"Comput Methods Appl Mech Eng"},{"key":"1829_CR52","doi-asserted-by":"crossref","first-page":"712","DOI":"10.1016\/j.cma.2017.07.035","volume":"332","author":"KN Chau","year":"2018","unstructured":"Chau KN, Chau KN, Ngo T, Hackl K, Nguyen HX (2018) A polytree-based adaptive polygonal finite element method for multi-material topology optimization. Comput Methods Appl Mech Eng 332:712\u2013739","journal-title":"Comput Methods Appl Mech Eng"},{"key":"1829_CR53","doi-asserted-by":"crossref","first-page":"158","DOI":"10.1016\/j.compstruct.2009.04.046","volume":"91","author":"E Lund","year":"2009","unstructured":"Lund E (2009) Buckling topology optimization of laminated multimaterial composite shell structures. Compos Struct 91:158\u2013167","journal-title":"Compos Struct"},{"key":"1829_CR54","doi-asserted-by":"crossref","first-page":"1136","DOI":"10.1016\/j.cma.2018.08.015","volume":"346","author":"C Wu","year":"2019","unstructured":"Wu C, Fang J, Li Q (2019) Multimaterial topology optimization for thermal buckling criteria. Comput Methods Appl Mech Eng 346:1136\u20131155","journal-title":"Comput Methods Appl Mech Eng"},{"key":"1829_CR55","doi-asserted-by":"crossref","first-page":"632","DOI":"10.1016\/j.cma.2013.10.003","volume":"268","author":"X Guo","year":"2019","unstructured":"Guo X, Zhang W, Zhong W (2019) Stress-related topology optimization of continuum structures involving multi-phase materials. Comput Methods Appl Mech Eng 268:632\u2013655","journal-title":"Comput Methods Appl Mech Eng"},{"key":"1829_CR56","doi-asserted-by":"crossref","first-page":"800","DOI":"10.1002\/nme.5979","volume":"268","author":"S Chu","year":"2019","unstructured":"Chu S, Xiao M, Gao L, Li H (2019) A level set-based method for stress-constrained multimaterial topology optimization of minimizing a global measure of stress. Int J Numer Methods Eng 268:800\u2013818","journal-title":"Int J Numer Methods Eng"},{"key":"1829_CR57","doi-asserted-by":"crossref","first-page":"113453","DOI":"10.1016\/j.cma.2020.113453","volume":"373","author":"S Xu","year":"2021","unstructured":"Xu S, Liu J, Zou B, Li Q, Ma Y (2021) Stress constrained multimaterial topology optimization with the ordered SIMP method. Comput Methods Appl Mech Eng 373:113453","journal-title":"Comput Methods Appl Mech Eng"},{"key":"1829_CR58","first-page":"113453","volume":"54","author":"Z Han","year":"2022","unstructured":"Han Z, Wei K, Gui Z, Ma X, Yang X (2022) Stress-constrained multimaterial topology optimization via an improved alternating active-phase algorithm. Eng Optim 54:113453","journal-title":"Eng Optim"},{"key":"1829_CR59","volume-title":"Introduction to the mechanics of a continuous medium","author":"EM Lawrence","year":"1969","unstructured":"Lawrence EM (1969) Introduction to the mechanics of a continuous medium. Prentice-Hall, Englewood Cliffs"},{"key":"1829_CR60","volume-title":"Extended finite element method","author":"Z Zhuang","year":"2014","unstructured":"Zhuang Z, Liu Z, Cheng B, Liao J (2014) Extended finite element method. Elsevier, New York"},{"key":"1829_CR61","volume-title":"Smoothed finite element methods","author":"GR Liu","year":"2010","unstructured":"Liu GR, Nguyen TT (2010) Smoothed finite element methods. Taylor and Francis Group, New York"},{"key":"1829_CR62","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-0575-3","volume-title":"Introductory functional analysis","author":"BD Reddy","year":"1998","unstructured":"Reddy BD (1998) Introductory functional analysis. Springer, New York"},{"key":"1829_CR63","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1002\/nme.1620240207","volume":"24","author":"K Svanberg","year":"1987","unstructured":"Svanberg K (1987) The method of moving asymptotes\u2014a new method for structural optimization. Int J Numer Methods Eng 24:359\u2013373","journal-title":"Int J Numer Methods Eng"},{"key":"1829_CR64","doi-asserted-by":"crossref","first-page":"1783","DOI":"10.1007\/s00158-019-02374-9","volume":"60","author":"S Townsend","year":"2019","unstructured":"Townsend S, Kim HA (2019) A level set topology optimization method for the buckling of shell structures. Struct Multidiscip Optim 60:1783\u20131800","journal-title":"Struct Multidiscip Optim"},{"key":"1829_CR65","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1007\/BF01742705","volume":"8","author":"AP Seyranian","year":"1994","unstructured":"Seyranian AP, Lund E, Olhoff N (1994) Multiple eigenvalues in structural optimization problems. Struct Optim 8:207\u2013227","journal-title":"Struct Optim"},{"key":"1829_CR66","doi-asserted-by":"crossref","first-page":"436","DOI":"10.1007\/s00158-003-0294-7","volume":"25","author":"NL Pedersen","year":"2003","unstructured":"Pedersen NL, Nidlsen AK (2003) Optimization of practical trusses with constraints on eigenfrequencies, displacements, stresses, and buckling. Struct Multidiscip Optim 25:436\u2013445","journal-title":"Struct Multidiscip Optim"},{"key":"1829_CR67","doi-asserted-by":"crossref","first-page":"967","DOI":"10.1016\/j.jsv.2005.03.028","volume":"289","author":"JS Jensen","year":"2006","unstructured":"Jensen JS, Pedersen NL (2006) On maximal eigenfrequency separation in two-material structures: the 1D and 2D scalar cases. J Sound Vib 289:967\u2013986","journal-title":"J Sound Vib"},{"key":"1829_CR68","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1007\/s00158-007-0101-y","volume":"34","author":"J Du","year":"2007","unstructured":"Du J, Olhoff N (2007) Topological design of freely vibrating continuum structures for maximum values of simple and multiple eigenfrequencies and frequency gaps. Struct Multidiscip Optim 34:91\u2013110","journal-title":"Struct Multidiscip Optim"},{"key":"1829_CR69","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1007\/s00158-006-0087-x","volume":"33","author":"O Sigmund","year":"2007","unstructured":"Sigmund O (2007) Morphology-based black and white filters for topology optimization. Struct Multidiscip Optim 33:401\u2013424","journal-title":"Struct Multidiscip Optim"},{"key":"1829_CR70","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1007\/s00366-017-0540-z","volume":"34","author":"M Cui","year":"2018","unstructured":"Cui M, Zhang Y, Yang X, Luo C (2018) Multi-material proportional topology optimization based on the modified interpolation scheme. Eng Comput 34:287\u2013305","journal-title":"Eng Comput"},{"key":"1829_CR71","doi-asserted-by":"crossref","first-page":"1081","DOI":"10.1007\/s00158-018-1953-z","volume":"58","author":"D Li","year":"2018","unstructured":"Li D, Kim IY (2018) Multi-material topology optimization for practical lightweight design. Struct Multidiscip Optim 58:1081\u20131094","journal-title":"Struct Multidiscip Optim"},{"key":"1829_CR72","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1007\/s00158-022-03479-4","volume":"66","author":"TT Banh","year":"2023","unstructured":"Banh TT, Lieu XQ, Lee J, Kang J, Lee D (2023) A robust dynamic unified multi-material topology optimization method for functionally graded structures. Struct Multidiscip Optim 66:25","journal-title":"Struct Multidiscip Optim"},{"key":"1829_CR73","doi-asserted-by":"crossref","first-page":"356","DOI":"10.1016\/j.cma.2018.01.035","volume":"333","author":"L Xia","year":"2018","unstructured":"Xia L, Zhang L, Xia Q, Shi T (2018) Stress-based topology optimization using bi-directional evolutionary structural optimization method. Comput Methods Appl Mech Eng 333:356\u2013370","journal-title":"Comput Methods Appl Mech Eng"}],"container-title":["Engineering with Computers"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00366-023-01829-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00366-023-01829-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00366-023-01829-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,4,21]],"date-time":"2024-04-21T02:43:12Z","timestamp":1713667392000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00366-023-01829-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5,12]]},"references-count":73,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2024,4]]}},"alternative-id":["1829"],"URL":"https:\/\/doi.org\/10.1007\/s00366-023-01829-4","relation":{},"ISSN":["0177-0667","1435-5663"],"issn-type":[{"value":"0177-0667","type":"print"},{"value":"1435-5663","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,5,12]]},"assertion":[{"value":"12 January 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 April 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 May 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}