{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,24]],"date-time":"2026-04-24T09:52:17Z","timestamp":1777024337272,"version":"3.51.4"},"reference-count":62,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2026,2,1]],"date-time":"2026-02-01T00:00:00Z","timestamp":1769904000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,2,1]],"date-time":"2026-02-01T00:00:00Z","timestamp":1769904000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["52305249"],"award-info":[{"award-number":["52305249"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["52305099"],"award-info":[{"award-number":["52305099"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"name":"the Guizhou Provincial Basic Research Program","award":["ZK [2024] general 084"],"award-info":[{"award-number":["ZK [2024] general 084"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Engineering with Computers"],"published-print":{"date-parts":[[2026,2]]},"DOI":"10.1007\/s00366-026-02282-9","type":"journal-article","created":{"date-parts":[[2026,2,8]],"date-time":"2026-02-08T08:58:58Z","timestamp":1770541138000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Smooth topological design of design-dependent fluidic pressure-loaded continuum structures using a floating projection method"],"prefix":"10.1007","volume":"42","author":[{"given":"Kui","family":"Luo","sequence":"first","affiliation":[]},{"given":"Jie","family":"Hu","sequence":"additional","affiliation":[]},{"given":"Jiachun","family":"Li","sequence":"additional","affiliation":[]},{"given":"Wenkang","family":"Cao","sequence":"additional","affiliation":[]},{"given":"Xing","family":"Chen","sequence":"additional","affiliation":[]},{"given":"Yupeng","family":"Sun","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2026,2,8]]},"reference":[{"key":"2282_CR1","doi-asserted-by":"crossref","unstructured":"Baker C, Johnson T, Flynn D, Hemida H, Quinn A, Soper D, Sterling M (2019) Chapter 8\u2014Aerodynamic loads on trackside structures, passing trains and people. Train Aerodynamics. Butterworth-Heinemann, pp. 151\u2013179","DOI":"10.1016\/B978-0-12-813310-1.00008-3"},{"issue":"15","key":"2282_CR2","doi-asserted-by":"publisher","DOI":"10.1016\/j.oceaneng.2023.115755","volume":"290","author":"FAP Morales","year":"2023","unstructured":"Morales FAP, Serfaty R, Vedovotto JM, Cavallini A, Villar MM, Da Silveira Neto A (2023) Fluid\u2013structure interaction with a finite element\u2013immersed boundary approach for compressible flows. Ocean Eng 290(15):115755. https:\/\/doi.org\/10.1016\/j.oceaneng.2023.115755","journal-title":"Ocean Eng"},{"issue":"3","key":"2282_CR3","doi-asserted-by":"publisher","first-page":"600","DOI":"10.3390\/s25030600","volume":"25","author":"SMM Lazi\u0107","year":"2025","unstructured":"Lazi\u0107 SMM, Tanaskovi\u0107 D, Ra\u0161lji\u0107-Rafajilovi\u0107 M, Cvetanovi\u0107 K, Milinkovi\u0107 E, Bo\u0161kovi\u0107 MV, Andri\u0107 S, Joki\u0107 I, Poljak P, Frantlovi\u0107 M (2025) Novel MEMS multisensor chip for aerodynamic pressure measurements. Sensors 25(3):600. https:\/\/doi.org\/10.3390\/s25030600","journal-title":"Sensors"},{"issue":"4","key":"2282_CR4","doi-asserted-by":"publisher","DOI":"10.3390\/s18041248","volume":"18","author":"L Zhang","year":"2018","unstructured":"Zhang L, Sun C (2018) Simulation analysis of fluid-structure interaction of high velocity environment influence on aircraft wing materials under different Mach numbers. Sensors 18(4):1248. https:\/\/doi.org\/10.3390\/s18041248","journal-title":"Sensors"},{"issue":"3","key":"2282_CR5","doi-asserted-by":"publisher","first-page":"1747","DOI":"10.1007\/s00366-024-02043-6","volume":"41","author":"D Di Cristofaro","year":"2025","unstructured":"Di Cristofaro D, Frangi A, Cremonesi M (2025) 3d fluid\u2013structure interaction simulation with an Arbitrary\u2013Lagrangian\u2013Eulerian approach with applications to flying objects. Eng Comput 41(3):1747\u20131769. https:\/\/doi.org\/10.1007\/s00366-024-02043-6","journal-title":"Eng Comput"},{"key":"2282_CR6","doi-asserted-by":"publisher","unstructured":"Koreanschi A, Oliviu SG, Botez RM. (2015). Experimental Validation of an Optimized Wing Geometry Using Small Wind Tunnel Testing. 33rd AIAA Applied Aerodynamics Conference. https:\/\/doi.org\/10.2514\/6.2015-338610.2514\/6.2015-3386","DOI":"10.2514\/6.2015-338610.2514\/6.2015-3386"},{"issue":"5","key":"2282_CR7","doi-asserted-by":"publisher","DOI":"10.3390\/jmse10050686","volume":"10","author":"H Zhou","year":"2022","unstructured":"Zhou H, Feng B, Liu Z, Chang H, Cheng X (2022) NURBS-based parametric design for ship hull form. J Mar Sci Eng 10(5):686. https:\/\/doi.org\/10.3390\/jmse10050686","journal-title":"J Mar Sci Eng"},{"key":"2282_CR8","doi-asserted-by":"publisher","DOI":"10.1016\/j.ress.2024.110741","volume":"256","author":"Z Yao","year":"2025","unstructured":"Yao Z, Hao J, Li C, Jiang Z, Zhao J (2025) Reliability-based design optimization of fluid-conveying pipeline structure subjected to in-service loadings. Reliab Eng Syst Saf 256:110741. https:\/\/doi.org\/10.1016\/j.ress.2024.110741","journal-title":"Reliab Eng Syst Saf"},{"issue":"5","key":"2282_CR9","doi-asserted-by":"publisher","first-page":"1005","DOI":"10.1007\/s00158-015-1376-z","volume":"53","author":"C Wang","year":"2016","unstructured":"Wang C, Zhao M, Ge T (2016) Structural topology optimization with design-dependent pressure loads. Struct Multidiscip Optim 53(5):1005\u20131018. https:\/\/doi.org\/10.1007\/s00158-015-1376-z","journal-title":"Struct Multidiscip Optim"},{"issue":"5","key":"2282_CR10","doi-asserted-by":"publisher","first-page":"1877","DOI":"10.1007\/s00158-019-02443-z","volume":"61","author":"R Sivapuram","year":"2020","unstructured":"Sivapuram R, Picelli R (2020) Topology design of binary structures subjected to design-dependent thermal expansion and fluid pressure loads. Struct Multidiscip Optim 61(5):1877\u20131895. https:\/\/doi.org\/10.1007\/s00158-019-02443-z","journal-title":"Struct Multidiscip Optim"},{"key":"2282_CR11","doi-asserted-by":"publisher","first-page":"1393","DOI":"10.1016\/j.jmapro.2024.06.064","volume":"124","author":"E Kurkin","year":"2024","unstructured":"Kurkin E, Pioquinto JGQ, Kurkina E, Pechenik E, Chertykovtseva V (2024) Heuristic algorithm for the topological optimization of runner system for the thermoplastics injection molding. J Manuf Process 124:1393\u20131409. https:\/\/doi.org\/10.1016\/j.jmapro.2024.06.064","journal-title":"J Manuf Process"},{"issue":"7","key":"2282_CR12","doi-asserted-by":"publisher","DOI":"10.1007\/s00158-023-03618-5","volume":"66","author":"S Qian","year":"2023","unstructured":"Qian S, Lou S, Wang W, Yu M (2023) Multidisciplinary topology optimization design of cold plate for active phased antenna array. Struct Multidiscip Optim 66(7):155. https:\/\/doi.org\/10.1007\/s00158-023-03618-5","journal-title":"Struct Multidiscip Optim"},{"key":"2282_CR13","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2025.118109","volume":"444","author":"J Hu","year":"2025","unstructured":"Hu J, Li J, Chen X, Xu J, Huang X (2025) Multi-material topology optimization of vibro-acoustic structures with acoustic, poroelastic and elastic media under mass constraint. Comput Meth Appl Mech Eng 444:118109. https:\/\/doi.org\/10.1016\/j.cma.2025.118109","journal-title":"Comput Meth Appl Mech Eng"},{"key":"2282_CR14","doi-asserted-by":"publisher","DOI":"10.1016\/j.mechmachtheory.2022.104743","volume":"172","author":"S Koppen","year":"2022","unstructured":"Koppen S, Langelaar M, van Keulen F (2022) A simple and versatile topology optimization formulation for flexure synthesis. Mech Mach Theory 172:104743. https:\/\/doi.org\/10.1016\/j.mechmachtheory.2022.104743","journal-title":"Mech Mach Theory"},{"issue":"6545","key":"2282_CR15","doi-asserted-by":"publisher","DOI":"10.1126\/science.abg1487","volume":"372","author":"D Gu","year":"2021","unstructured":"Gu D, Shi X, Poprawe R, Bourell DL, Setchi R, Zhu J (2021) Material-structure-performance integrated laser-metal additive manufacturing. Science 372(6545):eabg1487. https:\/\/doi.org\/10.1126\/science.abg1487","journal-title":"Science"},{"issue":"1","key":"2282_CR16","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1007\/s00158-010-0591-x","volume":"44","author":"Z Liu","year":"2011","unstructured":"Liu Z, Gao Q, Zhang P, Xuan M, Wu Y (2011) Topology optimization of fluid channels with flow rate equality constraints. Struct Multidiscip Optim 44(1):31\u201337. https:\/\/doi.org\/10.1007\/s00158-010-0591-x","journal-title":"Struct Multidiscip Optim"},{"issue":"4","key":"2282_CR17","doi-asserted-by":"publisher","first-page":"455","DOI":"10.1007\/s00158-011-0646-7","volume":"44","author":"S Shojaee","year":"2011","unstructured":"Shojaee S, Mohammadian M (2011) Piecewise constant level set method for structural topology optimization with MBO type of projection. Struct Multidiscip Optim 44(4):455\u2013469. https:\/\/doi.org\/10.1007\/s00158-011-0646-7","journal-title":"Struct Multidiscip Optim"},{"issue":"6","key":"2282_CR18","doi-asserted-by":"publisher","first-page":"837","DOI":"10.1007\/s00466-008-0287-x","volume":"42","author":"Q Xia","year":"2008","unstructured":"Xia Q, Wang MY (2008) Topology optimization of thermoelastic structures using level set method. Comput Mech 42(6):837\u2013857. https:\/\/doi.org\/10.1007\/s00466-008-0287-x","journal-title":"Comput Mech"},{"key":"2282_CR19","doi-asserted-by":"publisher","first-page":"711","DOI":"10.1016\/j.cma.2016.07.018","volume":"310","author":"X Guo","year":"2016","unstructured":"Guo X, Zhang W, Zhang J, Yuan J (2016) Explicit structural topology optimization based on moving morphable components (MMC) with curved skeletons. Comput Meth Appl Mech Eng 310:711\u2013748. https:\/\/doi.org\/10.1016\/j.cma.2016.07.018","journal-title":"Comput Meth Appl Mech Eng"},{"key":"2282_CR20","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.cma.2016.06.027","volume":"310","author":"Y Zhou","year":"2016","unstructured":"Zhou Y, Zhang W, Zhu J, Xu Z (2016) Feature-driven topology optimization method with signed distance function. Comput Methods Appl Mech Eng 310:1\u201332. https:\/\/doi.org\/10.1016\/j.cma.2016.06.027","journal-title":"Comput Methods Appl Mech Eng"},{"issue":"1","key":"2282_CR21","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-020-16599-6","volume":"11","author":"M Baandrup","year":"2020","unstructured":"Baandrup M, Sigmund O, Polk H, Aage N (2020) Closing the gap towards super-long suspension bridges using computational morphogenesis. Nat Commun 11(1):2735. https:\/\/doi.org\/10.1038\/s41467-020-16599-6","journal-title":"Nat Commun"},{"issue":"9","key":"2282_CR22","doi-asserted-by":"publisher","first-page":"635","DOI":"10.1007\/s004190050248","volume":"69","author":"MP Bends\u00f8e","year":"1999","unstructured":"Bends\u00f8e MP, Sigmund O (1999) Material interpolation schemes in topology optimization. Arch Appl Mech 69(9):635\u2013654. https:\/\/doi.org\/10.1007\/s004190050248","journal-title":"Arch Appl Mech"},{"issue":"3","key":"2282_CR23","doi-asserted-by":"publisher","first-page":"393","DOI":"10.1007\/s00466-008-0312-0","volume":"43","author":"X Huang","year":"2009","unstructured":"Huang X, Xie YM (2009) Bi-directional evolutionary topology optimization of continuum structures with one or multiple materials. Comput Mech 43(3):393\u2013401. https:\/\/doi.org\/10.1007\/s00466-008-0312-0","journal-title":"Comput Mech"},{"issue":"4","key":"2282_CR24","doi-asserted-by":"publisher","first-page":"2101","DOI":"10.1007\/s00158-020-02598-0","volume":"62","author":"R Picelli","year":"2020","unstructured":"Picelli R, Ranjbarzadeh S, Sivapuram R, Gioria RS, Silva ECN (2020) Topology optimization of binary structures under design-dependent fluid-structure interaction loads. Struct Multidiscip Optim 62(4):2101\u20132116. https:\/\/doi.org\/10.1007\/s00158-020-02598-0","journal-title":"Struct Multidiscip Optim"},{"key":"2282_CR25","doi-asserted-by":"publisher","DOI":"10.1016\/j.advengsoft.2020.102921","volume":"150","author":"Y Fu","year":"2020","unstructured":"Fu Y, Rolfe B, Chiu LNS, Wang Y, Huang X, Ghabraie K (2020) SEMDOT: smooth-edged material distribution for optimizing topology algorithm. Adv Eng Softw 150:102921. https:\/\/doi.org\/10.1016\/j.advengsoft.2020.102921","journal-title":"Adv Eng Softw"},{"key":"2282_CR26","doi-asserted-by":"publisher","DOI":"10.1016\/j.engstruct.2020.110330","volume":"208","author":"X Huang","year":"2020","unstructured":"Huang X (2020) Smooth topological design of structures using the floating projection. Eng Struct 208:110330. https:\/\/doi.org\/10.1016\/j.engstruct.2020.110330","journal-title":"Eng Struct"},{"key":"2282_CR27","doi-asserted-by":"publisher","DOI":"10.1016\/j.advengsoft.2020.102942","volume":"151","author":"X Huang","year":"2021","unstructured":"Huang X (2021) On smooth or 0\/1 designs of the fixed-mesh element-based topology optimization. Adv Eng Softw 151:102942. https:\/\/doi.org\/10.1016\/j.advengsoft.2020.102942","journal-title":"Adv Eng Softw"},{"key":"2282_CR28","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2022.115444","volume":"399","author":"X Huang","year":"2022","unstructured":"Huang X, Li W (2022) Three-field floating projection topology optimization of continuum structures. Comput Methods Appl Mech Eng 399:115444. https:\/\/doi.org\/10.1016\/j.cma.2022.115444","journal-title":"Comput Methods Appl Mech Eng"},{"issue":"4","key":"2282_CR29","doi-asserted-by":"publisher","first-page":"1637","DOI":"10.1007\/s00158-019-02442-0","volume":"61","author":"P Kumar","year":"2020","unstructured":"Kumar P, Frouws JS, Langelaar M (2020) Topology optimization of fluidic pressure-loaded structures and compliant mechanisms using the Darcy method. Struct Multidiscip Optim 61(4):1637\u20131655. https:\/\/doi.org\/10.1007\/s00158-019-02442-0","journal-title":"Struct Multidiscip Optim"},{"issue":"4","key":"2282_CR30","doi-asserted-by":"publisher","DOI":"10.1007\/s00158-023-03533-9","volume":"66","author":"P Kumar","year":"2023","unstructured":"Kumar P (2023) TOPress: a MATLAB implementation for topology optimization of structures subjected to design-dependent pressure loads. Struct Multidiscip Optim 66(4):97. https:\/\/doi.org\/10.1007\/s00158-023-03533-9","journal-title":"Struct Multidiscip Optim"},{"key":"2282_CR31","doi-asserted-by":"publisher","DOI":"10.2514\/6.2004-452610.2514\/6.2004-4526","author":"X Gao","year":"2004","unstructured":"Gao X, Zhao K, Gu Y (2004) Topology optimization with design-dependent loads by level set approach. Multidisc Anal Optim Conf. https:\/\/doi.org\/10.2514\/6.2004-452610.2514\/6.2004-4526","journal-title":"Multidisc Anal Optim Conf"},{"key":"2282_CR32","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1016\/j.cma.2014.09.022","volume":"283","author":"Q Xia","year":"2015","unstructured":"Xia Q, Wang MY, Shi T (2015) Topology optimization with pressure load through a level set method. Comput Meth Appl Mech Eng 283:177\u2013195. https:\/\/doi.org\/10.1016\/j.cma.2014.09.022","journal-title":"Comput Meth Appl Mech Eng"},{"issue":"4","key":"2282_CR33","doi-asserted-by":"publisher","first-page":"1313","DOI":"10.1007\/s00158-019-02339-y","volume":"60","author":"R Picelli","year":"2019","unstructured":"Picelli R, Neofytou A, Kim HA (2019) Topology optimization for design-dependent hydrostatic pressure loading via the level-set method. Struct Multidiscip Optim 60(4):1313\u20131326. https:\/\/doi.org\/10.1007\/s00158-019-02339-y","journal-title":"Struct Multidiscip Optim"},{"key":"2282_CR34","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2020.113387","volume":"372","author":"J Hu","year":"2020","unstructured":"Hu J, Yao S, Huang X (2020) Topology optimization of dynamic acoustic\u2013mechanical structures using the ersatz material model. Comput Methods Appl Mech Eng 372:113387. https:\/\/doi.org\/10.1016\/j.cma.2020.113387","journal-title":"Comput Methods Appl Mech Eng"},{"issue":"1","key":"2282_CR35","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1016\/S0168-874X(00)00021-4","volume":"37","author":"B Chen","year":"2001","unstructured":"Chen B, Kikuchi N (2001) Topology optimization with design-dependent loads. Finite Elem Anal Des 37(1):57\u201370. https:\/\/doi.org\/10.1016\/S0168-874X(00)00021-4","journal-title":"Finite Elem Anal Des"},{"issue":"13\u201316","key":"2282_CR36","doi-asserted-by":"publisher","first-page":"1874","DOI":"10.1016\/j.cma.2006.09.021","volume":"196","author":"O Sigmund","year":"2007","unstructured":"Sigmund O, Clausen PM (2007) Topology optimization using a mixed formulation: an alternative way to solve pressure load problems. Comput Meth Appl Mech Eng 196(13\u201316):1874\u20131889. https:\/\/doi.org\/10.1016\/j.cma.2006.09.021","journal-title":"Comput Meth Appl Mech Eng"},{"issue":"6","key":"2282_CR37","doi-asserted-by":"publisher","first-page":"535","DOI":"10.1007\/s00158-008-0317-5","volume":"38","author":"B Zheng","year":"2009","unstructured":"Zheng B, Chang C, Gea HC (2009) Topology optimization with design-dependent pressure loading. Struct Multidiscip Optim 38(6):535\u2013543. https:\/\/doi.org\/10.1007\/s00158-008-0317-5","journal-title":"Struct Multidiscip Optim"},{"key":"2282_CR38","doi-asserted-by":"publisher","DOI":"10.1016\/j.mechmachtheory.2022.104871","volume":"174","author":"P Kumar","year":"2022","unstructured":"Kumar P, Langelaar M (2022) Topological synthesis of fluidic pressure-actuated robust compliant mechanisms. Mech Mach Theory 174:104871. https:\/\/doi.org\/10.1016\/j.mechmachtheory.2022.104871","journal-title":"Mech Mach Theory"},{"issue":"9","key":"2282_CR39","doi-asserted-by":"publisher","first-page":"2205","DOI":"10.1002\/nme.6618","volume":"122","author":"P Kumar","year":"2021","unstructured":"Kumar P, Langelaar M (2021) On topology optimization of design\u2010dependent pressure\u2010loaded three\u2010dimensional structures and compliant mechanisms. Int J Numer Methods Eng 122(9):2205\u20132220. https:\/\/doi.org\/10.1002\/nme.6618","journal-title":"Int J Numer Methods Eng"},{"issue":"1","key":"2282_CR40","doi-asserted-by":"publisher","first-page":"459","DOI":"10.1007\/s11081-023-09811-1","volume":"25","author":"G Oheneba Agyekum","year":"2024","unstructured":"Oheneba Agyekum G, Cang\u00e9mi L, Jouve F (2024) Homogenization based topology optimization of fluid-pressure loaded structures using the Biot-Darcy Model. Optim Eng 25(1):459\u2013490. https:\/\/doi.org\/10.1007\/s11081-023-09811-1","journal-title":"Optim Eng"},{"issue":"6","key":"2282_CR41","doi-asserted-by":"publisher","first-page":"901","DOI":"10.1007\/s10338-022-00351-2","volume":"35","author":"H Huang","year":"2022","unstructured":"Huang H, Hu J, Liu S, Liu Y (2022) A thermal-solid\u2013fluid method for topology optimization of structures with design-dependent pressure load. Acta Mech Solida Sin 35(6):901\u2013912. https:\/\/doi.org\/10.1007\/s10338-022-00351-2","journal-title":"Acta Mech Solida Sin"},{"issue":"9","key":"2282_CR42","doi-asserted-by":"publisher","first-page":"1049","DOI":"10.1002\/nme.1900","volume":"70","author":"GH Yoon","year":"2007","unstructured":"Yoon GH, Jensen JS, Sigmund O (2007) Topology optimization of acoustic-structure interaction problems using a mixed finite element formulation. Int J Numer Methods Eng 70(9):1049\u20131075. https:\/\/doi.org\/10.1002\/nme.1900","journal-title":"Int J Numer Methods Eng"},{"issue":"2","key":"2282_CR43","doi-asserted-by":"publisher","first-page":"779","DOI":"10.1007\/s00158-019-02236-4","volume":"60","author":"CB Dilgen","year":"2019","unstructured":"Dilgen CB, Dilgen SB, Aage N, Jensen JS (2019) Topology optimization of acoustic mechanical interaction problems: a comparative review. Struct Multidiscip Optim 60(2):779\u2013801. https:\/\/doi.org\/10.1007\/s00158-019-02236-4","journal-title":"Struct Multidiscip Optim"},{"issue":"6","key":"2282_CR44","doi-asserted-by":"publisher","first-page":"1135","DOI":"10.1007\/s00158-015-1272-6","volume":"52","author":"P Kumar","year":"2015","unstructured":"Kumar P, Saxena A (2015) On topology optimization with embedded boundary resolution and smoothing. Struct Multidiscip Optim 52(6):1135\u20131159. https:\/\/doi.org\/10.1007\/s00158-015-1272-6","journal-title":"Struct Multidiscip Optim"},{"issue":"5","key":"2282_CR45","doi-asserted-by":"publisher","first-page":"1641","DOI":"10.1007\/s00158-016-1597-9","volume":"55","author":"G Yi","year":"2017","unstructured":"Yi G, Kim NH (2017) Identifying boundaries of topology optimization results using basic parametric features. Struct Multidiscip Optim 55(5):1641\u20131654. https:\/\/doi.org\/10.1007\/s00158-016-1597-9","journal-title":"Struct Multidiscip Optim"},{"issue":"4","key":"2282_CR46","doi-asserted-by":"publisher","first-page":"2581","DOI":"10.1007\/s00366-023-01936-2","volume":"40","author":"W Li","year":"2024","unstructured":"Li W, Hu J, Lu G, Huang X (2024) Topology optimization of acoustic bandgap crystals for topological insulators. Eng Comput 40(4):2581\u20132594. https:\/\/doi.org\/10.1007\/s00366-023-01936-2","journal-title":"Eng Comput"},{"issue":"10","key":"2282_CR47","doi-asserted-by":"publisher","first-page":"1324","DOI":"10.1080\/0305215X.2014.963069","volume":"47","author":"R Picelli","year":"2015","unstructured":"Picelli R, Vicente WM, Pavanello R (2015) Bi-directional evolutionary structural optimization for design-dependent fluid pressure loading problems. Eng Optim 47(10):1324\u20131342. https:\/\/doi.org\/10.1080\/0305215X.2014.963069","journal-title":"Eng Optim"},{"issue":"2","key":"2282_CR48","doi-asserted-by":"publisher","first-page":"309","DOI":"10.1007\/s10999-022-09591-z","volume":"18","author":"M Gon\u00e7alves","year":"2022","unstructured":"Gon\u00e7alves M, Dias-de-Oliveira JA, Valente R (2022) A new bidirectional algorithm for topology optimization of thermoelastic structural problems. Int J Mech Mater Des 18(2):309\u2013325. https:\/\/doi.org\/10.1007\/s10999-022-09591-z","journal-title":"Int J Mech Mater Des"},{"key":"2282_CR49","doi-asserted-by":"publisher","DOI":"10.1016\/j.engstruct.2023.116843","volume":"295","author":"J Hu","year":"2023","unstructured":"Hu J, Li W, Li J, Chen X, Yao S, Huang X (2023) Topology optimization of porous structures by considering acoustic and mechanical characteristics. Eng Struct 295:116843. https:\/\/doi.org\/10.1016\/j.engstruct.2023.116843","journal-title":"Eng Struct"},{"issue":"13","key":"2282_CR50","doi-asserted-by":"publisher","DOI":"10.1002\/nme.7480","volume":"125","author":"A Soares Da Costa Azev\u00eado","year":"2024","unstructured":"Soares Da Costa Azev\u00eado A, Li H, Ishida N, Siqueira LO, Cortez RL, Nelli Silva EC, Nishiwaki S, Picelli R (2024) Body\u2010fitted topology optimization via integer linear programming using surface capturing techniques. Int J Numer Methods Eng 125(13):e7480. https:\/\/doi.org\/10.1002\/nme.7480","journal-title":"Int J Numer Methods Eng"},{"issue":"2","key":"2282_CR51","doi-asserted-by":"publisher","first-page":"120","DOI":"10.1007\/s001580050176","volume":"21","author":"O Sigmund","year":"2001","unstructured":"Sigmund O (2001) A 99 line topology optimization code written in Matlab. Struct Multidiscip Optim 21(2):120\u2013127. https:\/\/doi.org\/10.1007\/s001580050176","journal-title":"Struct Multidiscip Optim"},{"issue":"5","key":"2282_CR52","doi-asserted-by":"publisher","first-page":"725","DOI":"10.1007\/s00158-010-0527-5","volume":"42","author":"T Gao","year":"2010","unstructured":"Gao T, Zhang W (2010) Topology optimization involving thermo-elastic stress loads. Struct Multidiscip Optim 42(5):725\u2013738. https:\/\/doi.org\/10.1007\/s00158-010-0527-5","journal-title":"Struct Multidiscip Optim"},{"key":"2282_CR53","doi-asserted-by":"publisher","DOI":"10.1080\/0305215X.2025.2466825","author":"J Zhou","year":"2025","unstructured":"Zhou J, Wang Y, Chiu LNS, Ghabraie K (2025) On the suitability of simplified sensitivity estimation for partial elements in topology optimization. Eng Optimiz. https:\/\/doi.org\/10.1080\/0305215X.2025.2466825","journal-title":"Eng Optimiz"},{"issue":"2","key":"2282_CR54","doi-asserted-by":"publisher","first-page":"359","DOI":"10.1002\/nme.1620240207","volume":"24","author":"K Svanberg","year":"1987","unstructured":"Svanberg K (1987) The method of moving asymptotes-a new method for structural optimization. Int J Numer Methods Eng 24(2):359\u2013373. https:\/\/doi.org\/10.1002\/nme.1620240207","journal-title":"Int J Numer Methods Eng"},{"key":"2282_CR55","doi-asserted-by":"publisher","DOI":"10.1016\/j.finel.2021.103650","volume":"199","author":"J Hu","year":"2022","unstructured":"Hu J, Yao S, Huang X (2022) Topological design of sandwich structures filling with poroelastic materials for sound insulation. Finite Elem Anal Des 199:103650. https:\/\/doi.org\/10.1016\/j.finel.2021.103650","journal-title":"Finite Elem Anal Des"},{"key":"2282_CR56","unstructured":"Fu Y, Rolfe B, Chiu L, Wang Y, Huang X, Ghabraie K (2020) Topology optimization of continuum structures using smooth boundary representation. The 13th World Congress of Structural and Multidisciplinary Optimization. https:\/\/www.researchgate.net\/publication\/339228395"},{"key":"2282_CR57","doi-asserted-by":"publisher","DOI":"10.1016\/j.compstruc.2020.106213","volume":"231","author":"Y Fu","year":"2020","unstructured":"Fu Y, Rolfe B, Chiu LNS, Wang Y, Huang X, Ghabraie K (2020) Smooth topological design of 3D continuum structures using elemental volume fractions. Comput Struct 231:106213. https:\/\/doi.org\/10.1016\/j.compstruc.2020.106213","journal-title":"Comput Struct"},{"issue":"6","key":"2282_CR58","doi-asserted-by":"publisher","first-page":"3071","DOI":"10.1007\/s00158-020-02654-9","volume":"62","author":"Z Zhang","year":"2020","unstructured":"Zhang Z, Zhao Y, Du B, Chen X, Yao W (2020) Topology optimization of hyperelastic structures using a modified evolutionary topology optimization method. Struct Multidiscip Optim 62(6):3071\u20133088. https:\/\/doi.org\/10.1007\/s00158-020-02654-9","journal-title":"Struct Multidiscip Optim"},{"issue":"4\u20135","key":"2282_CR59","doi-asserted-by":"publisher","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(4\u20135):401\u2013424. https:\/\/doi.org\/10.1007\/s00158-006-0087-x","journal-title":"Struct Multidiscip Optim"},{"issue":"4","key":"2282_CR60","doi-asserted-by":"publisher","DOI":"10.1007\/s00158-025-04009-8","volume":"68","author":"J Zhou","year":"2025","unstructured":"Zhou J, Wang Y, Chiu LNS, Ghabraie K (2025) Increasing boundary resolution in topology optimization using a novel formulation of partial elements. Struct Multidiscip Optim 68(4):71. https:\/\/doi.org\/10.1007\/s00158-025-04009-8","journal-title":"Struct Multidiscip Optim"},{"key":"2282_CR61","doi-asserted-by":"publisher","DOI":"10.1016\/j.apacoust.2024.110347","volume":"228","author":"J Xu","year":"2025","unstructured":"Xu J, Hu J, Li J, Li Y, Gan N, Tao M, Cao W (2025) Smooth topological design of lightweight vibro-acoustic sandwich structures by maximizing sound transmission loss. Appl Acoust 228:110347. https:\/\/doi.org\/10.1016\/j.apacoust.2024.110347","journal-title":"Appl Acoust"},{"issue":"2","key":"2282_CR62","doi-asserted-by":"publisher","first-page":"175","DOI":"10.5194\/ms-2-175-2011","volume":"2","author":"BS Lazarov","year":"2011","unstructured":"Lazarov BS, Schevenels M, Sigmund O (2011) Robust design of large-displacement compliant mechanisms. Mechanical sciences (G\u00f6ttingen) 2(2):175\u2013182. https:\/\/doi.org\/10.5194\/ms-2-175-2011","journal-title":"Mechanical sciences (G\u00f6ttingen)"}],"container-title":["Engineering with Computers"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00366-026-02282-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00366-026-02282-9","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00366-026-02282-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,24]],"date-time":"2026-04-24T09:00:35Z","timestamp":1777021235000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00366-026-02282-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,2]]},"references-count":62,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2026,2]]}},"alternative-id":["2282"],"URL":"https:\/\/doi.org\/10.1007\/s00366-026-02282-9","relation":{},"ISSN":["0177-0667","1435-5663"],"issn-type":[{"value":"0177-0667","type":"print"},{"value":"1435-5663","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,2]]},"assertion":[{"value":"2 August 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 January 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 February 2026","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":"Competing interest"}}],"article-number":"41"}}