{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,18]],"date-time":"2025-10-18T20:32:22Z","timestamp":1760819542428},"reference-count":31,"publisher":"Elsevier BV","issue":"1","license":[{"start":{"date-parts":[[1991,5,1]],"date-time":"1991-05-01T00:00:00Z","timestamp":673056000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computer Methods in Applied Mechanics and Engineering"],"published-print":{"date-parts":[[1991,5]]},"DOI":"10.1016\/0045-7825(91)90144-u","type":"journal-article","created":{"date-parts":[[2003,3,14]],"date-time":"2003-03-14T09:47:03Z","timestamp":1047635223000},"page":"15-34","source":"Crossref","is-referenced-by-count":42,"title":["Integrated topology and boundary shape optimization of 2-D solids"],"prefix":"10.1016","volume":"87","author":[{"given":"Martin Philip","family":"Bends\u00f8e","sequence":"first","affiliation":[]},{"given":"Helder Carrico","family":"Rodrigues","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/0045-7825(91)90144-U_BIB1","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1016\/0045-7825(86)90072-1","article-title":"Structural shape optimization \u2014 A survey","volume":"57","author":"Haftka","year":"1986","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"key":"10.1016\/0045-7825(91)90144-U_BIB2","doi-asserted-by":"crossref","first-page":"985","DOI":"10.1016\/0045-7949(86)90307-X","article-title":"Shape optimization of structures: A literature survey","volume":"24","author":"Ding","year":"1986","journal-title":"Comput. & Structures"},{"key":"10.1016\/0045-7825(91)90144-U_BIB3","first-page":"183","article-title":"Optimal design in elasticity and plasticity","volume":"2","author":"Kohn","year":"1986","journal-title":"Internat. J. Numer. Methods Engrg."},{"key":"10.1016\/0045-7825(91)90144-U_BIB4_1","first-page":"1","article-title":"Optimal design and relaxation of variational problems","volume":"39","author":"Kohn","year":"1986","journal-title":"Comm. Pure Appl. Math."},{"key":"10.1016\/0045-7825(91)90144-U_BIB4_2","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1002\/cpa.3160390202","article-title":"Optimal design and relaxation of variational problems","volume":"39","author":"Kohn","year":"1986","journal-title":"Comm. Pure Appl. Math."},{"key":"10.1016\/0045-7825(91)90144-U_BIB4_3","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1002\/cpa.3160390305","article-title":"Optimal design and relaxation of variational problems","volume":"39","author":"Kohn","year":"1986","journal-title":"Comm. Pure Appl. Math."},{"key":"10.1016\/0045-7825(91)90144-U_BIB5","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1016\/0045-7825(88)90086-2","article-title":"Generating optimal topologies in structural design using a homogenization method","volume":"71","author":"Bends\u00f8e","year":"1988","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"key":"10.1016\/0045-7825(91)90144-U_BIB6","series-title":"Proc. GAMM \u2014 Seminar on Discretization Methods and Structural Optimization \u2014 Procedures and Applications","first-page":"40","article-title":"Shape optimization as a discrete optimization problem \u2014 Solution procedures using continuous approximations","volume":"Vol. 48","author":"Bends\u00f8e","year":"1988"},{"key":"10.1016\/0045-7825(91)90144-U_BIB7","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1016\/0045-7825(88)90164-8","article-title":"Shape optimal design of elastic bodies using a mixed variational formulation","volume":"69","author":"Rodrigues","year":"1988","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"key":"10.1016\/0045-7825(91)90144-U_BIB8","doi-asserted-by":"crossref","DOI":"10.1016\/0045-7825(88)90164-8","article-title":"Shape optimal design of elastic bodies using a mixed variational formulation","author":"Rodrigues","year":"1988"},{"key":"10.1016\/0045-7825(91)90144-U_BIB9","doi-asserted-by":"crossref","first-page":"1134","DOI":"10.1115\/1.3167196","article-title":"On structural optimization","volume":"50","author":"Olhoff","year":"1983","journal-title":"J. Appl. Mech."},{"key":"10.1016\/0045-7825(91)90144-U_BIB10","series-title":"Homogenization and Effective Moduli of Materials and Media, The IMA Volumes on Mathematics and Its Applications","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/978-1-4613-8646-9_1","article-title":"Generalized plate models and optimal design","author":"Bends\u00f8e","year":"1986"},{"key":"10.1016\/0045-7825(91)90144-U_BIB11","series-title":"Asymptotic Analysis for Periodic Structures","author":"Bensoussan","year":"1978"},{"key":"10.1016\/0045-7825(91)90144-U_BIB12","series-title":"Proceedings 14th IUTAM Congress","first-page":"119","article-title":"Analyse fonctionelle et mechanique des millieux continus. Application \u00e0 l'\u00e9tude des materiaux composites elastiques a structure periodique-homogeneisation","author":"Duvaut","year":"1976"},{"key":"10.1016\/0045-7825(91)90144-U_BIB13","article-title":"Non-homogeneous media and vibration theory","volume":"127","author":"Sanchez-Palencia","year":"1980"},{"key":"10.1016\/0045-7825(91)90144-U_BIB14","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1007\/BF01650949","article-title":"Shape design as a material distribution problem","volume":"1","author":"Bends\u00f8e","year":"1989","journal-title":"Structural Optim."},{"key":"10.1016\/0045-7825(91)90144-U_BIB15","series-title":"Composite Material Response: Constitutive Relations and Damage Mechanisms","first-page":"155","article-title":"Recent progress in the mathematical modelling of composite materials","author":"Kohn","year":"1988"},{"key":"10.1016\/0045-7825(91)90144-U_BIB16","doi-asserted-by":"crossref","first-page":"1216","DOI":"10.1137\/0147082","article-title":"Optimal bounds and microgeometries for elastic twophase composites","volume":"47","author":"Avellaneda","year":"1987","journal-title":"SIAM J. Appl. Math."},{"key":"10.1016\/0045-7825(91)90144-U_BIB17","series-title":"Variational Methods in Elasticity and Plasticity","author":"Washizu","year":"1983"},{"key":"10.1016\/0045-7825(91)90144-U_BIB18","article-title":"Studies on optimal shape design problems","volume":"41","author":"Murat","year":"1976"},{"key":"10.1016\/0045-7825(91)90144-U_BIB19","first-page":"1089","article-title":"Material derivative (or speed) method for shape optimization","volume":"II","author":"Zolesio","year":"1981"},{"key":"10.1016\/0045-7825(91)90144-U_BIB20","series-title":"Design Sensitivity Analysis of Structural Systems","author":"Haug","year":"1986"},{"key":"10.1016\/0045-7825(91)90144-U_BIB21","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1016\/0020-7683(84)90041-6","article-title":"An interpretation for min-max structural design problems including a method for relaxing constraints","volume":"20","author":"Taylor","year":"1984","journal-title":"Internat. J. Solids and Structures"},{"key":"10.1016\/0045-7825(91)90144-U_BIB22","article-title":"Shape optimization and free boundary value problems with grid adaptation","author":"Chung","year":"1985"},{"key":"10.1016\/0045-7825(91)90144-U_BIB23","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1016\/0045-7825(86)90071-X","article-title":"Adaptive finite element methods for shape optimization of linearly elastic structures","volume":"57","author":"Kikuchi","year":"1986","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"key":"10.1016\/0045-7825(91)90144-U_BIB24","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1016\/0045-7825(86)90089-7","article-title":"Adaptive grid-design methods for finite element analysis","volume":"55","author":"Kikuchi","year":"1986","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"key":"10.1016\/0045-7825(91)90144-U_BIB25","series-title":"Numerical Grid Generation, Foundations and Applications","author":"Thompson","year":"1985"},{"key":"10.1016\/0045-7825(91)90144-U_BIB26","doi-asserted-by":"crossref","first-page":"342","DOI":"10.1016\/0021-9991(82)90020-1","article-title":"Adaptive zoning for singular problems in two dimensions","volume":"46","author":"Blackbill","year":"1982","journal-title":"J. Comput. Phys."},{"key":"10.1016\/0045-7825(91)90144-U_BIB27","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1007\/BF01637666","article-title":"An optimal orientation of orthotropic materials","volume":"1","author":"Pedersen","year":"1989","journal-title":"Structural Optim."},{"key":"10.1016\/0045-7825(91)90144-U_BIB28","series-title":"Numerical Methods in Extremal Problems","author":"Pshenichny","year":"1978"},{"key":"10.1016\/0045-7825(91)90144-U_BIB29","series-title":"Proc. GAMM \u2014 Seminar on Discretization Methods and Structural Optimization \u2014 Procedures and Applications","first-page":"284","article-title":"Interactive shape optimization with design elements","volume":"Vol. 48","author":"Rasmussen","year":"1988"}],"container-title":["Computer Methods in Applied Mechanics and Engineering"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:004578259190144U?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:004578259190144U?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2019,3,26]],"date-time":"2019-03-26T15:59:54Z","timestamp":1553615994000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/004578259190144U"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1991,5]]},"references-count":31,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1991,5]]}},"alternative-id":["004578259190144U"],"URL":"https:\/\/doi.org\/10.1016\/0045-7825(91)90144-u","relation":{},"ISSN":["0045-7825"],"issn-type":[{"value":"0045-7825","type":"print"}],"subject":[],"published":{"date-parts":[[1991,5]]}}}