{"title":"关于形状优化的一些最新进展","authors":"Grégoire Allaire , Antoine Henrot","doi":"10.1016/S1620-7742(01)01349-6","DOIUrl":null,"url":null,"abstract":"<div><p>In this Note we give a short review on recent developements in shape optimization. We explain how the generic non-existence of solutions can be circumvent. Either one can impose some geometric restrictions on the class of admissible domains to get existence (we then explain how to write the usual optimality conditions), or generalized designs are allowed which leads to relaxation by homogenization techniques (we thus obtain topology optimization methods).</p></div>","PeriodicalId":100302,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series IIB - Mechanics","volume":"329 5","pages":"Pages 383-396"},"PeriodicalIF":0.0000,"publicationDate":"2001-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1620-7742(01)01349-6","citationCount":"36","resultStr":"{\"title\":\"On some recent advances in shape optimization\",\"authors\":\"Grégoire Allaire , Antoine Henrot\",\"doi\":\"10.1016/S1620-7742(01)01349-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this Note we give a short review on recent developements in shape optimization. We explain how the generic non-existence of solutions can be circumvent. Either one can impose some geometric restrictions on the class of admissible domains to get existence (we then explain how to write the usual optimality conditions), or generalized designs are allowed which leads to relaxation by homogenization techniques (we thus obtain topology optimization methods).</p></div>\",\"PeriodicalId\":100302,\"journal\":{\"name\":\"Comptes Rendus de l'Académie des Sciences - Series IIB - Mechanics\",\"volume\":\"329 5\",\"pages\":\"Pages 383-396\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2001-05-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/S1620-7742(01)01349-6\",\"citationCount\":\"36\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Comptes Rendus de l'Académie des Sciences - Series IIB - Mechanics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S1620774201013496\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Comptes Rendus de l'Académie des Sciences - Series IIB - Mechanics","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1620774201013496","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
In this Note we give a short review on recent developements in shape optimization. We explain how the generic non-existence of solutions can be circumvent. Either one can impose some geometric restrictions on the class of admissible domains to get existence (we then explain how to write the usual optimality conditions), or generalized designs are allowed which leads to relaxation by homogenization techniques (we thus obtain topology optimization methods).
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