{"title":"基于矩平方和层次的框架结构整体拓扑刚度优化","authors":"M. Tyburec, J. Zeman, M. Kružík, D. Henrion","doi":"10.21495/5896-3-492","DOIUrl":null,"url":null,"abstract":": This contribution develops an efficient formulation for the topology optimization of frame structures with fixed-aspect-ratio cross-sections, solvable to global optimality by the moment-sum-of-squares hierarchy. While the hierarchy generates a sequence of non-decreasing lower-bounds, we develop a sequence of feasible upper-bounds, allowing to assess the optimized design quality in each relaxation. Finally, these bounds provide a means of establishing a new sufficiency condition of global ε-optimality.","PeriodicalId":383836,"journal":{"name":"Engineering Mechanics 2020","volume":"222 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"GLOBAL TOPOLOGY STIFFNESS OPTIMIZATION OF FRAME STRUCTURES BY MOMENT-SUM-OF-SQUARES HIERARCHY\",\"authors\":\"M. Tyburec, J. Zeman, M. Kružík, D. Henrion\",\"doi\":\"10.21495/5896-3-492\",\"DOIUrl\":null,\"url\":null,\"abstract\":\": This contribution develops an efficient formulation for the topology optimization of frame structures with fixed-aspect-ratio cross-sections, solvable to global optimality by the moment-sum-of-squares hierarchy. While the hierarchy generates a sequence of non-decreasing lower-bounds, we develop a sequence of feasible upper-bounds, allowing to assess the optimized design quality in each relaxation. Finally, these bounds provide a means of establishing a new sufficiency condition of global ε-optimality.\",\"PeriodicalId\":383836,\"journal\":{\"name\":\"Engineering Mechanics 2020\",\"volume\":\"222 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Engineering Mechanics 2020\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.21495/5896-3-492\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Engineering Mechanics 2020","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.21495/5896-3-492","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
GLOBAL TOPOLOGY STIFFNESS OPTIMIZATION OF FRAME STRUCTURES BY MOMENT-SUM-OF-SQUARES HIERARCHY
: This contribution develops an efficient formulation for the topology optimization of frame structures with fixed-aspect-ratio cross-sections, solvable to global optimality by the moment-sum-of-squares hierarchy. While the hierarchy generates a sequence of non-decreasing lower-bounds, we develop a sequence of feasible upper-bounds, allowing to assess the optimized design quality in each relaxation. Finally, these bounds provide a means of establishing a new sufficiency condition of global ε-optimality.
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