Zepeng Wen , Qiong Pan , Xiaoya Zhai , Hongmei Kang , Falai Chen
{"title":"基于 PHT-样条线的壳体结构自适应等值拓扑优化","authors":"Zepeng Wen , Qiong Pan , Xiaoya Zhai , Hongmei Kang , Falai Chen","doi":"10.1016/j.compstruc.2024.107565","DOIUrl":null,"url":null,"abstract":"<div><div>This paper proposes an adaptive isogeometric topology optimization framework for shell structures by utilizing a continuous density field represented as Polynomial splines over Hierarchical T-meshes (PHT-splines). This framework ensures an exact representation of shell structures, eliminating the geometric inaccuracies commonly associated with topology optimization. In the meanwhile, the meshes used for design and analysis are refined adaptively and locally along the density boundary to achieve a smooth material layout with reduced degrees of freedom (DOF). The adaptive sensitivity filter is tailored to the characteristics of PHT-splines, where the filter radius is determined automatically and adaptively, without the need to specify parameters in advance. Numerical experiments conducted on various shell structures validate the efficacy of the proposed adaptive framework. In comparison with isogeometric topology optimization based on non-adaptive cases (i.e. B-splines), the proposed adaptive framework demonstrates a notable enhancement in computational efficiency, with a <span><math><mn>50</mn><mtext>%</mtext><mo>−</mo><mn>80</mn><mtext>%</mtext></math></span> reduction in running time and a <span><math><mn>30</mn><mtext>%</mtext><mo>−</mo><mn>60</mn><mtext>%</mtext></math></span> reduction in DOF. Additionally, we offer a detailed comparison between PHT-splines and other locally refinable splines in the context of shell topology optimization. Numerical experiments exhibit that the efficient and localized refinement capability of PHT-splines provides advantages in both computational efficiency and structural performance for topology optimization.</div></div>","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":"305 ","pages":"Article 107565"},"PeriodicalIF":4.4000,"publicationDate":"2024-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Adaptive isogeometric topology optimization of shell structures based on PHT-splines\",\"authors\":\"Zepeng Wen , Qiong Pan , Xiaoya Zhai , Hongmei Kang , Falai Chen\",\"doi\":\"10.1016/j.compstruc.2024.107565\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>This paper proposes an adaptive isogeometric topology optimization framework for shell structures by utilizing a continuous density field represented as Polynomial splines over Hierarchical T-meshes (PHT-splines). This framework ensures an exact representation of shell structures, eliminating the geometric inaccuracies commonly associated with topology optimization. In the meanwhile, the meshes used for design and analysis are refined adaptively and locally along the density boundary to achieve a smooth material layout with reduced degrees of freedom (DOF). The adaptive sensitivity filter is tailored to the characteristics of PHT-splines, where the filter radius is determined automatically and adaptively, without the need to specify parameters in advance. Numerical experiments conducted on various shell structures validate the efficacy of the proposed adaptive framework. In comparison with isogeometric topology optimization based on non-adaptive cases (i.e. B-splines), the proposed adaptive framework demonstrates a notable enhancement in computational efficiency, with a <span><math><mn>50</mn><mtext>%</mtext><mo>−</mo><mn>80</mn><mtext>%</mtext></math></span> reduction in running time and a <span><math><mn>30</mn><mtext>%</mtext><mo>−</mo><mn>60</mn><mtext>%</mtext></math></span> reduction in DOF. Additionally, we offer a detailed comparison between PHT-splines and other locally refinable splines in the context of shell topology optimization. Numerical experiments exhibit that the efficient and localized refinement capability of PHT-splines provides advantages in both computational efficiency and structural performance for topology optimization.</div></div>\",\"PeriodicalId\":50626,\"journal\":{\"name\":\"Computers & Structures\",\"volume\":\"305 \",\"pages\":\"Article 107565\"},\"PeriodicalIF\":4.4000,\"publicationDate\":\"2024-10-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Computers & Structures\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0045794924002943\",\"RegionNum\":2,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computers & Structures","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0045794924002943","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
Adaptive isogeometric topology optimization of shell structures based on PHT-splines
This paper proposes an adaptive isogeometric topology optimization framework for shell structures by utilizing a continuous density field represented as Polynomial splines over Hierarchical T-meshes (PHT-splines). This framework ensures an exact representation of shell structures, eliminating the geometric inaccuracies commonly associated with topology optimization. In the meanwhile, the meshes used for design and analysis are refined adaptively and locally along the density boundary to achieve a smooth material layout with reduced degrees of freedom (DOF). The adaptive sensitivity filter is tailored to the characteristics of PHT-splines, where the filter radius is determined automatically and adaptively, without the need to specify parameters in advance. Numerical experiments conducted on various shell structures validate the efficacy of the proposed adaptive framework. In comparison with isogeometric topology optimization based on non-adaptive cases (i.e. B-splines), the proposed adaptive framework demonstrates a notable enhancement in computational efficiency, with a reduction in running time and a reduction in DOF. Additionally, we offer a detailed comparison between PHT-splines and other locally refinable splines in the context of shell topology optimization. Numerical experiments exhibit that the efficient and localized refinement capability of PHT-splines provides advantages in both computational efficiency and structural performance for topology optimization.
期刊介绍:
Computers & Structures publishes advances in the development and use of computational methods for the solution of problems in engineering and the sciences. The range of appropriate contributions is wide, and includes papers on establishing appropriate mathematical models and their numerical solution in all areas of mechanics. The journal also includes articles that present a substantial review of a field in the topics of the journal.