{"title":"针对具有广义周期性的晶格结构的基于能量的均质化方法","authors":"","doi":"10.1016/j.compstruc.2024.107478","DOIUrl":null,"url":null,"abstract":"<div><p>This paper presents an energy-based homogenization method (EBHM) to calculate the equivalent elastic properties of lattice structures with generalized periodicity. Unlike the traditional implementation of the homogenization method, expressions of closed-form are derived for the equivalent elastic matrix, equivalent coefficients of thermal stress and thermal expansion in terms of the elastic strain energy of the unit cell so that the tedious numerical solution and programming are avoided. It is shown that the elastic strain energy can easily be calculated by mapping the unit cell with the imposition of specific periodic boundary conditions. The implementation can resort to any available finite element tools. Numerical examples are used to compare the EBHM with the homogenization mapping method, classical homogenization method and direct finite element analysis (FEA). The computational accuracy is investigated to show the effectiveness of the EBHM.</p></div>","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":null,"pages":null},"PeriodicalIF":4.4000,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Energy-based homogenization method for lattice structures with generalized periodicity\",\"authors\":\"\",\"doi\":\"10.1016/j.compstruc.2024.107478\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This paper presents an energy-based homogenization method (EBHM) to calculate the equivalent elastic properties of lattice structures with generalized periodicity. Unlike the traditional implementation of the homogenization method, expressions of closed-form are derived for the equivalent elastic matrix, equivalent coefficients of thermal stress and thermal expansion in terms of the elastic strain energy of the unit cell so that the tedious numerical solution and programming are avoided. It is shown that the elastic strain energy can easily be calculated by mapping the unit cell with the imposition of specific periodic boundary conditions. The implementation can resort to any available finite element tools. Numerical examples are used to compare the EBHM with the homogenization mapping method, classical homogenization method and direct finite element analysis (FEA). The computational accuracy is investigated to show the effectiveness of the EBHM.</p></div>\",\"PeriodicalId\":50626,\"journal\":{\"name\":\"Computers & Structures\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.4000,\"publicationDate\":\"2024-07-19\",\"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/S0045794924002074\",\"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/S0045794924002074","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}
Energy-based homogenization method for lattice structures with generalized periodicity
This paper presents an energy-based homogenization method (EBHM) to calculate the equivalent elastic properties of lattice structures with generalized periodicity. Unlike the traditional implementation of the homogenization method, expressions of closed-form are derived for the equivalent elastic matrix, equivalent coefficients of thermal stress and thermal expansion in terms of the elastic strain energy of the unit cell so that the tedious numerical solution and programming are avoided. It is shown that the elastic strain energy can easily be calculated by mapping the unit cell with the imposition of specific periodic boundary conditions. The implementation can resort to any available finite element tools. Numerical examples are used to compare the EBHM with the homogenization mapping method, classical homogenization method and direct finite element analysis (FEA). The computational accuracy is investigated to show the effectiveness of the EBHM.
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.