{"title":"弱形式的周动力学","authors":"E. Madenci, Mehmet Dorduncu, A. Barut, N. Phan","doi":"10.2514/6.2018-1223","DOIUrl":null,"url":null,"abstract":"This chapter presents the weak form of the peridynamic (PD) governing field equations. They specifically concern the Poisson’s equation and Navier’s equation under in-plane loading conditions. Their weak forms derived based on the variational approach enable the direct imposition of nonlocal essential and natural boundary conditions. The numerical solution to these equations can be achieved by considering either a uniform or a nonuniform discretization.","PeriodicalId":129456,"journal":{"name":"Peridynamic Differential Operator for Numerical Analysis","volume":"100 1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Weak Form of Peridynamics\",\"authors\":\"E. Madenci, Mehmet Dorduncu, A. Barut, N. Phan\",\"doi\":\"10.2514/6.2018-1223\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This chapter presents the weak form of the peridynamic (PD) governing field equations. They specifically concern the Poisson’s equation and Navier’s equation under in-plane loading conditions. Their weak forms derived based on the variational approach enable the direct imposition of nonlocal essential and natural boundary conditions. The numerical solution to these equations can be achieved by considering either a uniform or a nonuniform discretization.\",\"PeriodicalId\":129456,\"journal\":{\"name\":\"Peridynamic Differential Operator for Numerical Analysis\",\"volume\":\"100 1 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\":\"Peridynamic Differential Operator for Numerical Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2514/6.2018-1223\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Peridynamic Differential Operator for Numerical Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2514/6.2018-1223","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
This chapter presents the weak form of the peridynamic (PD) governing field equations. They specifically concern the Poisson’s equation and Navier’s equation under in-plane loading conditions. Their weak forms derived based on the variational approach enable the direct imposition of nonlocal essential and natural boundary conditions. The numerical solution to these equations can be achieved by considering either a uniform or a nonuniform discretization.
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