{"title":"有限变形下p型有限元的无体积锁紧特性","authors":"U. Heisserer, S. Hartmann, A. Düster, Z. Yosibash","doi":"10.1002/CNM.1008","DOIUrl":null,"url":null,"abstract":"We demonstrate the locking-free properties of the displacement formulation of p-finite elements when applied to nearly incompressible Neo-Hookean material under finite deformations. For an axisymmetric model problem we provide semi-analytical solutions for a nearly incompressible Neo-Hookean material exploited to investigate the robustness of p-FEM with respect to volumetric locking. An analytical solution for the incompressible case is also derived to demonstrate the convergence of the compressible numerical solution towards the incompressible case when the compression modulus is increased.","PeriodicalId":51245,"journal":{"name":"Communications in Numerical Methods in Engineering","volume":"1 1","pages":"1019-1032"},"PeriodicalIF":0.0000,"publicationDate":"2007-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/CNM.1008","citationCount":"2","resultStr":"{\"title\":\"On volumetric locking‐free behaviour of p‐version finite elements under finite deformations\",\"authors\":\"U. Heisserer, S. Hartmann, A. Düster, Z. Yosibash\",\"doi\":\"10.1002/CNM.1008\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We demonstrate the locking-free properties of the displacement formulation of p-finite elements when applied to nearly incompressible Neo-Hookean material under finite deformations. For an axisymmetric model problem we provide semi-analytical solutions for a nearly incompressible Neo-Hookean material exploited to investigate the robustness of p-FEM with respect to volumetric locking. An analytical solution for the incompressible case is also derived to demonstrate the convergence of the compressible numerical solution towards the incompressible case when the compression modulus is increased.\",\"PeriodicalId\":51245,\"journal\":{\"name\":\"Communications in Numerical Methods in Engineering\",\"volume\":\"1 1\",\"pages\":\"1019-1032\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2007-06-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1002/CNM.1008\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Communications in Numerical Methods in Engineering\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1002/CNM.1008\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Numerical Methods in Engineering","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1002/CNM.1008","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On volumetric locking‐free behaviour of p‐version finite elements under finite deformations
We demonstrate the locking-free properties of the displacement formulation of p-finite elements when applied to nearly incompressible Neo-Hookean material under finite deformations. For an axisymmetric model problem we provide semi-analytical solutions for a nearly incompressible Neo-Hookean material exploited to investigate the robustness of p-FEM with respect to volumetric locking. An analytical solution for the incompressible case is also derived to demonstrate the convergence of the compressible numerical solution towards the incompressible case when the compression modulus is increased.
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