{"title":"Numerical approximations of thin structure deformations","authors":"Andrea Bonito, Diane Guignard, Angelique Morvant","doi":"10.5802/crmeca.201","DOIUrl":null,"url":null,"abstract":"We review different models for thin structures using bending as principal mechanism to undergo large deformations. Each model consists of minimizing a fourth order energy, potentially subject to a nonconvex constraint. Equilibrium deformations are approximated using local discontinuous Galerkin finite elements. The discrete energies relies on a discrete Hessian operator defined on discontinuous functions with better approximation properties than the piecewise Hessian. Discrete gradient flows are used to drive the minimization process. They are chosen for their robustness and ability to preserve the nonconvex constraint. Several numerical experiments are presented to showcase the variety of shapes achievable with these models.","PeriodicalId":10566,"journal":{"name":"Comptes Rendus. Chimie","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2023-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Comptes Rendus. Chimie","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5802/crmeca.201","RegionNum":4,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
We review different models for thin structures using bending as principal mechanism to undergo large deformations. Each model consists of minimizing a fourth order energy, potentially subject to a nonconvex constraint. Equilibrium deformations are approximated using local discontinuous Galerkin finite elements. The discrete energies relies on a discrete Hessian operator defined on discontinuous functions with better approximation properties than the piecewise Hessian. Discrete gradient flows are used to drive the minimization process. They are chosen for their robustness and ability to preserve the nonconvex constraint. Several numerical experiments are presented to showcase the variety of shapes achievable with these models.
期刊介绍:
The Comptes Rendus - Chimie are a free-of-charge, open access and peer-reviewed electronic scientific journal publishing original research articles. It is one of seven journals published by the Académie des sciences.
Its objective is to enable researchers to quickly share their work with the international scientific community.
The Comptes Rendus - Chimie also publish journal articles, thematic issues and articles reflecting the history of the Académie des sciences and its current scientific activity.