Numerical approximations of thin structure deformations

We review different (reduced) models for thin structures using bending as principal mechanism to undergo large deformations. Each model consists in the minimization of a fourth order energy, potentially subject to a nonconvex constraint. Equilibrium deformations are approximated using local disconti...

Full description

Saved in:
Bibliographic Details
Main Authors Bonito, Andrea, Guignard, Diane, Morvant, Angelique
Format Journal Article
LanguageEnglish
Published 22.12.2022
Subjects
Computer Science - Numerical Analysis
Mathematics - Numerical Analysis
Online AccessGet full text
DOI10.48550/arxiv.2212.11488

Cover

More Information
Summary:We review different (reduced) models for thin structures using bending as principal mechanism to undergo large deformations. Each model consists in the minimization of a fourth order energy, potentially subject to a nonconvex constraint. Equilibrium deformations are approximated using local discontinuous Galerkin (LDG) finite elements. The design of 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 put in place 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 large variety of shapes that can be achieved with these models.
DOI:10.48550/arxiv.2212.11488