Numerical approximations of thin structure deformations

IF 1.2 4区 化学 Q3 CHEMISTRY, MULTIDISCIPLINARY
Andrea Bonito, Diane Guignard, Angelique Morvant
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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.
薄结构变形的数值近似
我们回顾了不同的模型薄结构使用弯曲作为主要机制进行大变形。每个模型都包含最小化四阶能量,可能受到非凸约束。平衡变形用局部不连续伽辽金有限元逼近。离散能量依赖于定义在不连续函数上的离散Hessian算子,该算子具有比分段Hessian算子更好的近似性质。离散梯度流被用来驱动最小化过程。选择它们是因为它们具有鲁棒性和保持非凸约束的能力。几个数值实验展示了这些模型可以实现的各种形状。
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来源期刊
Comptes Rendus. Chimie
Comptes Rendus. Chimie 化学-化学综合
CiteScore
2.10
自引率
25.00%
发文量
89
审稿时长
3 months
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.
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