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arXiv · 2011.01086

LDG approximation of large deformations of prestrained plates

Andrea Bonito·Diane Guignard·Ricardo H. Nochetto·Shuo Yang
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Abstract

A reduced model for large deformations of prestrained plates consists of minimizing a second order bending energy subject to a nonconvex metric constraint. The former involves the second fundamental form of the middle plate and the later is a restriction on its first fundamental form. We discuss a formal derivation of this reduced model along with an equivalent formulation that makes it amenable computationally. We propose a local discontinuous Galerkin (LDG) finite element approach that hinges on the notion of reconstructed Hessian. We design discrete gradient flows to minimize the ensuing nonconvex problem and to find a suitable initial deformation. We present several insightful numerical experiments, some of practical interest, and assess various computational aspects of the approximation process.

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Andrea Bonito, Diane Guignard, Ricardo H. Nochetto, Shuo Yang. 2020-11-02. LDG approximation of large deformations of prestrained plates. https://arxiv.org/abs/2011.01086

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