Finite element methods for the stretching and bending of thin structures with folding
Pages 2031 - 2068
Abstract
In Bonito (J. Comput. Phys. 448:110719, 2022), a local discontinous Galerkin method was proposed for approximating the large bending of prestrained plates, and in Bonito (IMA J. Numer. Anal. 43:627-662, 2023) the numerical properties of this method were explored. These works considered deformations driven predominantly by bending. Thus, a bending energy with a metric constraint was considered. We extend these results to the case of an energy with both a bending component and a nonconvex stretching component, and we also consider folding across a crease. The proposed discretization of this energy features a continuous finite element space, as well as the discrete Hessian used in Bonito (J. Comput. Phys. 448:110719, 2022; IMA J. Numer. Anal. 43:627-662, 2023). We establish the -convergence of the discrete to the continuous energy and also present an energy-decreasing gradient flow for finding critical points of the discrete energy. Finally, we provide numerical simulations illustrating the convergence of minimizers and the capabilities of the model.
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© Crown 2024.
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Springer-Verlag
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Publication History
Published: 29 October 2024
Accepted: 07 October 2024
Revision received: 31 July 2024
Received: 08 November 2023
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