DG approach to large bending plate deformations with isometry constraint

DOI10.1142/S0218202521500044zbMATH Open1473.65287arXiv1912.03812MaRDI QIDQ5164205

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Publication date: 10 November 2021

Published in: (Search for Journal in Brave)

Abstract: We propose a new discontinuous Galerkin (dG) method for a geometrically nonlinear Kirchhoff plate model for large isometric bending deformations. The minimization problem is nonconvex due to the isometry constraint. We present a practical discrete gradient flow that decreases the energy and computes discrete minimizers that satisfy a prescribed discrete isometry defect. We prove $Gamma$-convergence of the discrete energies and discrete global minimizers. We document the flexibility and accuracy of the dG method with several numerical experiments.

Full work available at URL: https://arxiv.org/abs/1912.03812

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