DG Approach to Large Bending Plate Deformations with Isometry Constraint

Andrea Bonito; Ricardo H. Nochetto; Dimitrios Ntogkas

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arXiv · 1912.03812

DG Approach to Large Bending Plate Deformations with Isometry Constraint

Andrea Bonito·Ricardo H. Nochetto·Dimitrios Ntogkas

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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.

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Andrea Bonito, Ricardo H. Nochetto, Dimitrios Ntogkas. 2019-12-09. DG Approach to Large Bending Plate Deformations with Isometry Constraint. https://arxiv.org/abs/1912.03812

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