Virtual Element Method for large deformations of Single Layer Plates
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In this presentation, we introduce an ongoing work about a virtual element method (VEM) for approximating large deformations of plates with isometry constraints. In particular we study the single layer plates. The problem consists of minimizing a bending energy subject to a nonlinear and nonconvex constraint. % We propose a conforming virtual element method [1] for the approximation of the constrained minimization problem, whereas a discrete gradient flow is designed for computing discrete minimizers. The proposed method can formally allow arbitrary order of discretization. We show $\Gamma$-convergence of the discrete energy to the continuous one. Then we prove that the discrete gradient flow decreases the energy at each step and computes discrete minimizers with control of the isometry constraint defect. We also illustrate the performance of our algorithm with several insightful simulations.
