A DPG method for Reissner-Mindlin plates

TL;DR

This paper introduces a DPG method for Reissner-Mindlin plates that achieves quasi-optimal convergence and is locking-free for convex plates, validated through numerical experiments.

Contribution

It develops a novel DPG approach utilizing Helmholtz decomposition for improved plate bending modeling, ensuring convergence and locking-free performance.

Findings

Method converges quasi-optimally for various boundary conditions.

Lowest-order scheme is locking-free for convex plates.

Numerical experiments confirm theoretical results.

Abstract

We present a discontinuous Petrov-Galerkin (DPG) method with optimal test functions for the Reissner-Mindlin plate bending model. Our method is based on a variational formulation that utilizes a Helmholtz decomposition of the shear force. It produces approximations of the primitive variables and the bending moments. For any canonical selection of boundary conditions the method converges quasi-optimally. In the case of hard-clamped convex plates, we prove that the lowest-order scheme is locking free. Several numerical experiments confirm our results.