Virtual Elements for a shear-deflection formulation of Reissner-Mindlin plates

TL;DR

This paper introduces a virtual element method for Reissner-Mindlin plates that directly approximates shear strains and deflections on polygonal meshes, ensuring convergence uniform in plate thickness.

Contribution

The paper develops a conforming virtual element method for Reissner-Mindlin plates that avoids reduction operators and directly approximates shear strains, with proven uniform convergence.

Findings

Method achieves convergence estimates uniform in plate thickness

Numerical experiments demonstrate effective performance

Uses general polygonal meshes for flexibility

Abstract

We present a virtual element method for the Reissner-Mindlin plate bending problem which uses shear strain and deflection as discrete variables without the need of any reduction operator. The proposed method is conforming in $[H^{1}(\Omega)]^2 \times H^2(\Omega)$ and has the advantages of using general polygonal meshes and yielding a direct approximation of the shear strains. The rotations are then obtained by a simple postprocess from the shear strain and deflection. We prove convergence estimates with involved constants that are uniform in the thickness $t$ of the plate. Finally, we report numerical experiments which allow us to assess the performance of the method.