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arXiv · 1710.07330

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

Lourenço Beirão da Veiga·David Mora·Gonzalo Rivera
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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.

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Lourenço Beirão da Veiga, David Mora, Gonzalo Rivera. 2017-10-19. Virtual Elements for a shear-deflection formulation of Reissner-Mindlin plates. https://arxiv.org/abs/1710.07330

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