Lourenco Beirao-Da-Veiga, David Mora, Gonzalo Rivera:
A virtual element method for Reissner-Mindlin plates
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 H1 × H2 and has the advantages of using general polygonal meshes and yielding a direct approximation of the shear strains. The rotations are then obtained as 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.
This preprint gave rise to the following definitive publication(s):
Lourenco BEIRAO-DA-VEIGA, David MORA, Gonzalo RIVERA: Virtual elements for a shear-deflection formulation of Reissner-Mindlin plates. Mathematics of Computation, vol. 88, 315, pp. 149-178, (2019).