Virtual Elements for a shear-deflection formulation of Reissner-Mindlin plates
For computational mechanics researchers, this provides a new conforming method for plate bending that handles general polygonal meshes and avoids shear locking, though it is an incremental improvement over existing virtual element approaches.
The paper presents a virtual element method for Reissner-Mindlin plates that directly approximates shear strain and deflection without reduction operators, achieving convergence estimates uniform in plate thickness. Numerical experiments validate the method's performance.
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 $[H^{1}(Ω)]^2 \times H^2(Ω)$ 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.