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(Ω)]2× H2(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.
Da Veiga, L., Mora, D., Rivera, G. (2018). Virtual elements for a shear-deflection formulation of Reissner-Mindlin Plates. MATHEMATICS OF COMPUTATION, 88(315), 149-178 [10.1090/mcom/3331].
Virtual elements for a shear-deflection formulation of Reissner-Mindlin Plates
Da Veiga, L. Beirão;
2018
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 [H1(Ω)]2× H2(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.
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