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.
Articolo in rivista - Articolo scientifico
Error analysis; Polygonal meshes; Reissner-Mindlin plates; Virtual element method; Algebra and Number Theory; Computational Mathematics; Applied Mathematics
English
2018
88
315
149
178
none
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].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/212795
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