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

Authors: L. Beirão da Veiga, D. Mora and G. Rivera
Journal: Math. Comp. 88 (2019), 149-178
MSC (2010): Primary 65N30, 65N12, 74K20, 74S05, 65N15
Published electronically: April 5, 2018
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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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Additional Information

L. Beirão da Veiga
Affiliation: Dipartimento di Matematica e Applicazioni, Università di Milano-Bicocca, 20125 Milano, Italy

D. Mora
Affiliation: Departamento de Matemática, Universidad del Bío-Bío, Casilla 5-C, Concepción, Chile–and–CI$^{2}$MA, Universidad de Concepción, Concepción, Chile

G. Rivera
Affiliation: Departamento de Ciencias Exactas, Universidad de Los Lagos, Casilla 933, Osorno, Chile

Keywords: Virtual element method, Reissner--Mindlin plates, error analysis, polygonal meshes.
Received by editor(s): July 21, 2017
Received by editor(s) in revised form: October 4, 2017, and October 8, 2017
Published electronically: April 5, 2018
Additional Notes: The second author was partially supported by CONICYT-Chile through FONDECYT project 1140791 (Chile) and by DIUBB through project 151408 GI/VC, Universidad del Bío-Bío (Chile)
The third author was supported by a CONICYT fellowship (Chile).
Article copyright: © Copyright 2018 American Mathematical Society

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