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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.
DOI: https://doi.org/10.1090/mcom/3331
Published electronically: April 5, 2018
MathSciNet review: 3854054
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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
MR Author ID: 696855
Email: lourenco.beirao@unimib.it

D. Mora
Affiliation: Departamento de Matemática, Universidad del Bío-Bío, Casilla 5-C, Concepción, Chile–and–CI$^2$MA, Universidad de Concepción, Concepción, Chile
MR Author ID: 876029
Email: dmora@ubiobio.cl

G. Rivera
Affiliation: Departamento de Ciencias Exactas, Universidad de Los Lagos, Casilla 933, Osorno, Chile
MR Author ID: 1111154
Email: gonzalo.rivera@ulagos.cl

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