Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 
 

 

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


Authors: L. Beirão da Veiga, D. Mora and G. Rivera
Journal: Math. Comp.
MSC (2010): Primary 65N30, 65N12, 74K20, 74S05, 65N15
DOI: https://doi.org/10.1090/mcom/3331
Published electronically: April 5, 2018
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2010): 65N30, 65N12, 74K20, 74S05, 65N15

Retrieve articles in all journals with MSC (2010): 65N30, 65N12, 74K20, 74S05, 65N15


Additional Information

L. Beirão da Veiga
Affiliation: Dipartimento di Matematica e Applicazioni, Università di Milano-Bicocca, 20125 Milano, Italy
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
Email: dmora@ubiobio.cl

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

DOI: https://doi.org/10.1090/mcom/3331
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

American Mathematical Society