Convergence in the incompressible limit of new discontinuous Galerkin methods with general quadrilateral and hexahedral elements

Grieshaber, B. J., McBride, A. T. and Reddy, B. D. (2020) Convergence in the incompressible limit of new discontinuous Galerkin methods with general quadrilateral and hexahedral elements. Computer Methods in Applied Mechanics and Engineering, 370, 113233. (doi: 10.1016/j.cma.2020.113233)

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Abstract

Standard low-order finite elements, which perform well for problems involving compressible elastic materials, are known to under-perform when nearly incompressible materials are involved, commonly exhibiting the locking phenomenon. Interior penalty (IP) discontinuous Galerkin methods have been shown to circumvent locking when simplicial elements are used. The same IP methods, however, result in locking on meshes of quadrilaterals. The authors have shown in earlier work that under-integration of specified terms in the IP formulation eliminates the locking problem for rectangular elements. Here it is demonstrated through an extensive numerical investigation that the effect of using under-integration carries over successfully to meshes of more general quadrilateral elements, as would likely be used in practical applications, and results in accurate displacement approximations. Uniform convergence with respect to the compressibility parameter is shown numerically. Additionally, a stress approximation obtained here by postprocessing shows good convergence in the incompressible limit.

Item Type:Articles
Keywords:Discontinuous Galerkin, interior penalty, elasticity, locking, quadrilateral, under-integration.
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:McBride, Dr Andrew
Authors: Grieshaber, B. J., McBride, A. T., and Reddy, B. D.
College/School:College of Science and Engineering > School of Engineering > Infrastructure and Environment
Journal Name:Computer Methods in Applied Mechanics and Engineering
Publisher:Elsevier
ISSN:0045-7825
ISSN (Online):1879-2138
Published Online:15 June 2020
Copyright Holders:Copyright © 2020 The Authors
First Published:First published in Computer Methods in Applied Mechanics and Engineering: 370:113233
Publisher Policy:Reproduced under a Creative Commons licence
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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
300129Strategic Support Package: Engineering of Active Materials by Multiscale/Multiphysics Computational MechanicsChristopher PearceEngineering and Physical Sciences Research Council (EPSRC)EP/R008531/1ENG - Infrastructure & Environment