An adaptive finite element/meshless coupled method based on local maximum entropy shape functions for linear and nonlinear problems

Ullah, Z.; Coombs, W. M.; Augarde, C. E.

Authors

Dr Zahur Ullahzahur.ullah@durham.ac.uk
Associate Professor

Professor William Coombsw.m.coombs@durham.ac.uk
Professor

Professor Charles Augardecharles.augarde@durham.ac.uk
Head Of Department

Abstract

In this paper, an automatic adaptive coupling procedure is proposed for the finite element method (FEM) and the element-free Galerkin method (EFGM) for linear elasticity and for problems with both material and geometrical nonlinearities. In this new procedure, initially the whole of the problem domain is modelled using the FEM. During an analysis, those finite elements which violate a predefined error measure are automatically converted to an EFG zone. This EFG zone can be further refined by adding nodes, thus avoiding computationally expensive FE remeshing. Local maximum entropy shape functions are used in the EFG zone of the problem domain for two reasons: their weak Kronecker delta property at the boundaries allows straightforward imposition of essential boundary conditions and also provides a natural way to couple the EFG and FE regions compared to the use of moving least squares basis functions. The Zienkiewicz and Zhu error estimation procedure with the superconvergent patch method for strains and stresses recovery is used in the FE region of the problem domain, while the Chung and Belytschko error estimation procedure is used in the EFG region.

Citation

Ullah, Z., Coombs, W. M., & Augarde, C. E. (2013). An adaptive finite element/meshless coupled method based on local maximum entropy shape functions for linear and nonlinear problems. Computer Methods in Applied Mechanics and Engineering, 267, 111-132.https://doi.org/10.1016/j.cma.2013.07.018

Journal Article Type	Article
Publication Date	Dec 1, 2013
Deposit Date	Aug 29, 2013
Publicly Available Date	Oct 1, 2014
Journal	Computer Methods in Applied Mechanics and Engineering
Print ISSN	0045-7825
Electronic ISSN	1879-2138
Publisher	Elsevier
Peer Reviewed	Peer Reviewed
Volume	267
Pages	111-132
DOI	https://doi.org/10.1016/j.cma.2013.07.018
Keywords	Meshless method, Maximum entropy shape functions, FE–EFGM coupling, Error estimation, Adaptivity, Superconvergent patch recovery.
Public URL	https://durham-repository.worktribe.com/output/1479182

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Copyright Statement
NOTICE: this is the author’s version of a work that was accepted for publication in Computer Methods in Applied Mechanics and Engineering. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Computer Methods in Applied Mechanics and Engineering, 267, 2013, 10.1016/j.cma.2013.07.018.

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