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

Ullah, Zahur, Augarde, C. E and Coombs, W. M (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 . pp. 111-132. [Journal article]

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URL: http://www.sciencedirect.com/science/article/pii/S0045782513001941

DOI: 10.1016/j.cma.2013.07.018

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.

Item Type:Journal article
Keywords:Meshless method, Maximum entropy shape functions, FE–EFGM coupling, Error estimation, Adaptivity, Superconvergent patch recovery
Faculties and Schools:Faculty of Computing & Engineering
Faculty of Computing & Engineering > School of Engineering
ID Code:38492
Deposited By: Dr Zahur Ullah
Deposited On:29 Aug 2017 12:00
Last Modified:17 Oct 2017 16:31

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