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

Zahur Ullah, C. E Augarde, W. M Coombs

Research output: Contribution to journalArticle

20 Citations (Scopus)

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.
LanguageEnglish
Pages111-132
JournalComputer Methods in Applied Mechanics and Engineering
Volume267
DOIs
Publication statusAccepted/In press - 29 Jul 2013

Fingerprint

Entropy
Finite element method
Error analysis
Galerkin methods
Elasticity
Boundary conditions
Recovery

Keywords

  • Meshless method
  • Maximum entropy shape functions
  • FE–EFGM coupling
  • Error estimation
  • Adaptivity
  • Superconvergent patch recovery

Cite this

@article{f5f52a3246b1477f90d0b7e5d6c89aa3,
title = "An adaptive finite element/meshless coupled method based on local maximum entropy shape functions for linear and nonlinear problems",
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.",
keywords = "Meshless method, Maximum entropy shape functions, FE–EFGM coupling, Error estimation, Adaptivity, Superconvergent patch recovery",
author = "Zahur Ullah and Augarde, {C. E} and Coombs, {W. M}",
year = "2013",
month = "7",
day = "29",
doi = "10.1016/j.cma.2013.07.018",
language = "English",
volume = "267",
pages = "111--132",
journal = "Computer Methods in Applied Mechanics and Engineering",
issn = "0045-7825",
publisher = "Elsevier",

}

An adaptive finite element/meshless coupled method based on local maximum entropy shape functions for linear and nonlinear problems. / Ullah, Zahur; Augarde, C. E; Coombs, W. M.

In: Computer Methods in Applied Mechanics and Engineering, Vol. 267, 29.07.2013, p. 111-132.

Research output: Contribution to journalArticle

TY - JOUR

T1 - An adaptive finite element/meshless coupled method based on local maximum entropy shape functions for linear and nonlinear problems

AU - Ullah, Zahur

AU - Augarde, C. E

AU - Coombs, W. M

PY - 2013/7/29

Y1 - 2013/7/29

N2 - 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.

AB - 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.

KW - Meshless method

KW - Maximum entropy shape functions

KW - FE–EFGM coupling

KW - Error estimation

KW - Adaptivity

KW - Superconvergent patch recovery

U2 - 10.1016/j.cma.2013.07.018

DO - 10.1016/j.cma.2013.07.018

M3 - Article

VL - 267

SP - 111

EP - 132

JO - Computer Methods in Applied Mechanics and Engineering

T2 - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

SN - 0045-7825

ER -