Local Maximum Entropy Shape Functions Based FE-EFGM Coupling

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

Research output: Non-textual formWeb publication/site

Abstract

In this paper, a new method for coupling the finite element method (FEM)and the element-free Galerkin method (EFGM) is proposed for linear elastic and geometrically nonlinear problems using local maximum entropy shape functions in theEFG zone of the problem domain. These shape functions possess a weak Kroneckerdelta property at the boundaries which provides a natural way to couple the EFGand the FE regions as compared to the use of moving least square basis functions.In this new approach, there is no need for interface/transition elements between theEFG and the FE regions or any other special treatment for shape function continuity across the FE-EFG interface. One- and two-dimensional linear elastic and two-dimensional geometrically nonlinear benchmark numerical examples are solved by the new approach to demonstrate the implementation and performance of the current approach.
LanguageEnglish
Publication statusE-pub ahead of print - 1 Jul 2013

Fingerprint

Galerkin methods
Entropy
Finite element method

Keywords

  • FE-EFGM coupling
  • maximum entropy basis functions
  • linear-elasticity
  • non-linear elasticity
  • moving least square basis functions

Cite this

Ullah, Z. (Author), Augarde, C. E. (Author), & Coombs, W. M. (Author). (2013). Local Maximum Entropy Shape Functions Based FE-EFGM Coupling. Web publication/site, Retrieved from https://www.dur.ac.uk/resources/ecs/research/technical_reports/2013_07.pdf
Ullah, Zahur (Author) ; Augarde, C.E. (Author) ; Coombs, W. M. (Author). / Local Maximum Entropy Shape Functions Based FE-EFGM Coupling. [Web publication/site].
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author = "Zahur Ullah and C.E. Augarde and Coombs, {W. M.}",
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Ullah, Z, Augarde, CE & Coombs, WM, Local Maximum Entropy Shape Functions Based FE-EFGM Coupling, 2013, Web publication/site.
Local Maximum Entropy Shape Functions Based FE-EFGM Coupling. Ullah, Zahur (Author); Augarde, C.E. (Author); Coombs, W. M. (Author). 2013.

Research output: Non-textual formWeb publication/site

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T1 - Local Maximum Entropy Shape Functions Based FE-EFGM Coupling

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N2 - In this paper, a new method for coupling the finite element method (FEM)and the element-free Galerkin method (EFGM) is proposed for linear elastic and geometrically nonlinear problems using local maximum entropy shape functions in theEFG zone of the problem domain. These shape functions possess a weak Kroneckerdelta property at the boundaries which provides a natural way to couple the EFGand the FE regions as compared to the use of moving least square basis functions.In this new approach, there is no need for interface/transition elements between theEFG and the FE regions or any other special treatment for shape function continuity across the FE-EFG interface. One- and two-dimensional linear elastic and two-dimensional geometrically nonlinear benchmark numerical examples are solved by the new approach to demonstrate the implementation and performance of the current approach.

AB - In this paper, a new method for coupling the finite element method (FEM)and the element-free Galerkin method (EFGM) is proposed for linear elastic and geometrically nonlinear problems using local maximum entropy shape functions in theEFG zone of the problem domain. These shape functions possess a weak Kroneckerdelta property at the boundaries which provides a natural way to couple the EFGand the FE regions as compared to the use of moving least square basis functions.In this new approach, there is no need for interface/transition elements between theEFG and the FE regions or any other special treatment for shape function continuity across the FE-EFG interface. One- and two-dimensional linear elastic and two-dimensional geometrically nonlinear benchmark numerical examples are solved by the new approach to demonstrate the implementation and performance of the current approach.

KW - FE-EFGM coupling

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Ullah Z (Author), Augarde CE (Author), Coombs WM (Author). Local Maximum Entropy Shape Functions Based FE-EFGM Coupling 2013.