Solution of Elasto-Statics Problems Using the Element-Free Galerkin Method with Local Maximum Entropy Shape Functions

Zahur Ullah, C. E. Augarde

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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Abstract

The element free Galerkin method (EFGM) [1] is one of the most robust meshless methods for the solution of elasto-statics problems. In the EFGM, moving least squares (MLS) shape functions are used for the approximation of the field variable. The essential boundary conditions cannot be implemented directly as in the case of Finite Element Method (FEM), because the MLS shape functions do not possess the Kronecker-delta property and use Lagrange multipliers instead. In this paper the recently developed local maximum entropy shape functions are used in the EFGM for the approximation of the field variable instead of MLS. As the local maximum entropy shape functions possess the Kroneckerdelta property at the boundaries so the essential boundary conditions are enforced directly as in the case of FEM. Two benchmark problems, a cantilever beam subjected to parabolic traction at the free end and an infinite plate with circular hole subjected to unidirectional tension are solved to show the implementation and performance of the current approach. The displacement and stresses calculated by the current approach show good agreement with the analytical results.
Original languageEnglish
Title of host publicationUnknown Host Publication
Pages161-164
Number of pages4
Publication statusAccepted/In press - 29 Mar 2010
Event18th UK Conference of the Association for Computational Mechanics in Engineering (ACME) - University of Southampton, UK
Duration: 29 Mar 2010 → …

Conference

Conference18th UK Conference of the Association for Computational Mechanics in Engineering (ACME)
Period29/03/10 → …

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Galerkin methods
Entropy
Boundary conditions
Finite element method
Lagrange multipliers
Cantilever beams

Keywords

  • meshless methods
  • EFGM
  • moving least squares
  • maximum entropy shape functions

Cite this

Ullah, Z., & Augarde, C. E. (Accepted/In press). Solution of Elasto-Statics Problems Using the Element-Free Galerkin Method with Local Maximum Entropy Shape Functions. In Unknown Host Publication (pp. 161-164)
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Ullah, Z & Augarde, CE 2010, Solution of Elasto-Statics Problems Using the Element-Free Galerkin Method with Local Maximum Entropy Shape Functions. in Unknown Host Publication. pp. 161-164, 18th UK Conference of the Association for Computational Mechanics in Engineering (ACME), 29/03/10.

Solution of Elasto-Statics Problems Using the Element-Free Galerkin Method with Local Maximum Entropy Shape Functions. / Ullah, Zahur; Augarde, C. E.

Unknown Host Publication. 2010. p. 161-164.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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N2 - The element free Galerkin method (EFGM) [1] is one of the most robust meshless methods for the solution of elasto-statics problems. In the EFGM, moving least squares (MLS) shape functions are used for the approximation of the field variable. The essential boundary conditions cannot be implemented directly as in the case of Finite Element Method (FEM), because the MLS shape functions do not possess the Kronecker-delta property and use Lagrange multipliers instead. In this paper the recently developed local maximum entropy shape functions are used in the EFGM for the approximation of the field variable instead of MLS. As the local maximum entropy shape functions possess the Kroneckerdelta property at the boundaries so the essential boundary conditions are enforced directly as in the case of FEM. Two benchmark problems, a cantilever beam subjected to parabolic traction at the free end and an infinite plate with circular hole subjected to unidirectional tension are solved to show the implementation and performance of the current approach. The displacement and stresses calculated by the current approach show good agreement with the analytical results.

AB - The element free Galerkin method (EFGM) [1] is one of the most robust meshless methods for the solution of elasto-statics problems. In the EFGM, moving least squares (MLS) shape functions are used for the approximation of the field variable. The essential boundary conditions cannot be implemented directly as in the case of Finite Element Method (FEM), because the MLS shape functions do not possess the Kronecker-delta property and use Lagrange multipliers instead. In this paper the recently developed local maximum entropy shape functions are used in the EFGM for the approximation of the field variable instead of MLS. As the local maximum entropy shape functions possess the Kroneckerdelta property at the boundaries so the essential boundary conditions are enforced directly as in the case of FEM. Two benchmark problems, a cantilever beam subjected to parabolic traction at the free end and an infinite plate with circular hole subjected to unidirectional tension are solved to show the implementation and performance of the current approach. The displacement and stresses calculated by the current approach show good agreement with the analytical results.

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