A three-dimensional element-free Galerkin elastic and elastoplastic formulation

William Barry, Sunil Saigal

Research output: Contribution to journalArticlepeer-review

65 Scopus citations


A small strain, three-dimensional, elastic and elastoplastic Element-Free Galerkin (EFG) formulation is developed. Singular weight functions are utilized in the Moving-Least-Squares (MLS) determination of shape functions and shape function derivatives allowing accurate, direct nodal imposition of essential boundary conditions. A variable domain of influence EFG method is introduced leading to increased efficiency in computing the MLS shape functions and their derivatives. The elastoplastic formulations are based on the consistent tangent operator approach and closely follow the incremental formulations for non-linear analysis using finite elements. Several linear elastic and small strain elastoplastic numerical examples are presented to verify the accuracy of the numerical formulations.

Original languageEnglish (US)
Pages (from-to)671-693
Number of pages23
JournalInternational Journal for Numerical Methods in Engineering
Issue number5
StatePublished - Oct 20 1999
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • General Engineering
  • Applied Mathematics


  • EFG fracture mechanics analysis
  • Elastoplastic EFG analysis
  • Element Free Galerkin Methods (EFGM)
  • Moving Least Squares (MLS) interpolants
  • Three dimensional meshless methods
  • Variable domain of influence


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