A new and simple meshless LBIE-RBF numerical scheme in linear elasticity

E. J. Sellountos, D. Polyzos, S. N. Atluri

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

A new meshless Local Boundary Integral Equation (LBIE) method for solving two-dimensional elastostatic problems is proposed. Randomly distributed points without any connectivity requirement cover the analyzed domain and Local Radial Basis Functions (LRBFs) are employed for the meshless interpolation of displacements. For each point a circular support domain is centered and a local integral representation for displacements is considered. At the local circular boundaries tractions are eliminated with the aid of companion solution, while at the intersections between the local domains and the global boundary displacements and tractions are treated as independent variables avoiding thus derivatives of LRBFs. Stresses are evaluated with high accuracy and without derivatives of LRBFs via a LBIE valid for stresses. All the integrations are performed quickly and economically and in a way that renders the extension of the method to three-dimensional problems straightforward. Six representative numerical examples that demonstrate the accuracy of the proposed methodology are provided.

Original languageEnglish
Pages (from-to)513-551
Number of pages39
JournalCMES - Computer Modeling in Engineering and Sciences
Volume89
Issue number6
StatePublished - 2012

Keywords

  • Linear elasticity
  • Local Boundary Integral Equation (LBIE)
  • Local Radial Basis Functions (LRBF)
  • Meshless methods

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