Weakly-singular traction and displacement boundary integral equations and their meshless local Petrov-Galerkin approaches

Zhidong Han, Zhenhan Yao, S. N. Atluri

Research output: Contribution to journalArticle

5 Scopus citations

Abstract

The general meshless local Petrov-Galerkin (MLPG) weak forms of the displacement and traction boundary integral equations (BIEs) are presented for solids undergoing small deformations. Using the directly derived non-hyper-singular integral equations for displacement gradients, simple and straightforward derivations of weakly singular traction BIEs for solids undergoing small deformations are also presented. As a framework for meshless approaches, the MLPG weak forms provide the most general basis for the numerical solution of the non-hyper-singular displacement and traction BIEs. By employing the various types of test functions, several types of MLPG/BIEs are formulated. Numerical examples show that the present methods are very promising, especially for solving the elastic problems in which the singularities in displacements, strains, and stresses are of primary concern.

Original languageEnglish
Pages (from-to)1-7
Number of pages7
JournalTsinghua Science and Technology
Volume10
Issue number1
DOIs
StatePublished - Feb 2005

Keywords

  • Boundary integral equation (BIE)
  • MLPG/BIE
  • Meshless local Petrov-Galerkin (MLPG) approach
  • Moving least squares (MLS)
  • Non-hyper-singular dBIE/tBIE

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