Open Access

ARTICLE

A Galerkin Boundary Node Method for Two-Dimensional Linear Elasticity

Xiaolin Li¹, Jialin Zhu²

1 Corresponding author. College of Mathematics and Computer Science, Chongqing Normal University, Chongqing 400047, P R China. E-mail: lxlmath@163.com.
2 College of Mathematics and Physics, Chongqing University, Chongqing 400044, P R China.

Computer Modeling in Engineering & Sciences 2009, 45(1), 1-30. https://doi.org/10.3970/cmes.2009.045.001

Abstract

In this paper, a Galerkin boundary node method (GBNM) is developed for boundary-only analysis of 2D problems in linear elasticity. The GBNM combines the variational form of a boundary integral formulation for the elastic equations with the moving least-squares approximations for generating the trial and test functions. Unlike the boundary node method, the main idea here is to use the Galerkin scheme for numerical analysis, thus boundary conditions in the GBNM can be satisfied easily and directly in the weak formulation of the boundary integral equation. Another advantage with the Galerkin scheme is that the GBNM can keep the symmetry and positive definiteness of the variational problems. The error analysis and convergence study of the GBNM in Sobolev spaces are given. Numerical examples are also presented to show the efficiency of the method.

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Keywords

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