Open Access

ARTICLE

Symmetric Coupling of the Meshless Galerkin Boundary Node and Finite Element Methods for Elasticity

Xiaolin Li¹

1 College of Mathematics Science, Chongqing Normal University, Chongqing 400047, P R China. E-mail: lxlmath@163.com.

Computer Modeling in Engineering & Sciences 2014, 97(6), 483-507. https://doi.org/10.3970/cmes.2014.097.483

Abstract

Combining moving least square (MLS) approximations and boundary integral equations, a symmetric and boundary-only meshless method, the Galerkin boundary node method (GBNM), is developed in this paper for two- and threedimensional elasticity problems with mixed boundary conditions. Unlike other MLS-based meshless methods, boundary conditions in this meshless method can be applied directly and easily. In the GBNM, the stiffness matrices so obtained are symmetric. The property of symmetry is an added advantage in coupling the GBNM with the finite element method (FEM). Thus, a symmetric coupling of the GBNM and the FEM is also discussed for elasticity problems. Error analysis and convergence study of the GBNM and the coupled GBNM-FEM are given in Sobolev spaces. For demonstration purpose, some numerical examples are presented.

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