Localized method of fundamental solutions for two-dimensional anisotropic elasticity problems

Abstract

The purpose of the presented paper is to develop further the Localized Method of Fundamental Solutions (LMFS) for solving two-dimensional anisotropic elasticity problems. The computational domain is divided into overlapping subdomains. In the LMFS, the classical Method of Fundamental Solutions (MFS) is employed in each of these local subdomains to get an expression of the solution for the main node of this subdomain. The expression is structured by a linear combination of the solutions of the other nodes in this subdomain. Displacement or traction boundary conditions are satisfied at the boundary nodes. The solution is calculated from an equation set formed by the boundary conditions for the boundary nodes and expressions in the subdomain for the interior nodes. The presented three numerical examples demonstrate that the novel method is suitable for solving large-scale problems, and especially, the problems with complicated domains.