The method of fundamental solutions for two-dimensional elasticity problems based on the Airy stress function

Abstract

This paper presents a new version of the method of fundamental solutions (MFS) for two-dimensional linear elasticity problems based on the stress function (Airy stress function), which is different from the MFS utilizing the fundamental solutions of displacement. The displacement compatibilities are derived by the single-valuedness of displacements in multiply-connected region. Based on the strain and rotation of the line element on the boundary, the displacement boundary conditions are deduced in forms of the Airy stress function. Furthermore, the displacement conditions exclude pure rigid body motion, and are in the derivative forms instead of the integral ones. The interpolation equations are also reconstructed by the single-valuedness conditions of the displacements and the approximate solutions in a multiply-connected region. The numerical examples show that the proposed method has good effect and keeps high accuracy in all kinds of boundary conditions.