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.

本文提出了一种新版本的基于应力函数（艾里应力函数）的二维线性弹性问题的基本解法（MFS），它不同于利用位移基本解法的MFS。位移相容性由多连通区域位移的单值性导出。基于线单元在边界上的应变和旋转，以艾里应力函数的形式推导出位移边界条件。此外，位移条件排除了纯刚体运动，并且是导数形式而不是积分形式。插值方程也由位移的单值条件和多连通区域中的近似解重建。