A dual reciprocity boundary face method for 3D non-homogeneous elasticity problems

Abstract

The boundary face method is coupled with the dual reciprocity method (DRM) to solve non-homogeneous elasticity problems. We will analyze thin structures based on 3D solid elastic theory rather than the shell theory as in the finite element method (FEM). To circumvent the ill-conditioning problem that occurs in the radial basis function (RBF) approximation in thin structures, a special variation scheme for determining the RBF parameters is proposed. In addition, a new exponential RBF is used which has significantly improved the stability of the RBF, and its particular solution to the elasticity problem is derived for the first time. Comparisons of our method with the traditional DRM, the boundary element method (BEM) and the FEM have been made. Numerical examples have demonstrated that our method outperforms the BEM and FEM with respect to stability, accuracy and efficiency, especially when the structure in question has features of small size, such as thin shells.