The method of fundamental solutions for axisymmetric elasticity problems

We investigate the use of the Method of Fundamental. Solutions (MFS) for th e approximate solution of certain problems of three-dimensional elastostati cs in isotropic materials. Specifically, we consider problems in which the geometry is axisymmetric and the boundary conditions are either axisymmetri c or arbitrary. In each case, the problem reduces to one of solving a two-d imensional problem or a set of such problems in the radial and axial coordi nates. As in axisymmetric problems in potential theory and in acoustic scat tering and radiation, the fundamental solutions of the governing equations and their normal derivatives required in the formulation of the MFS are exp ressible in terms of complete elliptic integrals. We present the results of numerical experiments which demonstrate the efficacy of the MFS approach.