The method of fundamental solutions in Three-dimensional Elastostatics

Abstract

We consider the application of the Method of Fundamental Solutions (MFS) to isotropic elastostatics problems in three-space dimensions. The displacements are approximated by linear combinations of the fundamental solutions of the Cauchy-Navier equations of elasticity, which are expressed in terms of sources placed outside the domain of the problem under consideration. The final positions of the sources and the coefficients of the fundamental solutions are determined by enforcing the satisfaction of the boundary conditions in a least squares sense. The applicability of the method is demonstrated on various test problems. The numerical experiments indicate that accurate results can be obtained with relatively few degrees of freedom. © Springer-Verlag Berlin Heidelberg 2002.