Method of fundamental solutions for 3D elasticity with body forces by coupling compactly supported radial basis functions

In this paper, a meshless computational model by integrating the method of fundamental solutions (MFS) and the method of particular solutions fulfilled with compactly supported radial basis functions (CSRBF) is developed for three-dimensional (3D) linear elasticity with the presence of body forces. The corresponding displacement and stress particular solution kernels across the support radius are firstly derived using Galerkin vectors and then are used to modify the boundary conditions. Subsequently, the classical meshless MFS, in which the homogeneous part of the full solutions are approximated using the linear combination of displacement and stress fundamental solutions in 3D linear elasticity, is formulated for solving the homogeneous 3D linear elastic system. Finally, several examples are presented to demonstrate the accuracy and efficiency of the present meshless method and also the effect of sparseness of interpolation matrix in CSRBF interpolation is discussed.