The method of fundamental solutions applied to 3D elasticity problems using a continuous collocation scheme

This paper presents a new formulation of the Method of Fundamental Solutions (MFS) for three-dimensional elasticity problems. The idea of the presented formulation is to integrate both sides of the conventional MFS superposition equation over the body surface. This leads to the proposed “continuous collocation”. Therefore, the surface of the analysed body has to be discretised into boundary elements. In order to make use of the conventional MFS advantage of being a meshless method, a mixed formulation, using the proposed continuous collocation formulation and the conventional meshless formulation, is employed. The present formulation proved its validity and accuracy when analysing problems with non-constant boundary conditions and when computing the tangential stress component on the boundary. It is also shown that the proposed formulation is suitable and accurate for the analysis of thin and slender bodies.