Non-singular method of fundamental solutions for elasticity problems in three-dimensions

In this paper, the Non-singular Method of Fundamental Solutions (NMFS) is extended to three-dimensional (3D) isotropic linear elasticity problems. In order to avoid the singularities in the classical Method of Fundamental Solutions (MFS), are the source points outside the problem domain replaced by normalizing the volume integral of the fundamental solutions over the sphere around the singularity on the physical boundary. The derivatives of the fundamental solutions at the singularity, required in the traction boundary conditions, are calculated from three reference solutions of the linearly varying simple displacement fields. The artificial boundary appearing in MFS is with this operations removed in NMFS. A comparison between NMFS and MFS solutions and analytical solutions for two single and two bi-material elasticity problems is used to assess the feasibility and the accuracy of the newly developed 3D method. Although NMFS results are slightly less accurate than MFS results in all spectra of performed tests, all NMFS results converge to the analytical solution. The lack of artificial boundary is particularly advantageous when using NMFS in multibody problems. The developments describe a first use of NMFS for 3D solid mechanics problems.