Non-singular Method of Fundamental Solutions for anisotropic elasticity

The purpose of the present paper is to develop a Non-singular Method of Fundamental Solutions (NMFS) for two-dimensional anisotropic linear elasticity problems. The NMFS is based on the classical Method of Fundamental Solutions (MFS) with regularization of the singularities. This is achieved by replacing the concentrated point sources with distributed sources over disks around the singularity, as recently developed for isotropic elasticity problem. In case of the displacement boundary conditions, the values of distributed sources are calculated by a simple numerical procedure, since the closed form solution is not available. In case of traction boundary conditions, the respective desingularized values of the derivatives of the fundamental solution in the coordinate directions, as required in the calculations, are calculated indirectly by considering two reference solutions of the linearly varying simple displacement fields. The feasibility and accuracy of the newly developed method are demonstrated through comparison with MFS solutions and analytical solutions for a spectra of anisotropic plane strain elasticity problems, including bi-material arrangements. NMFS turns out to give similar results as the MFS in all spectra of performed tests. The lack of artificial boundary is particularly advantageous for using NMFS in multi-body problems.