Method of Fundamental Solutions Without Fictitious Boundary for Anisotropic Elasticity Problems Based on Mechanical Equilibrium Desingularization

Abstract

In this chapter, an Improved Non-singular Method of Fundamental Solutions (INMFS) is developed for solving the 2D anisotropic linear elasticity problems. In the INMFS, the artificial boundary, present in the classical Method of Fundamental Solutions (MFS), is removed. The singularities are substituted by the normalized area integrals of the Fundamental Solution (FS) over small squares, covering the source points that intersect with the collocation points. The singularities of the fundamental traction are dealt with considering the mechanical equilibrium, calculated by the boundary integration of the forces on the considered body. This more appropriate approach avoids solving the problem two times as in Non-singular MFS (NMFS), developed by Liu and Sarler in 2014. The integral over a small disk in NMFS is replaced by a small square in INMFS, amenable to be solved analytically. The viability and superiority of INMFS in comparison with the MFS and the NMFS is assessed in details. The advantage of having no artificial boundary and the straightforward implementation of the INMFS on problems with different materials in contact is demonstrated.