The singular boundary method: Mathematical background and application in orthotropic elastic problems

The singular boundary method (SBM) is a recent strong-form boundary discretization numerical technique and can be viewed as one kind of modified method of fundamental solutions (MFSs). Although the method has been successfully used in many fields of engineering analysis, there has been no attempt yet to present a work discussing the mathematical background of the method. This paper fills this gap in the SBM and documents the first attempt to apply the method to the solution of orthotropic elastic problems. Three benchmark numerical problems are tested to demonstrate the feasibility and accuracy of the proposed method through detailed comparisons with the MFS and the boundary element method (BEM).