A general integral equation formulatin for homogeneous orthotropic potential problems

In this paper an integral equation formulation is proposed for the analysis of orthotropic potential problems. The two primary integral equations of the method are derived from the original governing differential equation firstly by rewriting it in a slightly different form and then applying the direct boundary element method formulation. The solution procedure is based on the use of the fundamental solutions for the isotropic potential case and special attention is given to the differentiation of a singular integral which yields an additional term as well as to the evaluation of the resulting Cauchy principal value integral. A simple discretization for the boundary and its interior domain is adopted in order to express the primary integral equations of the method in matrix form. Three examples are presented, the results of which illustrate the satisfactory accuracy of the method. The main feature of the proposed formulation is its generality, which makes possible its direct extension to solve such as heat conduction or subsurface flow in anisotropic media and, foremost, to orthotropic and anisotropic elasticity or elastoplasticity.