Trefftz functions using the fundamental solution with the singularity outside the domain

Abstract

Two types of Trefftz (T -) functions are often used - fundamental solutions with their singularities outside the given region and general solutions of homogenous differential equations. For elasticity problems the general solution of the homogeneous differential equation (equilibrium equation in displacements known as Lame- Navier equations) can be found in the polynomial form. In this paper we present the first type of T-functions. The paper deals with the investigation of accuracy and stability of the resulting system of discretized equations in relation to the position of the source (singularity) point. In this way non-singular reciprocity based boundary integral equations relate the boundary tractions and the boundary displacements of the searched solution to corresponding quantities of the known solutions. It was found that there exist an optimal relation of the distance of the singularity to the distance of the collocation points where both the integration accuracy and numerical stability are good.