A hyper-singular traction boundary integral equation method for stress intensity factor computation in a finite cracked body

Abstract

This paper attempts to answer the commonly raised question: what are the parameters controlling the solution accuracy and stability when the hyper-singular traction boundary-integral equations (BIEs) are used for the dynamic (time-harmonic) linear elastic fracture analysis of a finite cracked structure. The usage of the traction BIEs together with the parabolic discretization mesh leads to hyper-singularity, when the crack lies on the boundary, even after application of a regularization procedure. In this paper two new ways, average method and shifted point method to overcome this difficulty, are proposed and compared. It is shown by numerical experiments on the examples of a cracked rectangular plate and of a cracked infinite plane that the accuracy and the convergence of the method solution depends mainly on the smoothness requirements of the solution at all collocation points.