Reduction of a Coupled Dual Trigonometric Series to a Set of Singular Integral Equations and Their Solutions.

摘要

In this paper we study a coupled pair of dual trigonometric series that arise in the study of contact problem of an inclusion as well as a set of curvilinear cracks. The dual series is reduced to a coupled pair of integral equations. Simple identities of the Kernel functions allow us to decouple these integral equations into a set of uncoupled singular integral equations. One of these integral equations has a logarithmic singularity and the other has a Cauchy type of singularity. The problem is then reformulated via a complex variable approach, and reduced to a Riemann-Hilbert problem leading to identical results. This equivalence may be useful in numerical computations if exact solutions cannot be obtained. (Author)