Interaction of Harmonic Longitudinal Shear Waves with V-Shaped Inclusions

Abstract

We solve the problem of determination of the stressed state in the vicinity of a tunnel rigid inclusion whose cross section consists of two segments originating out from the same point. The inclusion is placed in an infinite elastic medium with propagating plane harmonic longitudinal shear waves. The problem is reduced to the solution of a system of two singular integral equations with fixed singularities. For the approximate solution of this system, we apply a numerical method that takes into account the true asymptotics of the unknown functions and is based on the use of special quadrature formulas for the evaluation of singular integrals.