On Budaev and Bogy's approach to diffraction by the 2D traction free elastic wedge

TL;DR

This paper revisits Budaev and Bogy's semianalytical method for elastic wave diffraction by a 2D traction-free wedge, developing a new scheme and validating its effectiveness through comprehensive testing.

Contribution

It introduces a novel semianalytical scheme for solving the integral equations in Budaev and Bogy's diffraction approach, enhancing solution accuracy and validation.

Findings

The new scheme effectively solves the integral equations.

The solution aligns with the original diffraction problem.

Validation confirms the method's reliability.

Abstract

Several semianalytical approaches are now available for describing diffraction of a plane wave by the 2D (two dimensional) traction free isotropic elastic wedge. In this paper we follow Budaev and Bogy who reformulated the original diffraction problem as a singular integral one. This comprises two algebraic and two singular integral equations. Each integral equation involves two unknowns, a function and a constant. We discuss the underlying integral operators and develop a new semianalytical scheme for solving the integral equations. We investigate the properties of the obtained solution and argue that it is the solution of the original diffraction problem. We describe a comprehensive code verification and validation programme.