On the Interaction of Cracks and Stringers with a Heterogeneous Wedge-Shaped Body, Manufactured from Different Materials at an Antiplane Deformation

Abstract

The problem of stress state of an elastic piecewise-homogeneous wedge-shaped body at an antiplane deformation, consisting of heterogeneous wedges with different shear modules and opening of apex angles is considered, when a system of arbitrary finite number of collinear cracks is located on the interface line of the heterogeneous materials and the boundary faces of the compound wedge are reinforced with stringers of finite lengths. The solution of the problem is reduced to solving a system of three singular integral equations (SIE) using the Mellin integral transform, which based on quadrature formulas Gauss for calculating SIE with Cauchy kernel and ordinary integrals reduces to a system of systems of linear algebraic equations (SLAE). As a result, the characteristics of the problem are expressed by explicit simple structures algebraic formulas.