On one method of constructing the cauchy kernel of the singular integral equation for clarifie the stress-strain state of the wedge system under anti-plane deformation

Abstract

An analytical approach to the construction of a singular integral equation (SIE) with Cauchy kernel is proposed, which makes it possible to clarify the stress-strain state of multi-wedge system with loaded radial cracks. This approach is based on the use of the theory of residues and the clarification of the solutions periodicity of the multi-wedge system characteristic equation. It is illustrated on the example of the construction of a SIE with Cauchy kernel for a two-wedge system with a loaded interfacial crack under the conditions of anti-plane deformation. For particular cases of geometric and mechanical parameters of the two-wedge system, the values necessary for constructing such an equation were calculated.