Block Element Method for the Stamps of the no Classical Form

We present a block element method for solving 3D integral equations with difference kernel arising in boundary value problems of continuum mechanics and in mathematical physics. The approach has been induced by the Wiener–Hopf method, and its extension to the 3D case is called the integral factorization method and is mostly used in applications to domains with smooth boundary. In the present paper, the method is applied to domains with piecewise smooth boundary and corner points, which necessitates its generalization to the case of functions of two variables. Mixed boundary value problems have numerous applications in mechanics as well as in theoretical and technical physics. The method was tested on a vector contact problem for a wedge-shaped punch occupying the first quadrant. Techniques for obtaining various characteristics of solutions are described in detail. They are based on the inversion of a system of 1D linear integral equations typical of dynamic and static contact problems for strip punches.