Domains with Conical and Cylindrical Boundaries
A. B. Movchan, N. V. Movchan · 2020
In this chapter discusses boundary value problems, posed in domains with conical points on the boundary or with conical or cylindrical extensions at infinity. The formulation for an elastic half-space yields an auxiliary limit problem which describes the stress-strain state outside a neighbourhood of the conical notch. The chapter discusses some polynomial solutions of the homogeneous Lame system that have proved to be useful for the description of the displacement field in a thin rectangle. The middle layer, modelling an adhesive material, is assumed to be relatively thin and relatively soft in comparison with two other layers. The ends of a thin rectangle are fixed, and on the interface surfaces the ideal contact conditions hold. On the upper and lower parts of the boundary the traction boundary conditions are prescribed.