On the integrable case of a Riemann-Hilbert boundary value problem for two functions and the solutions of certain mixed problems for a composite elastic plane
A method for solving the Riemann-Hilbert boundary value problem with piecewise-constant coefficients is generalized. It is shown that the following static problems of a composite elastic plane with three kinds of connection conditions allow of exact solutions: 1) the splicing line is weakened by a system of loaded slots and a transverse shear crack or the edges of one of the slots are partially contacting, or one of the slots is cleaved by a rigid insert; 2) the splicing line is reinforced by a system of thin rigid inclusions and there is one arbitrarily located delamination zone; 3) the elastic half-planes are contacting (with slip) on a certain section of their boundaries, and mixed boundary conditions in the displacements and stresses are given on the rest of the boundaries.
scientific article; zbMATH DE number 3993093