On the subsonic stationary motion of stamps and flexible cover-plates on the boundary of an elastic half-plane and a composite plane
A mixed dynamic problem for an elastic half-plane on different sections of whose boundary shear and normal stresses and displacements are given simultaneously in four fundamental combinations is considered. It is assumed that all the sections move at an identical constant subsonic velocity along the half-plane boundary and their number and mutual arrangement are arbitrary. An analogously problem on the interaction of two half-planes of different materials (a composite plane) is examined under the formulation of six kinds of contact conditions simultaneously in two modifications. The solutions are constructed in quadratures on the basis of new representations of the complex Galin potentials [\textit{L. A. Galin}, Contact problems of elasticity and viscoelastic theories (1980; Zbl 0506.73100)]. The first problem is reduced to a scalar combined Hilbert-Riemann boundary value problem for a plane with slots, and the second to unrelated Hilbert-Riemann and Hilbert problems for the same domain. Both problems of the theory of analytic functions are solved by a new method. The problem of the wedging of a composite plane by a finite stamp moving at a sub-Rayleigh velocity, and the problem of the motion of a stamp and a flexible cover plate over a half-plane boundary at subsonic velocity are examined as examples.
representations of the complex Galin potentials
scalar combined Hilbert-Riemann boundary value problem
unrelated Hilbert-Riemann and Hilbert problems
scientific article; zbMATH DE number 4191240