Contact Problem With a Semi-Strip Deformable Stamp

The paper presents one of the methods for studying the contact problem for a deformable stamp on a layered deformable anisotropic composite, considered in the half-band region. Studying this contact problem would be impossible without a solution. Two previously studied contact problems are on the effect of a strip deformable stamp on an anisotropic composite and on the effect of an absolutely rigid half-strip stamp on the same medium. The first task showed a way to form a deformable stamp of arbitrary rheology. A method for constructing dispersion equations for determining discrete resonant frequencies, previously discovered by Academician I.I. Vorovich in contact problems with a deformable die, was also extracted from it. In addition, it developed an approach that makes it possible to build an accurate solution for a strip stamp using the Newton – Kantorovich method, starting from the parameters for both wide strips and narrow strips. It should be noted that the construction of solutions for dynamic contact problems turned out to be possible due to the use of the Mandelstam – Ignatovsky principle in integral equations to correctly describe the properties of solutions at infinity. But if, for the case of a stripe stamp, you can call If there are other approaches to approximate analytical or numerical construction of approximate solutions, then in the case of a half-strip stamp with an absolutely rigid stamp, the performed study was the only one. It incorporated both a number of approaches for the case of a strip stamp, and a new, first-developed approach to solving contact problems with a piecewise smooth boundary. In the problem with the case Compared to the case of an absolutely rigid die, there was a problem with constructing a block element with a carrier in the half-strip, which had not been done before. In this paper, this problem is solved for the first time, which made it possible to study the contact problem with a deformable stamp in such a field and construct its approximate solution with all the basic properties.