Contact interactions of multi-layer plates with a combined base

The study is devoted to the development of a mathematical model and a method for solving the problem of contact interaction of multilayer strip-plates with a combined base. An elastic filler is located between the strips, which transfers the reactive pressures to the bonding strips. In this article, a mathematical model was developed to assess the internal force factors in multilayer strips-plates with a combined base, taking into account the contact interaction. It is assumed that the cylindrical stiffness of the strip-plates has different values, and the external loads are arbitrary. A closed system of integro- differential equations for the problem under consideration is obtained. In this case, the kernel of the singular integral describing the settlement of the base is expanded in a series using the Chebyshev polynomial, and the solution of the problem is reduced to the study of infinite systems of algebraic equations. The regularity of infinite systems of algebraic equations is proved. Formulas are proposed that describe deflections, rotation angle, internal force factors, settlement and base pressure by the known solutions of algebraic equations. As a result of the study, a number of effects were revealed in the internal force factors in a three-layer beam plate interacting with combined bases.