Sachuk Y. Flat contact problems and the wear of an elastic half-plane with a canonical shape.

The dissertation is devoted to research of the problems of the contact interaction of hard dies of a canonical form (parabolic, cylindrical, elliptic, hyperbolic) with an elastic half-plane for determining the contact pressure and stress-strain state in an elastic half-plane, studying the problems of contact interaction of dies with an elastic half-plane, taking into account the wear of the material, including a half-plane, which is protected by a thin elastic layer. For a plane contact problem, an analytic solution of a singular integral equation for all forms of stamps is obtained, however, for cylindrical, hyperbolic and elliptic stamps, it is expressed in terms of complete elliptic integrals of the first and third kinds. An algorithm was developed and schemes for calculation of contact pressure and stress components were determined, yield strengths were determined. For a contact problem with wear of a half-plane, a singular integro-differential equation for determining the contact pressure is constructed. The developed method of separating variables for solving an integral equation, which reduces the problem to a generalized problem on its own values. The peculiarities of application of basic methods for finding approximate eigenvalues are investigated. The circuit of calculations and program modules for solving a generalized problem on their own values are constructed, the optimal number of eigenvalues for the reliability of the results is determined. The features of wear of the half-plane with canonical stamps for different curvature of stamps at different time points were investigated, and special effects of interaction of bodies were revealed. For a contact problem on Winkler's thin elastic layer wearing, a mathematical model of the problem was constructed and a method for solving using the Chebyshov polynomials was developed. A step-by-step algorithm for solving an integro-differential equation for contact pressure is developed, which reduces the problem to the solution of a system of linear algebraic equations. The features of coating wear with canonical stamps for various contact pairs with different ratios of elasticity and wear intensity are investigated.