Contact problem of the interaction of hard stamps with elastic halfplane surface protected by Winkler covering

Abstract

Formulation of the problems of contact interaction of stamps of canonical form (cylindrical,
elliptical, hyperbolic) with an elastic half-plane, which is protected by an elastic layer of Winkler
is done. The constructed mathematical model allows us to investigate the influence of physical and
mechanical properties of the covering on the process of exploitation of the components. A singular
integrodifferential equation to determine the contact pressure between the stamp and the covering
is constructed. The method of its solving using Chebyshev polynomials, which reduces the problem
to the system of linear algebraic equations is developed. Numerical calculations of the contact
pressure for fixed contact areas at variable parameters (covering hardness and thickness of
Winkler elastic layer) are carried out. The behavior of contact stresses for large and small areas
of contact are analyzed.