CONTACT PROBLEM FOR ELASTIC PRESTRESSED CYLINDERS OF CIRCULAR CROSS-SECTION (SOLID AND ANNULAR) AND HALF-SPACES WITH INITIAL STRESSES

Abstract

This article addresses contact problems involving cylindrical and ring punches interacting with pre-stressed bodies, without considering frictional forces. Specifically, it focuses on the pressure exerted by an elastic ring punch on a half-space with initial stresses and the pressure exerted by two pre-stressed half-spaces on an elastic cylindrical punch with initial stresses. Investigating the contact interaction of punches, which forms the main objective of this work, is highly relevant, as contact interaction is one of the most common methods of transmitting external loads in practical applications. The research was conducted within the framework of the theory of large initial (ultimate) deformations and two variants of the theory of small initial deformations, based on the linearized theory of elasticity with an elastic potential of arbitrary structure. Various fundamental results were employed in the analysis, including Hankel’s transformations, integral equations, orthogonal polynomials, and other methods from the contact problem theory of the linearized theory of elasticity.