Axisymmetric contact interaction of two coaxial pre-tighten these cylinders and elastic layer with initial (residual) stresses.

Abstract

The article deals with the coaxial mixed type task of measuring pressure of prestressed two coaxial cylinder punches upon a layer with initial (residual) stresses within the framework of linear elasticity theory. We consider the cases in the absence of the friction forces. In general, the research was carried out for the theory of great initial (ultimate) deforma-tions and different variants of the theory of small initial deformations with arbitrary structure of elastic potential. It is assumed that the elastic dies as well as the layer are made of different isotropous, transversely isotropic or composite materials and they are interacting on one of the dieses surfaces. The mode of deformation in elastic layer with initial (residual) stress will be defined with the help of harmonic functions as the Henkel integrals. We should note, although the Henkel-method does not provide exact solutions, but it lets us reduce the task to the Fredholm equations, which let us use the method of consecutive approximations. Consequently we got a components of potential vector and tenzor of deformations in the case of equal roots of axis-symetrical type task. So, the received solutions are defined by lines with the help of very many constants. These constants are defined with two systems of regular linear algebraic equations. The research was carried out on the problem of the influence of initial stresses on the law of distribution of contact disorders in the elastic layer with initial (residual) stresses.