INFLUENCE OF INITIAL STRESSES ON CONTACT INTERACTION OF PRE-STRESSED ANNULAR STAMP AND HALF SPA

Abstract

The article is devoted to the study of the contact interaction of a pre-stressed annular stamp and a half-space with initial stresses without taking friction forces into account. The study is presented in a general form for the theory of large initial (finite) deformations and two versions of the theory of small initial deformations in the framework of the linearized theory of elasticity for an arbitrary structure of the elastic potential. There is assumed that the initial states of the elastic annular stamp and the elastic half-space remain homogeneous and equal. The study is carried out in the coordinates of the initial deformed state, which are interrelated with Lagrange coordinates (natural state). In addition, the influence of the annular stamp causes small perturbations of the basic elastic deformed state. Also, it is assumed that the elastic annular stamp and the elastic half-space are made of different isotropic, transversal-isotropic or composite materials. Numerical analysis is presented in the form of graphs for the elastic potential of the simplest structure for an isotropic compressible body and corresponds to the quadratic approximation using algebraic invariants of the Green's strain tensor. The algorithm for solving this problem is implemented in the form of a computer program in the Maple 15 package The influence of the initial stress on the contact interaction between the elastic annular stamp and the elastic half-space of the potentials of a particular structure is investigated. The value of the studies carried out is that taking into account the influence of the initial (residual) stresses in the bodies on the law of distribution of the contact characteristics of elastic bodies at the points of their interaction can allow us to take into account, more effectively, the wear resistance of materials by properly estimating their strength reserves. Also, it can sufficiently reduce their material consumption, while retaining the necessary functional characteristics of materials. Consequently, the observed effect of the initial (residual) stresses is significant and must be taken into account when calculating the strength in structural details.