Contact Problem for a Pre-Stressed Annular Stamp and a Half-Space with Initial (Residual) Stresses (the Case of Equal Roots)
Abstract
The article is devoted to the study of the contact interaction of a prestressed ring stamp and a half-space (base) with initial (residual) stresses without taking friction forces into account. The problem is solved for the case of equal roots of the resolving equation. 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 ring stamp and the elastic half-space remain homogeneous and equal. The study is carried out in the coordinates of the initial (residual) deformed state, which are interrelated with Lagrange coordinates (natural state). In addition, the influence of the ring stamp causes small perturbations of the basic elastic deformed state.
Also, it is assumed that the elastic ring stamp and the elastic half-space are made of different isotropic, transversal-isotropic or composite materials.
Numerical analysis is presented by the form of graphs of contact stresses and displacements of a potential of a harmonic type.
The influence of the initial (residual) stress on the contact interaction between the elastic ring stamp and the elastic half-space of the potentials of a particular structure is investigated.
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