STUDY OF THE MATERIAL PROPERTIES INFLUENCE AND CONTACT CONDITIONS ON THE STRESS-STRAIN STATE DURING THE INTERACTION OF A STAMP AND A PLATE

Abstract

The article examines the results obtained when applying the perturbation method to the solution of individual contact problems.Attention is paid to the influence of non-ideal properties of materials of interaction bodies. The influence of the complex geometry of the contact zone is also taken into account. In the article, mathematical models of problems on the interaction of an elastic orthotropic semi-infinite plate with cylindrical anisotropy in the form of a curvilinear sector are constructed and considered. In the process of interaction between the stamp and the plate, there are areas of sliding and adhesion. The original problems of the theory of elasticity, difficult in their initial formulation, in the process of applying the perturbation method are reduced to the sequential solution of simpler problems of the theory of functions of a complex variable. Analytical solutions to the problem of the interaction of an elastic anisotropic semi-infinite plate in the form of a curvilinear sector and a rigid stamp were obtained, taking into account the presence of areas of sliding and adhesion in the contact zone. As significant results obtained after solving the formulated contact problems, it is possible to indicate the found regularities of stress distribution under the stamp, as well as the dependence of this distribution on the dimensions of the contact area. An analysis of the dependence of the size of the coupling zone on the stiffness characteristics of the sector was also carried out, taking into account different materials (for the sector), the opening angle of the sector and the dimensions of the stamp. In order to further develop the method and prove the convenience of applying the perturbation method in complex mixed boundary value problems, a study of the stress-strain state of an elastic anisotropic plate for an analogue of the Galin problem was carried out, while cases for different plate materials were considered. Corresponding analytical solutions were also obtained. The dependence of the size of the adhesion area on the dimensions of the stamp and the opening angle of the sector, as well as on the physical properties of the material of the sector, was analyzed. Possible boundary transitions are performed in the work and a comparison with known scientific results is made. The approach proposed by the authors makes it possible to obtain analytical solutions to practically important problems of contact interaction, to carry out possible assessments of the stress-strain state of thick-walled structures with reinforcing elements, stamps, overlays, etc. The results may also be useful. when designing mining works. At the same time, such important issues as the peculiarities of the physical properties of the materials of the interacting bodies, the complex geometry of the contact zone, the occurrence of areas of sliding and adhesion in the contact zone are taken into account.