АНАЛІЗ НАПРУЖЕНОГО СТАНУ ШАРУ З ДВОМА ЦИЛІНДРИЧНИМИ ВРІЗАНИМИ ОПОРАМИ ТА ЦИЛІНДРИЧНИМИ ВТУЛКАМИ

Abstract

The spatial problem of the theory of elasticity for a layer on cylindrical embedded supports with cylindrical sleeves (thick-walled pipes) located between each support and the layer is solved. Smooth contact conditions are set at the interface between the layer and the pipes. Stresses are specified on the surfaces of the layer, and displacements are specified on the inner surface of the pipe (rigidly conjugated to the support). The analytical and numerical solution of the problem is based on the Lamé equations written for the layer and each pipe. When the boundary conditions and the conditions of conjugation of the layer with the pipes are met, a system of integro-algebraic equations is created, which reduces to a system of linear algebraic equations. Each equation is written in its local coordinate system. For this purpose, the transition formulas of the generalized Fourier method are applied to the basic solutions of the Lamé equation. After solving the system of equations and finding the unknowns, the stress-strain state in the body of the layer and pipes was obtained. The reduction method was used to obtain numerical results. Fulfillment of the boundary conditions showed high convergence of the results, the accuracy of which depends on the order of the system of equations. The analysis of the stress-strain state of the layer and the pipe was carried out for different sleeve materials in places of stress concentration. The results indicate an increase in the stresses sφ and sz on cylindrical surfaces in the case of using polyamide bushings. The proposed method makes it possible to analyze the stress-strain state of a wide range of pipe structures. It also provides an opportunity to assess how changes in material and geometric parameters affect the stress distribution in such systems, which allows optimizing structures and ensuring their reliability. In the further development of this research topic, it is necessary to consider models where bushings are combined with other types of inhomogeneities (cavities, reinforcement) and other boundary conditions.