Analysis of the Stress State of a Layer with Two Cylindrical Swivel Joints and a Cylindrical Cavity

Abstract

In practice, connections in the form of cylindrical swivel joints are often encountered. However, exact methods for calculating such models are absent. Therefore, the development of algorithms to solve such problems is relevant. In this study, a spatial elasticity problem is solved for an infinite layer with two cylindrical swivel joints and a cylindrical cavity positioned parallel to each other and parallel to the layer surfaces. The embedded cylindrical swivel joints are represented as cavity with given contact-type conditions (normal displacements and tangential stresses). Stresses are specified on the layer surfaces and the cavity surface. The layer is considered in a Cartesian coordinate system, while the cylindrical cavities are considered in local cylindrical coordinates. The spatial elasticity problem is solved using the generalized Fourier method applied to the Lamé equations. Satisfying the boundary conditions results in a system of infinite linear algebraic equations, which undergo reduction methods. In the numerical study, the accuracy of boundary condition fulfillment reached 10-3 for stress values ranging from 0 to 1, with the equation system (Fourier series members) order of m=4. As the order of the system equations increases, the accuracy of calculations increases. Stress state analysis was conducted at varying distances between supports. The obtained results indicate that with an increased distance between supports, stresses on the supporting cylindrical surfaces of the layer and the cylindrical cavity surface decrease. These stresses are redistributed to the upper and lower surfaces of the layer, where the stresses increase and exceed the specified ones. The numerical outcomes can be applied to predict geometric parameters during design processes.