Analysis of the Stress-Strain State of a Layer with a Cylindrical Cavity and Embedded Supports with Bushings

Using cylindrical embedded supports for parts is common in the aerospace and mechanical engineering industries. Simplifications or approximations are used to calculate such connections. A method for calculating a layer on two longitudinally embedded cylindrical supports is proposed in this paper. There are bushings (thick-walled pipes) between the supports and the layer; the layer is weakened by a longitudinal cylindrical cavity. Stresses are set on the lower and upper surfaces of the layer, smooth contact conditions are set on the inner surfaces of the pipes, and stresses are set on the surface of the cavity. To solve the problem, the Lamé equation is used, where the Cartesian coordinate system is used for the layer, and local cylindrical systems are used for the pipes and the cylindrical cavity. The combination of basic solutions in different coordinate systems is performed using the generalized Fourier method. Based on the boundary conditions and conjugation conditions, an infinite system of integro-algebraic equations, which is reduced to linear algebraic equations of the second kind and solved using the reduction method, is obtained. The stress-strain state at each point of elastic connected bodies is also determined from the Lamé equation using the generalized Fourier method to the basis solutions. The accuracy of the results in this case depends on the approximation of the boundary surfaces to each other and on the order of the system of equations. Numerical studies have been carried out for a layer with supports and a cavity located in a straight line under the action of a cantilever load. The analysis of the stress state was obtained in the zones of cylindrical holes of the layer and in the body of the bushings. The maximum stresses exceed the specified ones and occur at the location of the cylindrical cavity. The proposed solution method makes it possible to obtain the results of the stress-strain state of cantilevered elements of aircraft structures, to evaluate the influence of material and geometric parameters on the values of stress distribution in other structures of machines and mechanisms that can be represented as models similar to the one under consideration.