Mathematical modeling of non-stationary deformation of cylindrical structures

Abstract

The paper investigates the dynamic behavior of a hollow elastic cylinder of finite length, placed in a rigid cylindrical shell, under a sharp change in internal pressure. A numerical solution of a two-dimensional dynamic problem is obtained using the method of spatial characteristics. The stress-strain state of an elastic cylinder is described by a system of hyperbolic equations with two circular conical surfaces as characteristic surfaces. The outer cones correspond to longitudinal waves; the inner ones correspond to transverse waves. The calculations were carried out under various conditions at the ends and the outer (contact) surface of the cylinder and shell. An analysis of the results for a cylinder with load-free ends shows that the absence of gluing the outer surface of the cylinder with the shell leads to a significant increase in the velocities of the points of the cylinder. Under the action of internal pressure, the ends move apart, resulting in a significant increase in the radial velocities of the internal channel. Qualitative patterns of behavior of the structures under consideration, which are widely used in mechanical engineering, on impact-type impacts, can be used to improve and optimize them at the design stage.