Instability of a Hollow Elastic Cylinder Under Tension, Torsion, and Inflation

Abstract

Background. Many papers on the elastic stability of both thin-walled and massive (three-dimensional) bodies regard the bifurcation of equilibrium in the case of compressive loads. Although, the elastic instability may also occur under tensile stresses. Method of Approach. In the present paper on the basis of three-dimensional equations of the nonlinear elasticity the instability of a stretched infinite hollow cylinder under torsion and inflation is investigated. The bifurcational method of stability analysis is used. Results. The critical surfaces and stability region in the space of loading parameters are defined for a Biderman material and special model of incompressible medium, which possess essential material nonlinearity. The influence of a wall thickness on the instability of a hollow cylinder is analyzed. Conclusions. Based on the obtained results, a simple and efficient practical criterion of stability under tension is formulated. This criterion can be represented in the form of the Drucker postulate, given in terms of external loads.