Stability of an elastic circular tube of arbitrary wall thickness subjected to an external pressure

Abstract

In the last decade it became clear that the loss of stability may occur not only in slender but in thick and thick-walled bodies as well. In the present paper the stability of an infinitely long circular cylinder of arbitrary wall thickness is investigated. The material of the cylinder is taken as incompressible and the cylinder is subjected to an external pressure. On a finite symmetric deformation of the cylinder is superposed a secondary infinitesimal deformation depending on the radial and hoop coordinates. A system of three coupled second order partial differential equations is obtained for three unknown functions, which is solved by the Frobenius series method. A nontrivial fulfillment of the boundary conditions leads to a characteristic equation for a deformation parameter. An approximate two term solution assuming Neo-Hookean material is analyzed. In the limit case of a thin shell the critical outer pressure is found to be in agreement with the known classical result. A numerical analysis for thick shells is also given.