Buckling of a compressible elastic ring

Abstract

We study stability of a circular ring subjected to uniform hydrostatic pressure. The constitutive equations of a ring are taken in a generalized form, allowing the compression of the ring axis. We show that the null space of the linearized differential equations has dimension three. On the basis of a single bifurcation equation the bifurcation diagram is obtained. It is shown that bifurcation could be both super- and subcritical, depending on the values of parameters.