The present paper contains a detailed analysis of the title problem. The buckled configuration is assumed to consist of two regions, viz., the detached region, where shallow arch approximations are adopted, and an attached region, where the ring assumes a constant curvature. The problem is treated as a variational problem with variable end points for which the variational formulation yields, in addition to the differential equations and boundary conditions, a transversality condition, determining the extent of the detached region. The results indicate that the ring will not buckle unless external disturbances are present. A discussion of energy barriers shows that the ring’s ability to sustain external disturbances diminishes as the contraction increases.

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