Postbuckling of Rings under Two Uniform Loads

The interaction effect of the normal and centrally directed pressures on the initial postbuckling behavior of a thin elastic circular ring buckling freely in its own plane is investigated by means of the perturbation method applied to the exact nonlinear differential equations of the engineering theory of curved beams. A dimensionless value of the postbuckling deflection is employed as the perturbation parameter. The analysis has yielded a simple formula representing the relationship between small increases in the buckling loads. This formula characterizes the initial postbuckling behavior of the ring subjected to the two interacting, uniformly distributed loads. Heretofore, the limited technical literature on the postbuckling characteristics of rings has dealt only with single distributed external pressure loads. In practice, the two types of static loads considered can be realized by compressing the ring by means of closely spaced, perfectly flexible spokes and simultaneously applying a gas pressure.