Bifurcation of Circular Rings Under Normal Concentrated Loads

Abstract

The deformation in bending of a circular ring loaded in its plane by concentrated forces is studied. The ring is assumed to be an elastica. The loads are of equal magnitudes and are equally spaced about the ring. Values of loading at which bifurcation of the symmetrical finite distortion shape occurs are determined for forces which remain normal to the ring. It is found that no bifurcation point exists for a ring under three loads. Buckling of a ring under two loads can occur only when the prebuckling configuration is an extremely distorted one. If the number of loads is five or greater, the critical average pressure does not differ greatly from the result for the ring under uniform pressure.