Corrugation of a flexible ring under external hydrostatic compression

The initial non-linearly elastic stage of a change in the shape of thin flexible ring under an external hydrostatic pressure is described. At this stage, the formation of alternating bulges and hollows in the ring in a circular direction is due to the balance of non-linearity and dispersion effects. A model is proposed which enables the dependence of the curvature of the deformed ring on the external pressure to be obtained. The shape of the ring is established from the known curvature by methods of differential geometry. Possible types of corrugation of the initial circular ring are obtained. The change in the shape of the ring around a rigid rod, placed inside the ring, is described. The strict relation between the amplitude of the bulges and hollows in the circumferential direction of the ring also prevents the formation of rigid edges on its surface.