The stability of a uniformly compressed ring surrounded by a rigid circular surface

Abstract As a first step in the study of the stability of the thin steel liner of a prestressed concrete pressure vessel, the states of equilibrium of a uniformly compressed elastic ring placed inside a rigid circular cylinder are analysed. It is shown that there is no critical load as defined by classical theory, but that there is a state of unstable equilibrium which can be reached by small displacements only from the unbuckled position and a state of stable equilibrium which necessitates large displacements. Work must always be done to displace the ring from the unbuckled state, but this is reduced as the uniform compression is increased. Buckling apparently takes place when some random disturbance occurs which is large enough to provide the effort needed.