Revisitation of elastic buckling of circular rings: Some analytical and numerical issues

Elastic buckling of circular rings under external pressure is one of the oldest and most ubiquitous problems in structural engineering and the first meaningful solution to it was proposed by Levy (1884). This basic solution, based on the Euler–Bernoulli beam model, can be found in the vast majority of textbooks on stability. However, there are a number of subtleties in the formulation of the problem which need to be taken into account so and one should always be well aware of the underlying analytical fundamentals, especially in the current world which strongly relies on numerical analyses. Therefore, starting from the general nonlinear kinematics of the problem, the buckling load is revisited by means of a direct energy approach and on the basis of an in-depth discussion of the classic kinematic hypotheses. Possibly different outcomes are pointed out and remarked. Finally, some inconsistencies which unexpectedly arise in pursuing the solution by means of commercial FE packages are presented and commented.