Buckling and Post-buckling of Circular Rings: Some Differential Geometry Issues

Buckling of circular rings under external pressure is one of the oldest problems in structural engineering and the first solution to it was proposed by Levy in 1884. The basic solution for the Euler-Bernouilli beam can be found in the vast majority of textbooks on stability. However, in a world which strongly relies on FE commercial packages, one should be always well aware of these fundamentals and in the present work some considerations arising from the numerical treatment of the problem by means of FE and from the classic analytical solutions of the differential equations are discussed in order point out some inconsistencies which may arise the numerical analyses.