Quelques considérations sur le flambement des anneaux et des arcs

ABSTRACT This article deals with elastic instabilities of arches and rings. The proposed approach is based on the Principle of Virtual Powers, which leads to express the equilibrium equations on the deformed geometry, these equations being projected on the local axis of the undeformed geometry. It is important to well precise the hypothesis concerning the orders of magnitude in the frame of the small perturbations analysis, which leads to appropriate approximations. The general case is analysed, as well as the case of the funicular arches. A resolution method is proposed and used for the resolution of some examples. To highlight certain difficulties, the classical case of the ring submitted to pressure is detailed in particular, which leads to confirm the value of the critical pressure given by Timoshenko. This focuses on the precautions which should be taken in the analysis of the instabilities of a structure submitted to pressure, when using a finite element analysis.