Local buckling in infinitely, long cylindrical shells subjected uniform external pressure

This paper presents a unique approach to analyze the buckling of an infinitely long cylindrical shell subjected to the external pressure. Buckling is considered to occur locally in the shell, spreading over a certain length along the longitudinal axis of the shell. A plausible function of the flexural displacement is created according to Timonshenkoʹs ring solution of the transverse collapse mode. The governing equations based on Donnell–МУШТАРИʹs shell theory are solved using Ritz method and the equilibrium conditions are educed. Numerical computations are performed for cases when shell thickness/radius ratios are 0.1, 0.05 and 0.03. In general, the pressure decreases sharply with a very slight increase of the normalized radial deflection just at the beginning of the initiation, then falls quite slowly till the two opposite points on the inner surface of the shell contact each other. It is found that the buckling pressure of the shell converges to the critical value given by Donnell–МУШТАРИʹs shell theory and the span of the buckling mode in the longitudinal axis of the shell is independent of material properties. Solutions given in this paper can be used to address the problem of steady-state buckle propagation in the shells.