Buckle Propagation: Steady‐State Finite‐Element Analysis

An innovative finite‐element technique for the analysis of buckle propagation in cylindrical shells subjected to external pressure is presented. Advantage is taken of the steady‐state nature of propagation, permitting a robust and efficient formulation to be implemented within the framework of large displacement/rotation elastoplastic finite‐element analysis. The procedure relies on the fact that the history of deformation that any material point undergoes during buckle propagation can be traced by marching in the longitudinal direction, along the pipe generator through the point, from the front to the tail in a snapshot of the propagating profile. Thus, the state of deformation and stress everywhere in the pipe can be determined from the propagating profile. A scheme is described in which suitable initial estimates of the propagation pressure and the propagating profile are selected, and improved estimates are obtained by means of equilibrium iterations. The computational requirements are rather low, and parametric studies can be conducted easily for a wide range of values of the diameter‐to‐thickness ratio. In this paper, the technique, its implementation, and results for stainless steel pipes are presented. Excellent agreement is found between the analytical results and previously reported experimental data.