Perturbation analysis of instability for non-uniform cylindrical shells with initial imperfection

Buckle propagation in subsea corroded pipelines is one of the most concerned problems in offshore industries, while locating the plastic hinges in the corroded pipeline is the crux in determining the buckle propagation pressure. This paper presents a methodology to determine the locations of plastic hinges in non-uniform shells subjected to external pressure. The non-uniform shell used to model the corroded pipeline has two Regions: Region 1 of reduced, inconstant thickness and Region 2 of nominal thickness. Analytical formulas for the bifurcation load, radial deformation, initial yield pressure and stress distribution in the non-uniform shell are derived from perturbation analysis using WKB expansion. The locations of plastic hinges are identified at the stress peaks by taking the derivative of the stress with respect to circumferential coordinate. Imperfection sensitivity of the non-uniform shell is assessed with an emphasis on the role of initial yield pressure and the locations of plastic hinges. Special case when the thickness of Region 2 is constantly reduced is examined. It is found that both the initial yield pressure and the locations of plastic hinges depend on the non-uniform conditions of the cylindrical shell.