Stability of Inelastic Tubes under External Pressure and Bending

Abstract

This paper investigates the stability of externally pressurized tubes subjected to bending. A rigorous analytical technique based on the finite element method and accounting for geometric and material nonlinearities is described. Its advantages over existing analytical tools include the capability of simulating tubes of arbitrary thickness and the introduction of a “pressure node, “which facilitates the transition over limit pressure points. The formulation is applicable to pipe analysis in two as well as three dimensions. Results, presented in the form of pressure‐curvature interaction diagrams, indicate good agreement with the available experimental data. In agreement with earlier work, it is shown that ultimate tube strength is sensitive to loading path. A simple stability criterion is employed and leads to proper characterization of instability for all histories of pressure and curvature. Finally, the three‐dimensional simulation of the common experimental procedure, in which end rotations are applied to the specimen by means of welded plates, shows that curvature may not be nearly constant lengthwise, and, therefore, care must be exercised in extracting a characteristic value that is independent of end conditions. Suggestions, based on findings from several three‐dimensional analyses, are made concerning this matter.