This conference paper was submitted for presentation at the NAFEMS World Congress 2025, held in Salzburg, Austria from May 19–22, 2025.

Abstract

Ring-stiffened cylinders under hydrostatic pressure are subjected to several modes of collapse. For instance, collapse can be caused by a structural detail that experiences high stresses. Such a collapse mode can easily be avoided by minor modifications in the design. Another collapse mode consists of the tripping of stiffeners, showing rotation of the ring stiffener about the tangential axis. Prevention of this mode requires a sound choice of the stiffener dimensions with minor impact on the total weight. With respect to the collapse modes considered here, it can be stated that the ultimate solution in nonlinear Finite Element Analyses (FEA) may show large areas in yield condition without a clear indication on where the plastic capacity is lost first, and the collapse is initiated. Considering large areas in yield the most important collapse modes consist of: (i) yielding of the shell (interframe collapse), or (ii) yielding of the ring frame (global or overall collapse). Regarding (i): when considering weight optimization, it must be noted that the shell contributes the most to the total weight, and this emphasizes the need to focus on minimum thickness. This draws the attention to interframe collapse; however, global collapse cannot be decoupled from shell behaviour. A substantial part of the shell participates in the bending stiffness of the ring frame and yielding of the shell decreases this bending stiffness. Regarding (ii): if the ring stiffener starts to yield first, then the shell'™s support decreases, and this initiates yielding of the shell. In the FE simulations, a close observation of the deformation and resulting stress as the applied pressure increases gives a better understanding than analysing the stress situation at the ultimate pressure. For twelve pressure hull geometries, radial deformation and von Mises stress distribution versus hydrostatic pressure are assessed, and the nature of collapse (global or interframe) is established. These geometries comprise pressure hulls that are designed to fail by global collapse, as well as designs that aim for minimum weight and therefore minimum thickness. Analytical methods that can be found in the guidelines of Classification Societies are also considered. These methods make a clear distinction between the two collapse modes under consideration, and an interaction between collapse modes is not taken into account. Nonlinear FE analysis shows the response in the shell and the ring stiffener to the hydrostatic pressure and the resulting plots reveal in most cases the nature of collapse. However, the analytical methods produce misleading results. In some cases, the predicted collapse pressures are close to the ultimate pressures given by FE analyses, but the corresponding collapse modes are incorrect. For interframe collapse, it is obvious that the analytical approach gives erroneous results since this method is based on axisymmetric behaviour. Out-of-Circularity produces additional bending stresses between the frames that are not covered by the analytical methods. This gives non-conservative predictions of interframe collapse pressures. Analytical methods to analyse bending stresses in the ring-frame do incorporate the Out-of-Circularity, but the difference with the nonlinear FE analysis outcomes is significant. Understanding the nature of collapse follows from carefully observing: von Mises stress plots at the ultimate pressure; the progress of radial deflection and stress towards the ultimate pressure. The latter is imperative to distinguish the influence of the stiffener and the shell mid-bay on the collapse. This distinction is also important to review the quality of the analytical approach to predict stiffener collapse versus interframe collapse. This presentation will demonstrate the discrepancies of the analytical formulations on predicting the collapse pressures of pressure hulls, by a comparison to FEA.