The Relevance of Analytical Formulations Predicting Stiffener Tripping

Abstract

In search for the governing failure mode of externally pressurized submarine pressure hulls the focus is, due to its loading, drawn to elastic buckling, although the dimensioning of general pressure hull design and material limitations make them prone to collapse or plastic buckling. Collapse occurs due to the loss of plastic capacity after a non-linear growth of the fundamental deformation mode. Plastic buckling occurs if the fundamental deformation mode of the pressure hull is transitioned in a buckling mode, i.e. a mode with lower strain energy, and the plastic capacity is lost due to the extent of the deformation. A true bifurcation point is often hardly observed due to imperfections, which initiate the governing buckling mode. Question is why to spend so much effort to determine the elastic buckling pressures other than to ensure they are well above the collapse pressure and plastic buckling pressure? This paper focuses on the value of elastic buckling evaluation of the pressure hull frames, generally referred to as frame tripping. Some latest attempts in improving the accuracy of the analytical formulations will be questioned. Firstly, this study will compare non-linear buckling with linear-elastic material behaviour to elastic buckling by means of finite element analysis. Secondly, the non-linear elastic-plastic effects will be included too. Doing so, the effect of the geometrical non-linearity and material elastic-plastic non-linearity will be visible separately and will give an indication of the relevance of frame tripping results predicted by analytical elastic buckling formulations. Literature offers a variety on analytical formulations, each with an underlying idea to remove undesired assumptions that impair results. Even recently comprehensive formulations are published to establish an accurate value of the elastic tripping pressures. This paper will show whether those methods are still relevant in modern pressure hull design or not.