Cylindrical Shell Buckling Theories

This course covers the comprehensive understanding of equilibrium equations for cylindrical shells using both small and finite deflection theories. It begins with the derivation of these equations and the impact of initial curvature on membrane action due to secondary middle surface forces. The course further explains how these forces are expressed in terms of mid-plane displacement components. For instance, it discusses how compressive loads are considered negative as per sign convention. The course also delves into the derivation of Donnell's equation and how to solve it to find the critical load of an axially loaded cylindrical shell. It introduces the F-w formulation, which consists of two coupled governing differential equations in terms of stress function F and displacement w. The course concludes with the analysis of the post-buckling behavior of axially compressed cylinders, highlighting the impact of initial imperfections on the maximum load a cylinder can support.