Stability Analysis of Axisymmetric Thin Shells

Abstract

Thin shells are prone to fail by buckling. In most of the practical situations, shell structures have membrane stresses as well as bending stresses and the response of these shells becomes nonlinear. Linearization of the nonlinear equilibrium equations gives rise to an algebraic eigenvalue problem, solving which, buckling load is obtained. Eigenvalue buckling analysis is computationally much cheaper than nonlinear analysis involving tracing the load-deflection path and finding the corresponding collapse load. But buckling loads obtained by eigenvalue buckling analysis are always overestimated, and for systems with large prebuckling rotations this approach may give highly unconservative results. For better prediction of the actual buckling load of a structure, a new methodology involving the proper combination of eigenvalue buckling analysis and geometric nonlinear analysis is used here. This method is computationally cheaper than nonlinear buckling analysis but more reliable than linear buckling analysis. The methodology is used to calculate the buckling load of shells of revolution. The conical frustum shell element with two nodal circles is used in the present study. Also discussed is how to include the effect of initial geometric imperfection in buckling analysis.