STABILITY ANALYSIS OF AXISYMMETRICAL THIN SHELLS

Thin shells are prone to fail by buckling. In most of the practical si tuations, shell structures have membrane stresses as well as bending s tresses and the response of these shells becomes nonlinear. Linearizat ion of the nonlinear equilibrium equations gives rise to an algebraic eigenvalue problem, solving which, buckling load is obtained. Eigenval ue buckling analysis is computationally much cheaper than nonlinear an alysis involving tracing the load-deflection path and finding the corr esponding collapse load. But buckling loads obtained by eigenvalue buc kling analysis are always overestimated, and for systems with large pr ebuckling rotations this approach may give highly unconservative resul ts. For better prediction of the actual buckling load of a structure, a new methodology involving the proper combination of eigenvalue buckl ing analysis and geometric nonlinear analysis is used here. This metho d is computationally cheaper than nonlinear buckling analysis but more reliable than Linear buckling analysis. The methodology is used to ca lculate the buckling load of shells of revolution. The conical frustum shell element with two nodal circles is used in the present study. Al so discussed is how to include the effect of initial geometric imperfe ction in buckling analysis.