Stability analysis of shells of revolution by the finite-element method.

Abstract

An extension of the finite-element displacement method to the analysis of linear bifurcation buckling of general shells of revolution under static axisymmetric loading is presented. A systematic procedure for the formulation of the problem is based upon the criterion that the condition for neutral stability of a system is the vanishing of the second variation of the total potential energy from the stable equilibrium state to the perturbed bifurcation state; this results in an eigenvalue problem. For solution, the shell is discretized into either a series of conical frusta or of frusta with meridional curvature. The prebuckling equilibrium solution is axisymmetric, but the perturbation-displacement field within each element is represented by Fourier circumferential components of the generalized displacements which are defined at the nodal circles. The present formulation is applied to a number of shells of revolution with arid without meridional curvature, and comparisons are made with other theoretical and available experimental results.