Influence of extra terms on asymptotic analysis of imperfection sensitivity of toroidal shell segment with random imperfection

The bifurcation of a toroidal shell segment with initial imperfection which are subjected to lateral or hydrostatic pressure is studied under the assumption that the initial imperfection are Gaussian random stress-free displacement whose mean and autocorrelation function are given. We use a perturbation scheme developed by Amazigo [Amazigo, J.C., 1971. Buckling of stochastically imperfect columns on nonlinear elastic foundation. Quart. Appl. Math. 403-491]. A simple approximate asymptotic expression is obtained for the bifurcation load for small magnitudes of the imperfection. The result is compared with results obtained earlier under secondary bifurcation analysis for the imperfections in the shape of the buckling mode and the results in the literature, which shows some significant differences as a result of inclusion of extra terms in the buckling equation.