Convex Models of Uncertainty in Radial Pulse Buckling of Shells

The buckling of shells subject to radial impulse loading has been studied by many investigators, and it is well known that the severity of the buckling response is greatly amplified by initial geometrical imperfections in the shell shape. Traditionally, these imperfections have been modeled stochastically. In this study convex models provide a convenient alternative to probabilistic representation of uncertainty. Convex models are well suited to the limitations of the available information on the nature of the geometrical uncertainties. A n ellipsoidal convex model is employed and the maximum pulse response is evaluated. The ellipsoidal convex model is based on three types of information concerning the initial geometrical uncertainty of the shell: (1) which mode shapes contribute to the imperfections, (2) bounds on the relative amplitudes of these modes, and (3) the magnitude of the maximum initial deviation of the shell from its nominal shape. The convex model analysis yields reasonable results in comparison with a probabilistic analysis due to Lindberg (1992a,b). We also consider localized imperfections of the shell. Results with a localized envelope-bound convex model indicate that very small regions of localized geometrical imperfections result in buckling damage which is a substantial fraction of the damage resulting from full circumferential initial imperfection.