CONVEX MODELS OF UNCERTAINTY IN RADIAL PULSE BUCKLING OF SHELLS

The buckling of shells subject to radial impulse loading has been stud ied by many investigators, and it is well known that the severity of t he buckling response is greatly amplified by initial geometrical imper fections in the shell shape. Traditionally, these imperfections have b een modeled stochastically. In this study convex models provide a conv enient alternative to probabilistic representation of uncertainty. Con vex models are well suited to the limitations of the available informa tion on the nature of the geometrical uncertainties. An ellipsoidal co nvex model is employed and the maximum pulse response is evaluated. Th e ellipsoidal convex model is based on three types of information conc erning the initial geometrical uncertainty of the shell: (1) which mod e shapes contribute to the imperfections, (2) bounds on the relative a mplitudes of these modes, and (3) the magnitude of the maximum initial deviation of the shell from its nominal shape. The convex model analy sis yields reasonable results in comparison with a probabilistic analy sis due to Lindberg (1992a,b). We also consider localized imperfection s of the shell. Results with a localized envelope-bound convex model i ndicate that very small regions of localized geometrical imperfections result in buckling damage which is a substantial fraction of the dama ge resulting from full circumferential initial imperfection.