Incontrovertible proof that the “discrepancies” in thin-shell-buckling studies are in the classical theory, not the test data

Abstract

It is shown here that the classical shell-buckling analyses have been fatally flawed since they were first derived. One reason cited is a failure to freeze the buckling stresses at the values at which buckling commenced, which resulted in consistent over estimates of the true buckling stresses by large factors. Another is the misinterpretation of the inextensibility criterion, which is customarily expressed in terms of the linear equations pertaining prior to buckling instead of the nonlinear equations that govern once buckling has commenced. The consequence of not acknowledging these errors is that, for many decades, it has been assumed incorrectly that the classical analyses for the various shell geometries are valid and that the major discrepancies can all be attributed to imperfections in the testing. It is shown here that this is not the case, by deriving different governing equations for shell buckling, starting from the geometrically nonlinear equilibrium equations for thin shells. These equilibrium equations are shown to include both the linear terms governing prior to buckling, with the remaining terms pertaining during buckling. This shows that buckling is resisted entirely by bending stresses alone, just as is known to be the case for flat-plate buckling, instead of by the combination of membrane and bending stresses. Specific equations are included for cylindrical shells, along with test data showing that the correct buckling stress for longitudinally compressed unpressurized cylinders is only half the classical prediction. Future papers will include full analyses of the buckling of spherical shells under external pressure at half the classical prediction, and of cylindrical shells under external pressure at one third of the classical prediction, as well as the buckling of pressurized and unpressurized cylindrical shells under longitudinal compression showing how, as the internal pressure is increased, the diamond-buckling stress increases from half the classical prediction for zero pressure to the classical ring-buckling stress for high pressure.