Robust knockdown factors for the design of spherical shells under external pressure: Development and validation

In this paper a physically based and deterministic design procedure for spherical shells under external pressure is introduced. Within the new design concept the membrane energy of a sphere is incrementally reduced by means of perturbation cutouts, until a bending energy dominate state is identified. The threshold between membrane energy state and bending energy state represents a robust plateau for the buckling pressure. A comprehensive numerical investigation was performed in order to study the influence of radius-to-thickness ratio (R/t) as well as the dome height-to-base radius ratio (H/r). The results verify that both geometric properties ratios significantly influence the lower-bound buckling pressure, especially if plastic buckling occurs. Improved shell buckling design factors are given in the form of an simple analytic equation. The corresponding threshold KDFs were validated with a large number of buckling experiments and deliver much higher KDFs than currently used empirical guidelines. Based on the new design criterion lower-bound estimation for the buckling pressure of a tori-spherical bulkhead and the inner dome of the cryogenic upper stage ESC-A from the European space launch-vehicle Ariane 5 are determined.