Geometric imperfection and lower-bound analysis of spherical shells under external pressure

For the design of thin-walled spherical shells under external pressure empirical knockdown factors are applied. These knockdown factors are based on experimental results from the beginning of the 20th century and have been shown to be very conservative for modern shell structures. In order to determine less conservative and physically based knockdown factors for the design of spherical shells, different analytical and numerical design approaches have been developed. In this paper common as well as new shell design approaches are presented in detail and evaluated regarding the lower-bound buckling pressure. Among these design approaches are the reduced stiffness method, measured geometric imperfections and perturbation approaches. Important analysis and modeling details of each design approach are described, and test examples are given and validated. Advantages and disadvantages of each approach are listed, and design recommendations are given. Practical shell buckling design examples are demonstrated by means of a tori-spherical bulkhead and a deep-sea spherical pressure hull. In addition, a collection of about 700 experimental knockdown factors for spherical shells under external pressure is given in the Elsevier repository.