Static and dynamic numerical analysis studies of hemispheres and spherical caps. Part II: Results and strength predictions

Abstract Shell-like structures are prevalent in nature. However, because of their slenderness they are prone to buckling, and to such an extent that this is often the dominant consideration in their design. Early attempts to determine buckling pressures were unsatisfactory. Although initial geometric distortions are now recognised as the cause of this, little comprehensive work has been conducted on doubly-curved shells, particularly hemispheres, subjected to external pressure and having asymmetric initial shapes. This paper presents the results of such a study, in two parts. In Part I, which was presented in the previous issue of Thin-Walled Structures, the background research on doubly-curved shells was briefly reviewed. The kinematic, equilibrium and constitutive equations used in the work were stated. The adopted numerical procedure which can generate static or dynamic solutions was described along with the results of convergence studies. In this Part, the effect of various initial shapes and their location is described: the critical combination is identified. The parameters selected to nondimensionalise the results are indicated, followed by those of the study which primarily involve initial deformation magnitude and shell slenderness. Two strength formulations which conveniently represent the results of the study are presented.