Properties of local buckling of spherical shell under external pressure

Abstract

An important property of localization in buckling of spherical shells under external pressure is discussed. It is shown that the localization is possible for structures with nonlinear softening. An analytical model of local buckling of spherical shell is developed. Rayleigh–Ritz method is used at small and moderate deflections. At large deflections corresponding to relatively small pressure (less than 20% of classical bucking load) it is based on asymptotic method. The asymptotic model is then expanded to the practically important range of the load. The response of the structure to local perturbations of different types (including radial probing force, prescribed deflection at the shell pole, and energy barrier) is studied. Special attention is paid to the energy barrier which is required for structure transition from initial equilibrium state to the post-buckling dimple-like state. Energy barrier criterion is used as a measure of metastability of the structure and applied for estimation of load level separating high and low sensitivity of the shell to local perturbations. Based on this pressure value, formulae for design buckling load are proposed and deliberated. Similarities and differences of local buckling of spherical shells under external pressure and axially compressed cylindrical shells are discussed.