From the Von Karman large deflection equation of the plate and by assuming that a plate has an initial deflection in form of a spherical cap, the equilibrium equation of a spherical cap subjected to hydrostatic pressure is obtained, simplified and solved in the same way as an equilibrium equation of a beam on elastic foundation subjected to the axial and lateral loads. The influence of prebuckling deformations and stresses on the buckling of the spherical shell may be evaluated and the relation between buckling strength of the spherical shell and the column is obtained by analysing the buckling problem of the beam on elas tic foundation. The presented formula for the calculation of the stability of the spherical shell gives a lower limit of buckling pressure and is in good agreement with test data recorded in literatures.
Timoshenko(1936) summarized the classical small deflection theory for the elastic buckling of a complete sphere as firs t developed by Zolley in 1916. However, the elastic buckling loads of roughly one - fourth those predicted by expression (1) were observed in earlier tests recorded in the literature. Various investigators have attempted to explain this large discrepancy by introducing nonlinear, large deflection shell equations. Although a" lower" buckling load was found by Karman and Tsien (1939) and is in fair agreement with the early experiments; following researches, as mentioned by Zhou (1979), find the reason why this lower buckling load is unsuitable for practical use. The solution provides an insight into the multibuckling modes of spherical cap and the correspondent critical pres- surest Furthermore, since the spherical cap is an isolated section of the spherical shell, some conclusion can be drawn on the stability of the spherical shell from the understanding of the buckling of spherical cap.