Axisymmetrical buckling of an initially deformed shallow spherical shell under external pressure

Axisymmetrical snap buckling of a clamped shallow spherical shell with initial deformation and subject to uniform pressure is analysed based on the finite-deformation theory. As a refinement to analyses given in the author's previous papers, a variable term in the deformation pattern is introduced and Galerkin's method is applied to the non-linear simultaneous differential equations, so that upper buckling pressures are obtained as a function of the geometrical parameter α. Non-uniqueness of solution is shown in the region of larger values of α, where the higher order of deformation mode takes place. Stability of a number of possible equilibrium states is checked by use of the second variation of total potential energy to clarify the actual buckling process. The remark- able decrease of buckling pressure is reasonably explained by introducing a small initial deflection, which explains the discrepancy between the classical buckling pressure and experimental results.