Buckling of spherical shells revisited

A study is presented of the post-buckling behaviour and imperfection sensitivity of complete spherical shells subject to uniform external pressure. The study builds on and extends the major contribution to spherical shell buckling by Koiter in the 1960s. Numerical results are presented for the axisymmetric large deflection behaviour of perfect spheres followed by an extensive analysis of the role axisymmetric imperfections play in reducing the buckling pressure. Several types of middle surface imperfections are considered including dimple-shaped undulations and sinusoidal-shaped equatorial undulations. Buckling occurs either as the attainment of a maximum pressure in the axisymmetric state or as a non-axisymmetric bifurcation from the axisymmetric state. Several new findings emerge: the abrupt mode localization that occurs immediately after the onset of buckling, the existence of an apparent lower limit to the buckling pressure for realistically large imperfections, and comparable reductions of the buckling pressure for dimple and sinusoidal equatorial imperfections.