Dynamic buckling of elastic-plastic complete spherical shells under step loading

The dynamic axisymmetrical behaviour of a perfect complete spherical shell made from a bilinear or work hardening material and subjected to a uniform external step pressure loading is investigated. A perturbation method of analysis leads to a Mathieu equation which gives the dynamic buckling pressure and associated mode for a complete spherical shell. The influence of the plastic parameter and damping on the dynamic buckling pressure and mode number are also discussed.