Axisymmetric and bifurcation creep buckling of externally pressurised spherical shells

Abstract

The creep buckling behavior of a geometrically imperfect complete spherical shell subjected to a uniform external pressure is examined using Sanders' equilibrium and kinematic equations appropriately modified to include the influence of initial stress-free imperfections in the radius. The Norton-Bailey constitutive equations are used to describe the secondary creep behavior and elastic effects are retained. The initial imperfections have the same shape as the classical axisymmetric elastic buckling mode and the initial elastic response is obtained analytically for external pressures smaller than the corresponding static collapse pressure. Numerical finite-difference procedures are used to obtain the axisymmetrical creep buckling behavior and to determine when a bifurcation or loss of uniqueness into a non-axisymmetric deformation state occurs.The numerical results for the creep buckling behavior of complete spherical shells are similar for hydrostatic and deadweight-type external pressures, at least for the particular parameters examined herein, and demonstrate that initial imperfections exercise an important influence on the critical times. It turns out from a practical viewpoint that axisymmetric creep buckling governs the behavior of the spherical shells examined in this article. It was observed from the present results that the creep buckling times of externally pressurised complete spherical shells are longer than those for “equivalent” axially loaded cylindrical shells.