Inelastic Buckling of Spherical Shells

A numerical procedure is presented for determining the unsymmetrical buckling pressure for clamped, elastic-plastic spherical shells. The general deep-shell equilibrium equations are used along with an incremental plasticity theory based on the Prandtl-Reuss equations. The material is assumed to obey a Ramberg-Osgood type uniaxial stress-strain law. A linear eigenvalue problem is formulated where the buckling pressure is obtained by plotting the pressure versus the determinant of the stability matrix. Coefficients in the governing system of homogeneous equations are evaluated by solving the nonlinear problem for the axisymmetric deformation prior to unsymmetrical buckling. Buckling pressures are computed for a wide range of geometries and compared with existing theoretical results.