  The critical buckling characteristics of hydrostatically pressurized complete
spherical shells filled with an elastic medium are demonstrated. A model based
on small deflection thin shell theory, the equations of which are solved in
conjunction with variational principles, is presented. In the exact
formulation, axisymmetric and inextensional assumptions are not used initially
and the elastic medium is modelled as a Winkler foundation, i.e., using
uncoupled radial springs with a constant foundation modulus that is independent
of wave numbers of shell buckling modes. Simplified approximations based on a
Rayleigh-Ritz approach are also introduced for critical buckling pressure and
mode number with a considerable degree of accuracy. Characteristic modal shapes
are demonstrated for a wide range of material and geometric parameters. A phase
diagram is established to obtain the requisite thickness to radius, and
stiffness ratios for a desired mode profile. The present exact formulation can
be readily extended to apply to more general cases of non-axisymmetric buckling
problems.
