Buckling of a spherical shell embedded in an elastic medium loaded by a far-field hydrostatic pressure

Elastic buckling of a spherical shell, embedded in an elastic material and loaded by a far-field hydrostatic pressure is analysed using the energy method together with a Rayleigh-Ritz trial function. For simplicity, only axisymmetric deformations are considered and inextensional buckling is assumed. The strains within the structure that are pre-critical are assumed to be small for the linear theory to be applicable. An expression is derived relating the pressure load to the buckling mode number, from which the upper-bound critical load can be determined. It is found that the presence of the surrounding elastic medium increases the critical load of the shell and the corresponding buckling mode number. However, the results also show that the strain of the shell at the point of instability may not be small for typical values of material and geometric constants.