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 met hod together with a Rayleigh-Ritz trial function. For simplicity, only axis ymmetric deformations are considered and inextensional buckling is assumed. The strains within the structure that are pre-critical are assumed to be s mall for the linear theory to be applicable. An expression is derived relat ing the pressure load to the buckling mode number, from which the upper-bou nd critical load can be determined. It is found that the presence of the su rrounding elastic medium increases the critical load of the shell and the c orresponding buckling mode number. However, the results also show that the strain of the shell at the point of instability may not be small for typica l values of material and geometric constants.