The critical buckling characteristics of hydrostatically pressurized complete spherical shells filled with an elastic medium are presented. A model based on small deflection thin shell theory, the equations of which are solved using exact methods in conjunction with variational principles, is presented. In the current 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. Critical buckling pressures and 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 formulation can be readily extended to apply to more general cases of non-axisymmetric buckling problems.
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