The critical buckling characteristics of hydrostatically pressurized completespherical shells filled with an elastic medium are demonstrated. A model basedon small deflection thin shell theory, the equations of which are solved inconjunction with variational principles, is presented. In the exactformulation, axisymmetric and inextensional assumptions are not used initiallyand the elastic medium is modelled as a Winkler foundation, i.e., usinguncoupled radial springs with a constant foundation modulus that is independentof wave numbers of shell buckling modes. Simplified approximations based on aRayleigh-Ritz approach are also introduced for critical buckling pressure andmode number with a considerable degree of accuracy. Characteristic modal shapesare demonstrated for a wide range of material and geometric parameters. A phasediagram is established to obtain the requisite thickness to radius, andstiffness ratios for a desired mode profile. The present exact formulation canbe readily extended to apply to more general cases of non-axisymmetric bucklingproblems.
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