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 nonaxisymmetric buckling problems.
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.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.