Buckling patterns of complete spherical shells filled with an elastic medium under external pressure

TL;DR

This paper presents an exact and approximate model for analyzing the buckling behavior of complete spherical shells filled with an elastic medium under external pressure, including modal shapes and stability criteria.

Contribution

It introduces a comprehensive formulation that accounts for non-axisymmetric buckling and elastic medium effects, extending previous simplified models.

Findings

Exact formulation without initial assumptions

Approximate methods with high accuracy

Characteristic modal shapes for various parameters

Abstract

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 non-axisymmetric buckling problems.