Axisymmetric buckling of hollow spheres and hemispheres

TLDR: In this paper, a nonlinear thin shell theory is derived for the axisymmetric buckling of spherical shells subjected to either a pressure or a centrally directed surface load, which is reduced to a boundary value problem for a system of four first order ordinary differential equations.

Abstract: : A nonlinear thin shell theory is derived for the axisymmetric buckling of spherical shells subjected to either a pressure or a centrally directed surface load. The theory is reduced to a boundary value problem for a system of four first order ordinary differential equations. Numerical solutions of this boundary value problem are obtained by the shooting and parallel shooting methods. An extensive numerical study is made of the nonlinear deformations of the shells. We find for example, that all solution branches that bifurcate from the eigenvalues of the linearized buckling theory are connected to each other by means of intermediate branches. Some implications of the numerical results concerning the buckling of spherical shells are discussed. (Author)