Localization in spherical shell buckling

Basile Audoly (1) , John Hutchinson (2)

1 LMS - Laboratoire de mécanique des solides
2 SEAS - Harvard John A. Paulson School of Engineering and Applied Sciences

This paper addresses localization of the deformation due to buckling that occurs immediately following the onset of bifurcation in the axisymmetric buckling of a perfect spherical elastic shell subject to external pressure. The localization process is so abrupt that the buckling mode of the classical eigenvalue analysis, which undulates over the entire shell, becomes modified immediately after bifurcation transitioning to an isolated dimple surrounded by an unbuckled expanse of the shell. The paper begins by revisiting earlier attempts to analyze the initial post-buckling behavior of the spherical shell, illustrating their severely limited range of validity. The unsuccessful attempts are followed by an approximate Rayleigh-Ritz solution which captures the essence of the localization process. The approximate solution reveals the pathway that begins at bifurcation from the classical mode shape to the localized dimple buckle. The second part of the paper presents an exact asymptotic expansion of the initial post-buckling behavior which accounts for localization and which further exposes the analytic details of the abruptness of the transition.

Mots clés: A Buckling; B Shells and membranes; C Stability and bifurcation; C Asymptotic analysis

Domaines: Mécanique des solides [physics.class-ph]; Mécanique des structures [physics.class-ph]; Physique mathématique [math-ph]

Basile Audoly, John Hutchinson. Localization in spherical shell buckling. Journal of the Mechanics and Physics of Solids, 2020, 136, pp.103720. ⟨10.1016/j.jmps.2019.103720⟩. ⟨hal-02347587⟩