Nonlinear Asymmetric Buckling of Truncated Spherical Shells

Abstract

This paper is concerned with the theoretical study of buckling of truncated spherical shells. Sander’s nonlinear equations for deep shells are used and the equations of equilibrium are expressed in terms of displacements for spherical shells. Based on these equations, analyses are made for calculating prebuckling axisymmetric equilibrium positions and then examining these equilibrium states for points of bifurcation into asymmetric buckling deformations. An eigenvalue problem is formulated and the buckling loads for truncated spherical shells of different geometrical parameters are obtained numerically. The numerical results for the prebuckling axisymmetric deformations and the points of bifurcation are shown on graphs.