Asymmetric Buckling of Clamped Shallow Spherical Shells

The problem of buckling of clamped shallow spherical shells has recently been considered in several theoretical investigations. Buck-ling loads under uniform external pressure were obtained in these investigations which show a surprisingly good agreement with each other, but show a marked disagreement with available experimental values. In all previous studies it has been assumed that the shell deformations are rotationally symmetric. In this paper, the buckling problem is re-examined by introducing asymmetric modes of deformation. The approach is to superimpose small asymmetric deflections on finite axisymmetric deflections, and to show that the symmetric states of deformation are unstable over certain ranges of load and geometry parameter. Numerical results are obtained by means of a digital computer and are compared with previous theoretical and experimental results.