The buckling of spherical shells under external pressure has been investigated by numerous researchers. Von Karman (Von Karman and Tsien 1939) developed a solution that fits experimental data very closely. Taking a buckled section of a spherical shell, Fig. 14-1, he made the following assumptions:

1. The deflected shape is rotationally symmetric

2. The buckled length is small

3. The deflection of any element of the shell is parallel to axis of rotational symmetry

4. The effect of lateral contraction due to Poisson's ratio is neglected