Nonlinear Deflections of Shallow Spherical Shells

The equations obtained by Chien for the nonlinear deflection of shallow spherical shells under uniform external pressure are solved by means of power series expansions following procedures introduced by Friedrichs and Stoker in their treatment of buckling of circular plates. These equations depend upon two parameters. One of these is related to the external pressure, while the other depends upon the dimensions of the shell. The equations are solved for several ranges of the parameters under boundary conditions corresponding to a fixed edge. The solution, carried out numerically on the Univac at New York University, yields a complete description of the stresses and deflections as functions of the polar angle over a wide range of values of the loading parameter and the dimensional parameter. Prediction of the upper buckling load is then made by means of a numerical criterion based on the load vs. deflection curve. For some cases, the post-buckling behavior is investigated. Finally, the results agree well with existing experimental and theoretical studies and cover a wide range of cases not previously treated.