On the Bending of Spherical Shells

The bending behavior of spherical shells is reduced to the solution of a second-order differential equation with complex coefficients. Influence coefficients and functions of truncated spherical shells are evaluated and presented in curve form for the analysis of structures composed of spherical segments. These coefficients are determined by an exact and an asymptotic solution of the governing equation. The asymptotic solution is valid over the entire range of the independent variable when the ratio of shell radius to thickness is greater than 100. An uncoupling criterion is given by which it is possible to establish whether the effect of loads applied at one edge of the shell is transmitted to the other edge. This criterion is determined by the cross-product terms in the influence coefficient matrix.