Finite Deformations of Shallow Shells

A method is described for the numerical solution of nonlinear shell equations. By application of the Rayleigh-Ritz procedure the differential shell equations are represented by a set of nonlinear algebraic equations which are solved by the Newton-Raphson iteration procedure; the occurrence of double roots is avoided by the use, when necessary, of a suitable displacement parameter as the independent variable. The numerical method of analysis is applied to a limited range of doubly-curved, shallow shells, which are rectangular in planform and loaded with a uniform pressure. The complex solution paths of symmetrical configuration states are traced completely from the unloaded to inverted configurations. Bifurcations from these primary paths are detected and some are traced. They are found to be the solution curves of unstable unsymmetrical configurations.