A comparison of the postbuckling behavior of plates and shells

There is a basic difference in the mathematical treatment of postbuckling of plates and shells. Whereas for plates the classical methods of bifurcation theory (Liapunov-Schmidt method, Singularity Theory) in general are applicable, these methods fail for the analysis of thin-walled shells. For shells in general solutions of the boundary layer type are found and hence the methods of singular perturbation theory are required for an appropriate analysis. Applications are given for the postbuckling of a rectangular plate and a spherical shell.