Chapter 6 - Shallow Shells

Abstract

This chapter focuses on shallow shells. Shallow shells are defined as shells that have a peak of not more than one-fifth of the smallest platform dimension of the shell. It has been widely accepted that extremely shallow shell equations should not be used for maximum span to minimum radius ratio of 0.5 or more. This restriction is needed to make sure that the theory is only applied in the region where it is accurate. Shallow shells can be thin or thick, and thus, two theories are usually used for shallow shells. The first is a classical shallow shell theory (CSST) and the second one is a shear deformation shallow shell theory (SDSST). Both theories of shallow shells do not offer a reduced order of the shell equations when compared with the general shell theories. They do, however, simplify the equations and reduce the number of terms significantly. Furthermore, unlike deep shells where there are many theories, there is one generally acceptable theory for shallow shells which has been developed and used by many researchers. The root of the equations developed for shallow shells goes back to the equations of Donnell and Mushtari.