An Invariant Membrane Stress Function for Shells

Abstract

Abstract Inextensional shells that have no thickness are idealized representations of real shells that have small bending stresses and small deformations. With certain restrictions, the stresses in these shells are derivable from a generalized Airy function. For shells of constant Gaussian curvature, the stress function is unrestricted, but, for other shells, it is expressed as a function of the Gaussian curvature. Although, in this respect, it is less general than Pucher’s stress function, it has the advantage that it may be used with any surface co-ordinates.