Pure Bending of Shallow Helicoidal Shells

Abstract

The solution of the problem of pure bending of shallow helicoidal shells is obtained in terms of elementary functions. Numerical results for the direct and bending stresses as well as for the overall stiffness coefficient of the shell are given for various pitch-to-thickness ratios. An interesting aspect of the analysis is that the displacement state of the shell is multivalued in the polar angle θ while the stress state is unsymmetric but periodic in θ. Moreover, unlike the problem of axial torsion and extension where there is no edge effect, the stress state for the present problem exhibits both an interior state and an edge zone state.