Analytical solutions for bending and flexure of helically reinforced cylinders

There has been a great deal of interest in the problems of modelling cables and ropes. A recent review by Cardou and Jolicoeur Appl. Mech. Rev. 50 (1997) 1] considers the modelling of a cable which consists of a central core surrounded by one or several helically wound wire layers. One approach has been to consider the deformations of an individual helical wire and to synthesise the model of a cable by using contact conditions between the various wires. Other authors have adopted a continuum approach regarding each layer as a transversely isotropic material whose principal direction is along a helix surrounding the central axis of the cable. In each layer the helix angle is constant so that, when referred to cylindrical polar co-ordinates, the cylinder has a constant stiffness matrix in each layer. The intention in this paper is to use the continuum approach and describe the analytical solutions that govern the simple bending, flexure, or bending under a uniform load, of an anisotropic elastic cylinder consisting of a single material of this type. The extension of this work to a composite cylinder consisting of several concentric layers, surrounding a central core, which are either bonded together or make a frictionless contact, is briefly described.