A method for prediction of the equilibrium state of a long and slender wire on a frictionless toroid applied for analysis of flexible pipe structures

This paper concerns the behavior of a helical wire on a frictionless cylindrical surface subjected to bending, such that the wire in the deformed state constitutes a curve on a toroid. In order to determine the equilibrium in the loaded state, a sixth order system of differential equations based on curved beam equilibrium and concepts from differential geometry will be presented. On this basis, a method for analysis of curved beams on frictionless toroids is established. Helically wound steel wires are widely used in flexible pipes, which have various applications in the offshore industry, in order to ensure the structural integrity against axial loads. The research presented in this paper constitutes a contribution to the field of wire mechanics, since it enables calculation of the frictionless wire equilibrium state within the wall of a flexible pipe.

► A helical beam on a cylindrical surface bent into a toriod is modeled.
► Neglecting friction the equilibrium state is determined solving a BVP.
► This is used to model armouring tendons of flexible pipes.
► Slip towards the geodesic of a toroid occurs in bending and tension.