Study of the effects of cross section shape on the structural behaviour of helical wires on a bent flexible structure

Helical wires are a type of structure winding around on an underneath layer in flexible structures. They constitute a structure layer that provides mechanical protection and sufficient flexibility. The cross section of a helical wire could differ from round to rectangular. The curvature increments of a helical wire on a bent flexible structure can be influenced by the cross section shape due to the contact restriction from the neighbouring layer. The shape effect causes a different mechanical behaviour of the wire itself. However, this effect is not fully understood up till now. This paper mainly investigates the curvature increments of helical wires with rectangular and round cross section by using numerical method. This model takes advantage of the properties belonging to solid elements and beam elements by embedding the latter into the former. The solid element is able to retain the geometry detail of the cross section as much as possible in order to get deep insight of the shape effect. The beam element based on Timoshenko beam theory with well defined Frenet-Serret frames can accurately output the curvature increments in three local directions. Then widly-used analytical models are presented and deployed to verify the numerical results. The research results show the application condition of the analytical expressions and benefit the cable/umbilical/flexible pipe designers.