Forces and Deformations in Arrays of Interacting Cylinders #

Robert J Whittaker, Jordan Kent

14:30 Tuesday in 4Q07.

Part of the Industrial mathematics session.

Abstract #

Large undersea cables usually comprise a number of individual cables bundled together within an outer casing. In designing such bundles, consideration needs to be given to the deformations and contact forces between the individual cables inside. Motivated by this set-up, we consider deformations of a 2D array of touching cylindrical shells, ignoring the mechanics of the cable cores and other interstitial material.

We present a simple framework to analyse such systems, which involves first computing the deformation of a single cylindrical shell under a single external point force or torque. The deformation of a shell under multiple contact forces can then be found by linear superposition. Finally, multiple cylinders can be coupled together by matching the forces and displacements at the contact points. This results in a linear system to solve for the unknown contact forces and the net translation and rotation of each cylinder.