|
Modelling Torsion in an Elastic Cable in Space |
|---|
Abstract
When an imperfectly flexible, elastic cable is suspended in a vertical plane under the sole influence of gravity and boundary conditions involving axial twist are then applied to the endpoints of the cable, its shape extends from the original vertical plane to a three-dimensional configuration in space. The aim of this paper is to develop a mathematical model (consisting of differential equations) for the configuration of and tension in such a twisted cable. The model is solved numerically for different boundary conditions. Although the final model delivers satisfactory results for small amounts of twist (inside the elastic deformation domain of the cable), realistic bounds for the amount of twist that may be applied (before plastic deformation of the cable causes model inaccuracies) are yet unknown. However, the effects of an increase in the amount of torsion applied at the endpoints of the cable are investigated numerically. The model seems capable of capturing first points of twisting bifurcation, when so much twist is applied at the endpoints that the cable jumps from an unstable equilibrium to a stable one.
An electronic version of the complete paper may be obtained here: [pdf].
Affiliations
1
Department of Applied Mathematics, Stellenbosch University, Private Bag X1, Matieland, 7602, Republic of South Africa, email: sbenecke@dip.sun.ac.za