MODELLING OF LARGE DISPLACEMENT MOTION OF ELASTIC CABLES

Abstract

Though in recent years considerable research has been carried out on cable problems, modelling of large displacement motion of low-tension cables remains relatively unexplored. In a few published papers which focused on this geometrically nonlinear problem, a finite difference method, known as the box scheme, was used. Applying the trapezoidal rule in both time and space domain, this scheme has a drawback as discovered in the research work reported herein. Specifically, spurious high-frequency response exists in the cable tension response. To resolve this problem, a numerical method, herein called the modified box scheme, is proposed. Based on the finite difference method, the proposed scheme applies the trapezoidal rule in space domain but backward difference in time domain. To increase the efficiency of the proposed numerical method, an iterative procedure is formulated to solve the nonlinear equations. The results and the computational efficiency compare favourably with those of the well-known Newton-Raphson procedure.

First, a cable dynamics problem involving low tension and large displacement motion, namely a cable free fall problem, is thoroughly studied. Numerical results are obtained by the proposed modified box scheme. For comparison, the box scheme as well as the finite element method with Newmark and Wilson- ? time-integration procedures are applied. In terms of cable configuration, these results are in good agreement with one another. The time histories of cable tension obtained by various schemes, however, are considerably different. Hence a physical experiment was conducted for verification. Among the different numerical schemes studied, the proposed modified box scheme is found to give the most accurate results.

Three other numerical examples are solved using the proposed modified box scheme. These examples include a suspension cable under seismic motion, an underwater cable subjected to water current, and a crane cable with moving ends. The results show that the modified box scheme performs satisfactorily in solving the nonlinear problem of large cable motion.