Static Analysis of the Lumped Mass Cable Model Using a Shooting Algorithm

Abstract

This paper focuses on a method to solve the static configuration for a lumped mass cable system. The method demonstrated here is intended to be used prior to performing a dynamics simulation of the cable. Conventional static analysis approaches resort to dynamics relaxation methods or root-finding algorithms (such as the Newton-Raphson method) to find the equilibrium profile. The alternative method demonstrated here is general enough for most cable configurations (slack or taut) and ranges of cable elasticity. The forces acting on the cable are attributable to elasticity, weight, buoyancy, and hydrodynamics. For the three-dimensional problem, the initial cable profile is obtained by solving three equations, regardless of the cable discretization resolution. This analysis discusses regions and circumstances under which failures in the method are encountered.