This paper presents a method of static analysis of a marine cable spanning two fixed points. The top tension of the cable is given, while the total arc length, equilibrium configuration, and top and bottom angles are to be determined. In the analysis, a functional is Introduced in which the potential energy of stretching and virtual work done by other forces are included The stationary condition of the functional and one of two equilibrium equations are used to solve the problem. Application of the finite element method yields a system of nonlinear equations, which is solved using the Newton-Raphson iterative procedure. Accuracy of the method is demonstrated by a comparison of the numerical results obtained with those of a catenary and a neutrally-buoyant cable.
In many designs, the top tension of a marine cable or mooring line spanning two fixed points is specified. The specified tension may be governed by the strength of the cable, the capacity of the Installation equipment, or the desired top force for operation. The problem of static analysis for the cable, therefore, is to find the cable configuration and the total arc length when the top tension is given. In contrast, an alternative problem is to find the configuration and maximum top tension with a given total arc length. This paper focuses on the former problem. Although the governing differential equations of a cable segment are simple, explicit solutions can be obtained only for simple cases due to the nonlinearity In the problem and, in general, solutions are obtained by numerical techniques. Literature of the analysis of mooring lines and cables can be found In several text books, for example Berteaux (1976), Irivne (1981), and Leonard (1988). Extensive reviews are given by Migliore (1979) and Webster (1982).