Strings are slender bodies having the properties that they cannot withstand compression nor bending or torsion. This particular model is largely used in static and quasi-static mooring studies to deal with chains and some wire ropes. Several methodologies are available to solve the catenary equation such as analytical and finite elements solvers which both present advantages and limitations. Analytical methodology benefits from strong accuracy, simplicity of modeling but limited application cases to standard catenary shapes. On the other hand, finite element methods (FEMs) cover a wider application field by introducing more physics but request a specific attention when setting up the model and adjusting numerical parameters to reach a required precision.

The present paper describes an alternative methodology based on shooting method, offering a compromise between the accuracy of analytical computation and the general application field of FEMs, keeping the approach and implementation simple.

In this paper the hanging mooring line is modeled as a nonlinear extensible elastic string handling only traction along the centerline. The two point boundary value problem (TPBVP) static equations are reminded with the introduction of 3D external distributed loads. The TPBVP is then solved iteratively as a succession of initial value problems (IVPs) using the shooting method. The multi-shooting method is also introduced to deal with multi-material segments and line assemblies. Three validation cases based on analytical formulations are presented in this paper.


Undersea cables and mooring lines static studies remain an important subject of simulation in offshore field whether for steady-state analysis or dynamic simulation initialization. In order to get the static equilibrium of mooring lines, two approaches exist based either on dynamic equations - such as dynamic relaxation - or on TPBVP static equations. The TPBVP for strings is constituted of a set of ordinary differential equations (ODEs) associated with two boundary conditions at segment extremities. In order to solve such problem, several well- known dedicated techniques exist such as: difference methods, variational methods, colocation methods, shooting methods, etc.

You can access this article if you purchase or spend a download.