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Finite element modelling of moored vessels. (English) Zbl 1005.93006

The authors develop a finite element model for a cable, suspended in water, and which is positioned to a moored vessel. Position mooring systems (PM) have been commercially available and have proven to be a cost-effective alternative to permanent platforms for off shore oil production. A finite element model (FEM) of a cable suspended in water is derived taking into account the hydrodynamic loads and internal damping. Bending and torsional stiffness are assumed to be negligible. The FEM model for the cable is assembled to give a model of a multi-cable mooring system, which is coupled to a rigid body model of the floating vessel. For the simplified equation describing the motion of a cable having negligible added mass and supported by fixed endpoints, the authors have shown the global existence and uniqueness of the solution of the truncated system, and conjecture this result for the initial boundary value problem. The initial-boundary problem is transformed into a weak form (Galerkin-Petrow method). Choosing the finite-dimensional subspaces, where unknown coefficients of the spanned base functions are nodal displacements, leads to a set of ordinary differential equations, which are treated like the equations of the finite element method.
In the simulation example, a vessel is considered with three degrees of freedom, i.e. horizontal motion of the vessel, which is turret-based and all cables are connected to the center of the turret. Linear viscous damping and negligible Coriolis and centripetal forces are assumed for the vessel. The simulation results are applicable to the real modeling of PM systems.

MSC:

93A30 Mathematical modelling of systems (MSC2010)
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
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References:

[1] O.M. Aamo, T.I. Fossen, Finite element modelling of moored vessels, J. Math. Comput. Model. Dyn. Syst., accepted for publication. · Zbl 1005.93006
[2] O.M. Faltinsen, Sea Loads on Ships and Offshore Structures, Cambridge University Press, Cambridge, 1990.
[3] H. Ormberg, I.J. Fylling, K. Larsen, N. Sødal, Coupled analysis of vessel motions and mooring and riser system dynamics, in: Proceedings of the 16th International Conference on Offshore Mechanics and Arctic Engineering, New York, 1997, pp. 91–100.
[4] G. Strang, G.J. Fix, An Analysis of the Finite Element Method, Prentice-Hall, Englewood Cliffs, 1973. · Zbl 0356.65096
[5] M.E. Taylor, Partial Differential Equations III, Springer, New York, 1996. · Zbl 0869.35001
[6] M.S. Triantafyllou, Cable mechanics with marine applications, lecture notes, Department of Ocean Engineering, Massachussetts Institute of Technology, Cambridge, MA 02139, USA, May 1990.
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