References
Each entry below supports a method CableDyn implements or a comparison reported in CableDyn verification and validation, and is cited where that method or comparison is described. To cite CableDyn itself, see How to cite.
Element formulation
Boyer, F., De Nayer, G., Leroyer, A. & Visonneau, M. (2011). Geometrically exact Kirchhoff beam theory: application to cable dynamics. Journal of Computational and Nonlinear Dynamics 6(4), 041004. https://doi.org/10.1115/1.4003625
Meier, C., Popp, A. & Wall, W. A. (2015). A locking-free finite element formulation and reduced models for geometrically exact Kirchhoff rods. Computer Methods in Applied Mechanics and Engineering 290, 314–341. https://doi.org/10.1016/j.cma.2015.02.029
Meier, C., Popp, A. & Wall, W. A. (2014). An objective 3D large deformation finite element formulation for geometrically exact curved Kirchhoff rods. Computer Methods in Applied Mechanics and Engineering 278, 445–478. https://doi.org/10.1016/j.cma.2014.05.017
Bergou, M., Wardetzky, M., Robinson, S., Audoly, B. & Grinspun, E. (2008). Discrete elastic rods. ACM Transactions on Graphics 27(3), 63. https://doi.org/10.1145/1360612.1360662
van der Heijden, G. H. M., Neukirch, S., Goss, V. G. A. & Thompson, J. M. T. (2003). Instability and self-contact phenomena in the writhing of clamped rods. International Journal of Mechanical Sciences 45(1), 161–196. https://doi.org/10.1016/S0020-7403(02)00183-2
Simo, J. C. (1985). A finite strain beam formulation. The three-dimensional dynamic problem. Part I. Computer Methods in Applied Mechanics and Engineering 49(1), 55–70. https://doi.org/10.1016/0045-7825(85)90050-7
Time integration and nonlinear solution
Chung, J. & Hulbert, G. M. (1993). A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-α method. Journal of Applied Mechanics 60(2), 371–375. https://doi.org/10.1115/1.2900803
Armijo, L. (1966). Minimization of functions having Lipschitz continuous first partial derivatives. Pacific Journal of Mathematics 16(1), 1–3. https://doi.org/10.2140/pjm.1966.16.1
Simo, J. C. & Tarnow, N. (1992). The discrete energy-momentum method. Conserving algorithms for nonlinear elastodynamics. Zeitschrift für angewandte Mathematik und Physik (ZAMP) 43(5), 757–792. https://doi.org/10.1007/BF00913408
Hydrodynamics and ocean environment
Morison, J. R., O’Brien, M. P., Johnson, J. W. & Schaaf, S. A. (1950). The force exerted by surface waves on piles. Journal of Petroleum Technology 2(5), 149–154. https://doi.org/10.2118/950149-G
Dean, R. G. & Dalrymple, R. A. (1991). Water Wave Mechanics for Engineers and Scientists. Advanced Series on Ocean Engineering, Vol. 2. World Scientific. https://doi.org/10.1142/1232
Wheeler, J. D. (1970). Method for calculating forces produced by irregular waves. Journal of Petroleum Technology 22(3), 359–367. https://doi.org/10.2118/2712-PA
Hasselmann, K., Barnett, T. P., Bouws, E., et al. (1973). Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP). Ergänzungsheft zur Deutschen Hydrographischen Zeitschrift, Reihe A, Nr. 12.
Dean, R. G. (1965). Stream function representation of nonlinear ocean waves. Journal of Geophysical Research 70(18), 4561–4572. https://doi.org/10.1029/JZ070i018p04561
Rienecker, M. M. & Fenton, J. D. (1981). A Fourier approximation method for steady water waves. Journal of Fluid Mechanics 104, 119–137. https://doi.org/10.1017/S0022112081002851
Pierson, W. J. & Moskowitz, L. (1964). A proposed spectral form for fully developed wind seas based on the similarity theory of S. A. Kitaigorodskii. Journal of Geophysical Research 69(24), 5181–5190. https://doi.org/10.1029/JZ069i024p05181
Ochi, M. K. & Hubble, E. N. (1976). Six-parameter wave spectra. Proceedings of the 15th Coastal Engineering Conference, Honolulu, 301–328. https://doi.org/10.9753/icce.v15.19
Torsethaugen, K. & Haver, S. (2004). Simplified double peak spectral model for ocean waves. Proceedings of the 14th International Offshore and Polar Engineering Conference, Toulon, ISOPE-I-04-048.
DNV (2021). Environmental conditions and environmental loads. Recommended Practice DNV-RP-C205.
Mooring-line models and synthetic ropes
Irvine, H. M. & Caughey, T. K. (1974). The linear theory of free vibrations of a suspended cable. Proceedings of the Royal Society of London A 341(1626), 299–315. https://doi.org/10.1098/rspa.1974.0189
Hall, M. & Goupee, A. (2015). Validation of a lumped-mass mooring line model with DeepCwind semisubmersible model test data. Ocean Engineering 104, 590–603. https://doi.org/10.1016/j.oceaneng.2015.05.035
Hall, M. (2020). MoorDyn V2: new capabilities in mooring system components and load cases. Proceedings of the ASME 2020 39th International Conference on Ocean, Offshore and Arctic Engineering, Vol. 9: Ocean Renewable Energy, V009T09A078. https://doi.org/10.1115/OMAE2020-19341
Hall, M., Duong, B. & Lozon, E. (2023). Streamlined loads analysis of floating wind turbines with fiber rope mooring lines. ASME 2023 5th International Offshore Wind Technical Conference (IOWTC2023). https://doi.org/10.1115/IOWTC2023-119524
Falkenberg, E., Åhjem, V. & Yang, L. (2017). Best practice for analysis of polyester rope mooring systems. Offshore Technology Conference, Houston, OTC-27761-MS. https://doi.org/10.4043/27761-MS
Verification and validation references
Bisshopp, K. E. & Drucker, D. C. (1945). Large deflection of cantilever beams. Quarterly of Applied Mathematics 3(3), 272–275. https://doi.org/10.1090/qam/13360
Lozon, E., Lekkala, M. R., Sirkis, L. & Hall, M. (2025). Reference mooring and dynamic cable designs for representative U.S. floating wind farms. Ocean Engineering 322, 120473. https://doi.org/10.1016/j.oceaneng.2025.120473
Gaertner, E., Rinker, J., Sethuraman, L., et al. (2020). Definition of the IEA 15-Megawatt Offshore Reference Wind Turbine. Technical Report NREL/TP-5000-75698, National Renewable Energy Laboratory. https://doi.org/10.2172/1603478
Allen, C., Viselli, A., Dagher, H., Goupee, A., Gaertner, E., Abbas, N., Hall, M. & Barter, G. (2020). Definition of the UMaine VolturnUS-S Reference Platform Developed for the IEA Wind 15-Megawatt Offshore Reference Wind Turbine. Technical Report NREL/TP-5000-76773, National Renewable Energy Laboratory. https://doi.org/10.2172/1660012
Holcombe, A., Hann, M., Brown, S., et al. (2025). Experimental–numerical model comparison of a dynamic power cable for a floating offshore wind turbine. Ocean Engineering 321, 120384. https://doi.org/10.1016/j.oceaneng.2025.120384
Bergdahl, L., Palm, J., Eskilsson, C. & Lindahl, J. (2016). Dynamically scaled model experiment of a mooring cable. Journal of Marine Science and Engineering 4(1), 5. https://doi.org/10.3390/jmse4010005
Comparison codes
MoorDyn-C (v2) and MoorDyn-F — open-source lumped-mass mooring models developed by M. Hall and co-workers (Hall & Goupee, 2015; Hall, 2020), https://github.com/FloatingArrayDesign/MoorDyn, used as comparison codes; MoorDyn-F is also the OpenFAST module whose interface the
CompMooring = 5module follows.OpenFAST — the open-source wind-turbine multiphysics framework maintained by NLR (National Laboratory of the Rockies, formerly NREL), https://github.com/OpenFAST/openfast, which hosts the
CompMooring = 5module.OrcaFlex 11.6d — the industry-standard offshore dynamics package used as the reference for the OrcaFlex comparisons in CableDyn verification and validation. OrcaFlex is a product of Orcina Ltd.