Static Analysis of the Lumped Mass Cable Model Using a Shooting Algorithm
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 138, Issue 2
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.
Get full access to this article
View all available purchase options and get full access to this article.
References
Chai, T., Varyani, K., and Barltrop, N. (2002). “Three-dimensional lumped-mass formulation of a catenary riser with bending, torsion and irregular seabed iteraction effects.” Ocean Eng., 29(12), 1503–1525.
De Zoysa, A. (1978). “Steady-state analysis of undersea cables.” Ocean Eng., 5(9), 209–223.
Driscoll, F. (1999). “Dynamics of a vertically tethered marine platform.” Ph.D. thesis, Univ. of Victoria, British Columbia, Canada.
Friswell, M. (1995). “Steady-state analysis of underwater cables.” J. Waterway, Port, Coastal, Ocean Eng., 121(2), 98–104.
Gobat, J. (2002). “The dynamics of geometrically moored compliant systems.” Ph.D. thesis, Massachusetts Institute of Technology/Woods Hole Oceanographic Institute, Cambridge, MA.
Huang, S. (1994). “Dynamics analysis of three-dimensional marine cables.” J. Waterway, Port, Coastal, Ocean Eng., 21(6), 587–605.
Irvine, M. (1992). Cable structures, Dover Publications, Mineola, NY.
Kamman, J., and Huston, R. (1999). “Modeling of variable length towed and tethered cable systems.” J. Guid. Control. Dyn., 22(4), 602–608.
Ketchman, J., and Lou, Y. (1975). “Application of the finite element method to towed cable dynamics.” Proc., MTS/IEEE OCEANS, Vol. 1, 98–107.
Malaeb, D. (1982). “Dynamic analysis of a tension leg platform.” Ph.D. thesis, Texas A&M Univ., College Station, TX.
Mekha, B., Johnson, C., and Roesset, J. (1996). “Implications of tendon modeling on nonlinear response of TLP.” J. Struct. Eng., 122(2), 142–149.
Merchant, H., and Kelf, M. (1973). “Non-linear analysis of submerged buoy systems.” Proc., MTS/IEEE OCEANS, Vol. 1, 390–395.
Nahon, M. (1999). Dynamics and control of a novel radio telescope antenna, American Institute of Aeronautics and Astronautics, Reston, VA.
Peyrot, A. (1980). “Marine cable structures.” J. Struct. Div., 106(12), 2391–2404.
Powell, G., and Simons, J. (1981). “Improve iteration strategy for nonlinear structures.” Int. J. Numer. Methods Eng., 17(10), 1455–1467.
Shugar, T. (1991). “Automated dynamic relaxation solution method for compliant structures.” Annual Meeting of the American Society of Mechanical Engineers, Vol. 4, ASME, New York, 1–12.
Strang, G. (1981). Linear algebra and its applications, Academic Press, New York.
Veslić, K. (1995). “Finite catenary and the method of lagrange.” J. Soc. Ind. Appl. Math., 37(2), 224–229.
Walton, T., and Polacheck, W. (1960). “Calculation of transient motion of submerged cables.” Math. Comput., 14(69), 27–46.
Webster, R. (1980). “On the static analysis of structures with strong geometric nonlinearity.” Comput. Struct., 11(1–2), 137–145.
Williams, P., and Trivaila, P. (2007). “Dynamics of circularly towed cable systems, part 1: Optimal configurations and their stability.” J. Guid. Control. Dyn., 30(3), 753–765.
Wilson, J. (2003). Dynamics of offshore structures, Wiley, Hoboken, NJ.
Wu, S. (1995). “Adaptive dynamic relaxation technique for static analysis of catenary mooring.” Mar. Struct., 8(5), 585–599.
Zueck, R. (1995). “Stable numerical solver for cable structures.” Int. Symp. on Cable Dynamics, 19–21.
Information & Authors
Information
Published In
Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 138 • Issue 2 • March 2012
Pages: 164 - 171
Copyright
© 2012 American Society of Civil Engineers.
History
Received: May 8, 2011
Accepted: Jul 21, 2011
Published online: Jul 25, 2011
Published in print: Mar 1, 2012
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.