Acta Mechanica

, Volume 230, Issue 1, pp 351–366 | Cite as

Isogeometric approach to the dynamics of the catenary exposed to large displacements

  • Zeljan LozinaEmail author
  • Damir Sedlar
  • Ivan Tomac
Original Paper


The paper presents the isogeometric and the Lagrangian approach to the deformable catenary dynamics undergoing large displacements. The benchmark examples are solved and compared with the finite element approach, solutions from independent sources, and analytical solution where available. The sensitivity to discretization and model parameters is demonstrated in selected cases. The isogeometric approach to the catenary dynamics is proved to be efficient and reliable.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



This paper is supported by the Croatian Science Foundation Project Number IP-2014-09-6130.


  1. 1.
    Bathe, K.-J.: Finite Element Procedures. Prentice Hall, Upper Saddle River (1996)zbMATHGoogle Scholar
  2. 2.
    Bathe, K.-J.: Conserving energy and momentum in nonlinear dynamics: a simple implicit time integration scheme. Comput. Struct. 85, 437–445 (2007)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Bathe, K.-J., Ramm, E., Wilson, E.L.: Finite element formulations for large deformations dynamic analysis. Int. J. Numer. Methods Eng. 9, 353–386 (1975)CrossRefGoogle Scholar
  4. 4.
    Bazilevs, Y., Cottrell, J.A., Thomas, J.R.H.: Isogeometric Analysis: Toward Integration of CAD and FEA. Wiley, New York (2009)zbMATHGoogle Scholar
  5. 5.
    Buffa, A., de Falcao, C., Sangalli, G.: Isogeometric analysis: stable elements for the 2d Stokes equation. Int. J. Numer. Methods Fluids 65(11–12), 1407–1422 (2011)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Buffa, A., Sangalli, G., Vazquez, R.: Isogeometric analysis in electromagnetics: B-splines approximation. Comput. Methods Appl. Mech. Eng. 65(17–20), 1143–1152 (2010)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Cazzani, A., Cattani, M., Mauro, R., Stochino, F.: A simplified model for railway catenary wire dynamics. Eur. J. Environ. Civ. Eng. 21(7–8), 936–959 (2016)Google Scholar
  8. 8.
    Chen, Z.H., Wu, Y.J., Yin, Y., Shan, C.: Formulation and application of multi-node sliding cable element for the analysis of suspen-dome structures. Finite Elem. Anal. Des. 46(9), 743–750 (2010)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Cottrell, J.A., Reali, A., Bazilevs, Y., Hughes, T.J.R.: Isogeometric analysis of structural vibrations. Comput. Methods Appl. Mech. Eng. 195, 5257–5297 (2006)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Coyette, J.P., Guisset, P.: Cable network analysis by a nonlinear programming technique. Eng. Struct. 10(1), 41–46 (1988)CrossRefGoogle Scholar
  11. 11.
    De Lorenzis, L., Temizer, I., Wriggers, P., Zavarise, G.: A large deformation frictional contact formulation using nurbs-based isogeometric analysis. Int. J. Numer. Methods Eng. 87(13), 1278–1300 (2011)MathSciNetzbMATHGoogle Scholar
  12. 12.
    Greco, L., Impollonia, N., Cuomo, M.: A procedure for the static analysis of cable structures following elastic catenary theory. Int. J. Solids Struct. 51(7–8), 1521–1533 (2014)CrossRefGoogle Scholar
  13. 13.
    Harada, K., Zhang, J., Ogawa, T.: Self-equilibrium analysis of cable structures based on isogeometric analysis. In: ICCM2014 (2014)Google Scholar
  14. 14.
    Hughes, T.J.R., Cottrell, J.A., Bazilevs, Y.: Isogeometric analysis: CAD, finite elements, nurbs, exact geometry, and mesh refinement. Comput. Methods Appl. Mech. Eng. 194, 4135–4195 (2005)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Impollonia, N., Ricciardi, G., Saitta, F.: Statics of elastic cables under 3d point forces. Int. J. Solids Struct. 48(9), 1268–1276 (2011)CrossRefGoogle Scholar
  16. 16.
    Jayarman, H.B., Knudson, W.C.: A curved element for the analysis of cable structures. Comput. Struct. 14(3–4), 325–333 (1981)CrossRefGoogle Scholar
  17. 17.
    Laura, P.A., Casarella, M.J.: A survey of publications on mechanical cables and cables systems. The Institute of Ocean Science and Engineering, The Catholic University of America (1968)Google Scholar
  18. 18.
    Newmark, N.M.: A method of computation for structural dynamics. ASCE J. Eng. Mech. Div. 85(3), 67–94 (1959)Google Scholar
  19. 19.
    Ozdemir, H.: A finite element approach for cable problems. Int. J. Solids Struct. 15, 427–437 (1979)CrossRefGoogle Scholar
  20. 20.
    Pevrot, A.H., Goulois, A.M.: Analysis of cable structures. Comput. Struct. 10, 805–813 (1979)CrossRefGoogle Scholar
  21. 21.
    Raknes, S.B., Deng, X., Bazilevs, Y., Benson, D.J., Mathisen, K.M., Kvamsdal, T.: Isogeometric rotation-free bending-stabilized cables: statics, dynamics, bending strips and coupling with shells. Comput. Methods Appl. Mech. Eng. 263, 127143 (2013)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Such, M., Jimenez-Octavio, J.R., Carnicero, A., Lopez-Garcia, O.: An approach based on the catenary equation to deal with static analysis of three dimensional cable structures. Eng. Struct. 31(9), 2162–2170 (2009)CrossRefGoogle Scholar
  23. 23.
    Thai, H.T., Kim, S.E.: Nonlinear static and dynamic analysis of cable structures. Finite Elem. Anal. Des. 47(3), 237–246 (2011)CrossRefGoogle Scholar
  24. 24.
    Thai, S., Kim, N.I., Lee, J.: Free vibration analysis of cable structures using isogeometric approach. Int. J. Comput. Methods 14(03), 1750033 (2017)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Thai, S., Kim, N.I., Lee, J.: Isogeometric cable elements based on B-spline curves. Meccanica 52(4–5), 1219–1237 (2017)MathSciNetCrossRefGoogle Scholar
  26. 26.
    Theetten, A., Grisoni, L., Andriot, C., Barsky, B.: Geometrically exact dynamic splines. Comput. Aided Des. 40, 3548 (2008)CrossRefGoogle Scholar
  27. 27.
    Yang, Y.B., Tsay, J.Y.: Geometric nonlinear analysis of cable structures with a two-node cable element by generalized displacement control method. Int. J. Struct. Stab. Dyn. 7(4), 571–588 (2007)MathSciNetCrossRefGoogle Scholar
  28. 28.
    Young, D.: Strings, chains and ropes. SIAM Review 48(4), 771–781 (2006)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Faculty of Electrical Engineering, Mechanical Engineering and Naval ArchitectureUniversity of SplitSplitCroatia

Personalised recommendations