SpringerLink
Log in

Nonlinear static isogeometric analysis of cable structures

  • Original
  • Published:
Archive of Applied Mechanics Aims and scope Submit manuscript

Abstract

The purpose of this paper is to develop and evaluate the efficiency of the cable element based on the Lagrangian formulation using the Isogeometric analysis (IGA) approach. Two Lagrangian formulations (Total Lagrangian and Updated Lagrangian) have been adopted in the static analysis of nonlinear behaviour of the cable structures. The same basis functions are used to represent the geometry of the cable as well as the cable displacement field. These two formulations are tested on benchmark examples and compared to each other and to the existing analysis methods. The influence of a different number of elements, the order of polynomials and the number of numerical integration points was examined. Compared to the other method, the obtained results in benchmark examples indicate the capability and accuracy of the presented approach. This paper demonstrates successful IGA implementation of the Lagrangian formulation for the nonlinear analysis of cable structures.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  1. Abad, S.S.A., Shooshtari, A., Esmaeili, V., Riabi, A.N.: Nonlinear analysis of cable structures under general loadings. Finite Elem. Anal. Des. 73, 11–19 (2013). https://doi.org/10.1016/j.finel.2013.05.002

    Article  Google Scholar 

  2. Bathe, K.: Finite Element Procedures, 2nd edn. Klaus-Jurgen Bathe, Berlin (2014)

    MATH  Google Scholar 

  3. Benson, D.J., Bazilevs, Y., Hsu, M.C., Hughes, T.J.R.: Isogeometric shell analysis: the Reissner–Mindlin shell. Comput. Methods Appl. Mech. Engrg. 199(5–8), 276–289 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  4. Cazzani, A., Malagu, M.: Isogeometric analysis of plane-curved beams. Math. Mech. Solids 21(5), 562–577 (2016). https://doi.org/10.1177/1081286514531265

    Article  MathSciNet  MATH  Google Scholar 

  5. 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, 743–750 (2010)

    Article  MathSciNet  Google Scholar 

  6. Chunjiang, W., Renpeng, W., Shilin, D., Ruojun, Q.: A new catenary cable element. Int. J. Space Struct. 18(4), 269–275 (2003)

    Article  Google Scholar 

  7. Cottrell, J.A., Hughes, T.J.R., Bazilevs, Y.: Isogeometric Analysis. Wiley, Hoboken (2009)

    Book  MATH  Google Scholar 

  8. Coyette, J., Guisset, P.: Cable network analysis by a nonlinear programming technique. Eng. Struct. 10(1), 41–46 (1988)

    Article  Google Scholar 

  9. Gambhir, M., Batchelor, B.: Finite element study of the free vibration of 3-d cable networks. Int. J. Solids Struct. 15, 127–136 (1979)

    Article  MATH  Google Scholar 

  10. Greco, L., Cuomo, M.: B-spline interpolation of kirchhoff-love space rods. Comput. Methods Appl. Mech. Engrg. 256, 251–269 (2013). https://doi.org/10.1016/j.cma.2012.11.017

    Article  MathSciNet  MATH  Google Scholar 

  11. Harada, K., Zhang, J., Ogawa, T.: Self-equilibrium Analysis of Cable Structures Based on Isogeometric Analysis, vol. ICCM2014, pp. 128–135. Cambridge, England (2014)

  12. Huynh, T.-A., Luu, A.-T., Lee, J.: Bending, buckling and free vibration analyses of functionally graded curved beams with variable curvatures using isogeometric approach. Meccanica 52, 1–20 (2017). https://doi.org/10.1007/s11012-016-0603-z

    Article  MathSciNet  Google Scholar 

  13. Impollonia, N., Ricciardi, G., Saitta, F.: Statics of elastic cables under 3d point forces. International Journal of Solids and Structures 48(9), 1268–1276 (2011). https://doi.org/10.1016/j.ijsolstr.2011.01.007. URL http://www.sciencedirect.com/science/article/pii/S0020768311000163

  14. Jayaraman, H., Knudson, W.: A curved element for the analysis of cable structures. Comput. Struct. 14(3–4), 325–333 (1981)

    Article  Google Scholar 

  15. Kiendl, J., Bletzinger, K.U., Linhard, J., Wuchner, R.: Isogeometric shell analysis with Kirchhoff-Love elements. Comput. Methods Appl. Mech. Eng. 198(49–52), 3902–3914 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  16. O’Brien, W., Francis, A.: Cable movements under two-dimensional loads. J. Struct. Div. ASCE 90, 89–124 (1964)

    Google Scholar 

  17. Ozdemir, H.: A finite element approach for cable problems. Int. J. Solids Struct. 15, 427–437 (1979)

    Article  MATH  Google Scholar 

  18. Pevrot, A., Goulois, A.: Analysis of cable structures. Comput. Struct. 10, 805–813 (1979)

    Article  Google Scholar 

  19. Philipp, B., Breitenberger, M., DAuria, I., Wuchnera, R., Bletzinger, K.-U.: Integrated design and analysis of structural membranes using the isogeometric b-rep analysis. Comput. Methods Appl. Mech. Engrg. 303, 312–340 (2016). https://doi.org/10.1016/j.cma.2016.02.003

    Article  MathSciNet  Google Scholar 

  20. Raknes, S., Deng, X., Bazilevs, Y., Benson, D., Mathisen, K., Kvamsdal, T.: Isogeometric rotation-free bending-stabilized cables: statics, dynamics, bending strips and coupling with shells. Comput. Methods Appl. Mech. Eng. 263, 127–143 (2013). https://doi.org/10.1016/j.cma.2013.05.005

    Article  MathSciNet  MATH  Google Scholar 

  21. 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). https://doi.org/10.1016/j.engstruct.2009.03.018. URL http://www.sciencedirect.com/science/article/pii/S014102960900128X

  22. Thai, S., Kim, N.I., Lee, J.: Free vibration analysis of cable structures using isogeometric approach. Int. J. Comput. Methods 14(2), 1750033–1–26, (2017). https://doi.org/10.1142/S0219876217500335

  23. Thai, S., Kim, N.-I., Lee, J.: Isogeometric cable elements based on b-spline curves. Meccanica 52(4), 1219–1237 (2017b). https://doi.org/10.1007/s11012-016-0454-7

    Article  MathSciNet  MATH  Google Scholar 

  24. Tran, L.V., Thai, C.H., Nguyen-Xuan, H.: An isogeometric finite element formulation for thermal buckling analysis of functionally graded plates. Finite Elem. Anal. Des. 73, 65–76 (2013)

    Article  Google Scholar 

  25. Uhm, T.K., Youn, S.K.: T-spline finite element method for the analysis of shell structures. Int. J. Numer. Methods Eng. 80(4), 507–536 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  26. Yang, Y., Tsay, J.: 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)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This paper is supported by the Croatian science foundation Project Number IP-2014-09-6130.

Author information

Authors and Affiliations

  1. University of Split, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, R. boskovica 32, 21000, Split, Croatia

    Damir Sedlar, Zeljan Lozina & Andjela Bartulovic

Authors
  1. Damir Sedlar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zeljan Lozina
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Andjela Bartulovic
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Damir Sedlar.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sedlar, D., Lozina, Z. & Bartulovic, A. Nonlinear static isogeometric analysis of cable structures. Arch Appl Mech 89, 713–729 (2019). https://doi.org/10.1007/s00419-018-1489-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00419-018-1489-0

Keywords

Search

Navigation