Nonlinear static isogeometric analysis of cable structures (original) (raw)

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.

Loading...

Loading Preview

Sorry, preview is currently unavailable. You can download the paper by clicking the button above.

References (26)

  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
  2. Bathe, K.: Finite Element Procedures, 2nd edn. Klaus-Jurgen Bathe, Berlin (2014)
  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)
  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
  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)
  6. Chunjiang, W., Renpeng, W., Shilin, D., Ruojun, Q.: A new catenary cable element. Int. J. Space Struct. 18(4), 269-275 (2003)
  7. Cottrell, J.A., Hughes, T.J.R., Bazilevs, Y.: Isogeometric Analysis. Wiley, Hoboken (2009)
  8. Coyette, J., Guisset, P.: Cable network analysis by a nonlinear programming technique. Eng. Struct. 10(1), 41-46 (1988)
  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)
  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
  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
  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)
  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)
  16. O'Brien, W., Francis, A.: Cable movements under two-dimensional loads. J. Struct. Div. ASCE 90, 89-124 (1964)
  17. Ozdemir, H.: A finite element approach for cable problems. Int. J. Solids Struct. 15, 427-437 (1979)
  18. Pevrot, A., Goulois, A.: Analysis of cable structures. Comput. Struct. 10, 805-813 (1979)
  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
  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
  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
  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)
  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)
  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)