Mechanical modeling of deepwater flexible structures with large deformation based on absolute nodal coordinate formulation

Abstract

In this paper, a mechanical analysis model is proposed on basis of the absolute nodal coordinate formulation (ANCF) and the theories of continuum mechanics and finite element method to accurately analyze the statics and dynamics of deepwater flexible structures with large deformation. In this model, the traditional angle coordinate is replaced with slope coordinate under the frame of overall coordinate system. The mapping relation of the parameters under current and reference configurations is established, and the method of describing the nonlinear geometric relationship of the element with the current configuration parameters is discussed. Then, based on the energy variation principle, the generalized elastic force and stiffness matrix of the element are derived, and the mass matrix and external load matrix of the element are combined to perform the element assembling using the finite element method, and the static and dynamic equilibrium equations are then formed. The calculation programs are compiled by FORTRAN language, whose reliability and accuracy are checked by the cases of beam model with theoretical solutions. Finally, a kind of steel lazy wave catenary riser is taken as an example, and its static and dynamic characteristics are analyzed systematically, which further verifies the effectiveness and practicability of the mechanical model.

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References

  1. 1.

    Ma G, Sun L (2014) Static analysis of the mooring line under large deformation by utilizing the global coordinate method. J Harbin Eng Univ 6:674–678

    Google Scholar 

  2. 2.

    Chai YT, Varyani KS, Barltrop NDP (2002) Three-dimensional Lump-Mass formulation of a catenary riser with bending, torsion and irregular seabed interaction effect[J]. Ocean Eng 29(12):1503–1525

    Article  Google Scholar 

  3. 3.

    Moulton DE, Lessinnes T, Goriely A (2013) Morphoelastic rods. Part I: a single growing elastic rod[J]. J Mech Phys Solids 61(2):398–427

    MathSciNet  Article  Google Scholar 

  4. 4.

    Wang Z, Tian Q, Hu H (2016) Dynamics of spatial rigid-flexible multibody systems with uncertain interval parameters. Nonlinear Dyn 84(2):527–548

    MathSciNet  Article  MATH  Google Scholar 

  5. 5.

    Sereshk MV, Salimi M (2011) Comparison of finite element method based on nodal displacement and absolute nodal coordinate formulation (ANCF) in thin shell analysis. Int J Numer Methods Biomed Eng 27(8):1185–1198

    MathSciNet  Article  MATH  Google Scholar 

  6. 6.

    Shabana A (1997) Definition of the slopes and the finite element absolute nodal coordinate formulation. Multibody Syst Dyn 1(3):339–348

    MathSciNet  Article  MATH  Google Scholar 

  7. 7.

    Berzeri M, Campanelli M, Ahmed A. Shabana (2001) Definition of the elastic forces in the finite-element absolute nodal coordinate formulation and the floating frame of reference formulation. Multibody Syst Dyn 5(1):21

    Article  MATH  Google Scholar 

  8. 8.

    Sugiyama H, Koyama H, Yamashita H (2010) Gradient deficient curved beam element using the absolute nodal coordinate formulation. J Comput Nonlinear Dyn 5(2):1090–1097

    Google Scholar 

  9. 9.

    Ebel H, Matikainen MK, Hurskainen VV et al (2017) Higher-order beam elements based on the absolute nodal coordinate formulation for three-dimensional elasticity. Nonlinear Dyn 88(2):1075–1091

    Article  Google Scholar 

  10. 10.

    Shabana AA, Yakoub RY (2001) Three dimensional absolute nodal coordinate formulation for beam elements: theory. J Mech Des 123(4):614–621

    Article  Google Scholar 

  11. 11.

    Weed D, Maqueda LG, Brown MA et al (2009) A new nonlinear multibody/finite element formulation for knee joint ligaments. Nonlinear Dyn 60(3):357–367

    Article  MATH  Google Scholar 

  12. 12.

    Recuero AM, Aceituno JF, Escalona JL et al (2015) A nonlinear approach for modeling rail flexibility using the absolute nodal coordinate formulation. Nonlinear Dyn 83:1–19

    MathSciNet  MATH  Google Scholar 

  13. 13.

    Yang CJ, Zhang WH, Zhang J et al (2017) Static form-finding analysis of a railway catenary using a dynamic equilibrium method based on flexible multibody system formulation with absolute nodal coordinates and controls. Multibody Syst Dyn 39(3):1–27

    MathSciNet  Article  Google Scholar 

  14. 14.

    Limoge DW, Bi PY, Annaswamy AM et al (2017) A reduced-order model of a lithium-ion cell using the absolute nodal coordinate formulation approach. IEEE Trans Control Syst Technol 26(99):1–14

    Google Scholar 

  15. 15.

    Bulín R, Hajžman M, Polach P (2017) Nonlinear dynamics of a cable-pulley system using the absolute nodal coordinate formulation. Mech Res Commun 82:21–28

    Google Scholar 

  16. 16.

    Wang L, Currao G, Han F et al (2017) An immersed boundary method for fluid–structure interaction with compressible multiphase flows. J Comput Phys 346:131–151

    MathSciNet  Article  MATH  Google Scholar 

  17. 17.

    Oleg Dmitrochenko (2008) Finite elements using absolute nodal coordinates for large-deformation flexible multibody dynamics. J Comput Appl Math 215(2):368–377

    MathSciNet  Article  MATH  Google Scholar 

  18. 18.

    Kang Z, Zhang C, Ma G et al (2018) A numerical investigation of two-degree-of-freedom VIV of a circular cylinder using the modified turbulence model. Ocean Eng 155:211–226

    Article  Google Scholar 

  19. 19.

    Shabana A (2008) Computational continuum mechanics. Cambridge University Press, New York

    Google Scholar 

  20. 20.

    Kang Z, Zhang C, Sun L (2017) Research on truncation method of FPSO and offloading system in model test. Appl Ocean Res 67(1):94–108

    Article  Google Scholar 

  21. 21.

    Kordkheili SAH, Bahai H, Mirtaheri M (2011) An updated Lagrangian finite element formulation for large displacement dynamic analysis of three-dimensional flexible riser structures. Ocean Eng 38(5–6):793–803

    Article  Google Scholar 

  22. 22.

    Elosta H, Huang S, Incecik A (2013) Dynamic response of steel catenary riser using a seabed interaction under random loads. Ocean Eng 69(C):34–43

    Article  Google Scholar 

  23. 23.

    Warburton GB (1976) The dynamical behaviour of structures (Second Edition). Pergamon Press, Oxford

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Acknowledgements

The work presented here is supported by the Ph.D. Student Research and Innovation Fund of the Fundamental Research Funds for the Central Universities [grant number HEUGIP201803]; the Fundamental Research Funds for the Central Universities [Grant number HEUCF180103]; the National Natural Science Foundation of China [Grant number 51879047], [Grant number 51509046], [Grant number 51509045]; the Natural Science Foundation of Heilongjiang Province of China [grant number E2017029]; and the National Science and Technology Major Project of China [Grant No. 2016ZX05057020].

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Correspondence to Zhuang Kang.

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Zhang, C., Kang, Z., Ma, G. et al. Mechanical modeling of deepwater flexible structures with large deformation based on absolute nodal coordinate formulation. J Mar Sci Technol 24, 1241–1255 (2019). https://doi.org/10.1007/s00773-018-00621-0

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Keywords

  • Absolute nodal coordinate formulation
  • Continuum mechanics
  • Finite element method
  • Mechanical model
  • Flexible structures
  • Large deformation