Acta Mechanica

, Volume 220, Issue 1–4, pp 183–198

A modification of the rigid finite element method and its application to the J-lay problem



This article presents the Rigid Finite Element Method (RFEM), which allows us to take into account the flexibility of a system. Beam-like structures are analyzed, in which large deformations occur. The RFEM has been developed many years ago and successfully applied to practical engineering problems. The main difference between this method and the classical Finite Element Method (FEM) is the element deformation during analysis. In RFEM, the finite elements generated in a discretization process are treated as nondeformable bodies, whilst in FEM the elements are deformable; in RFEM, flexible, mass-less elements with properly chosen coefficients are introduced. A modification of the stiffness coefficients used in RFEM is proposed and explained in the article. It is shown how these new coefficients applied in RFEM lead to the same energy of deformation as in the case when the system is discretized by the classical FEM. This means that the energy of deformation is identical to that obtained in FEM, which leads to identical deformations of the elements. It is of particular importance that the RFEM is a much simpler method, faster in calculations and easier to learn and interpret. Furthermore, the generation of the inertia and stiffness matrices is much faster than in FEM. Another advantage is relatively easy implementation for multicore processor architecture. The calculation examples investigated cover some practical problems related to the offshore pipe laying process. The J-lay method is simulated by the use of the author’s own computer model based on a modified RFEM. The model takes into account wave and sea current loads, hydrodynamic forces and material nonlinearity (plastic strains can develop during large deformation). The simulation results are compared with those obtained from the commercial package ANSYS.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Shabana A.A.: Dynamics of Multibody Systems. Wiley, New York (1989)MATHGoogle Scholar
  2. 2.
    Shabana A.A.: Flexible multibody dynamics: review of past and recent developments. Multibody Syst. Dyn. 1, 189–222 (1997)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Gerstmayr J., Shabana A.A.: Analysis of thin beams and cables using the absolute nodal co-ordinate formulation. Nonlinear Dyn. 45, 109–130 (2006)MATHCrossRefGoogle Scholar
  4. 4.
    Wojciech S., Adamiec-Wójcik I.: Nonlinear vibrations of spatial viscoelastic beams. Acta Mech. 98, 15–25 (1993)MATHCrossRefGoogle Scholar
  5. 5.
    Wojciech S., Adamiec-Wójcik I.: Experimental and computational analysis of large amplitude vibrations of spatial viscoelastic beams. Acta Mech. 106, 127–136 (1994)CrossRefGoogle Scholar
  6. 6.
    Kruszewski, J.: Application of the stiff finite element method for calculation of natural vibration frequency of ship structure. In: Third World Congress of the Theory of Machines and Mechanisms, Kupari, Yugoslavia, pp. 147–160 (1971)Google Scholar
  7. 7.
    Huston R.L.: Multi-body dynamics including the effect of flexibility and compliance. Comp. Struct. 14, 443–451 (1981)CrossRefGoogle Scholar
  8. 8.
    Nikravesh P., Chung I., Bendict R.L.: Plastic hinge approach to vehicle crash simulation. Comp. Struct. 16, 395–400 (1983)CrossRefGoogle Scholar
  9. 9.
    Winget J.M., Huston R.L.: Cable dynamics—a finite segment approach. Comput. Struct. 6(6), 475–480 (1976)CrossRefGoogle Scholar
  10. 10.
    Connelly J.D., Huston R.L.: The dynamics of flexible multibody systems: a finite segment approach I. Theoretical aspects. Comput. Struct. 50(2), 255–258 (1994)CrossRefGoogle Scholar
  11. 11.
    Connelly J.D., Huston R.L.: The dynamics of flexible multibody systems: a finite segment approach II. Example problems. Comput. Struct. 50(2), 259–262 (1994)CrossRefGoogle Scholar
  12. 12.
    Wittenburg J.: Dynamics of Systems of Rigid Bodies. Teubner, Stuttgart (1977)MATHGoogle Scholar
  13. 13.
    Banerjee A.K.: Dynamics and control of the WISP shuttle-antennae system. J. Astronaut. Sci. 1, 73–90 (1993)Google Scholar
  14. 14.
    Schiehlen W.O., Rauh J.: Modelling of flexible multibeam systems by rigid-elastic superelements. Revista Brasiliera de Cienclas Mecanicas 8(2), 151–163 (1986)Google Scholar
  15. 15.
    Wittbrodt E., Wojciech S.: Application of rigid finite element method to dynamic analysis of spatial systems. J. Guid. Control Dyn. 18(4), 891–898 (1995)CrossRefGoogle Scholar
  16. 16.
    Wojciech S., Kłosowicz M., Nadolski W.: Nonlinear vibration of a simply supported, viscoelastic inextensible beam and comparison of four methods. Acta Mech. 85, 43–54 (1990)CrossRefGoogle Scholar
  17. 17.
    Wojnarowski J., Wojciech S.: Application of the rigid finite element method to modelling of free vibrations of a band saw frame. Mech. Mach. Theory 40(2), 241–258 (2005)MATHCrossRefGoogle Scholar
  18. 18.
    Wittbrodt E., Adamiec-Wójcik I., Wojciech S.: Dynamics of Flexible Multibody Systems Rigid Finite Element Method. Springer, Berlin, Heidelberg (2006)MATHGoogle Scholar
  19. 19.
    Braestrup M.W., Andersen J.B., Andersen L.W., Bryndum M.B., Christensen J.C., Nielsen N.J.R.: Design and Installation of Marine Pipelines. Blackwell Science Ltd., Oxford (2005)Google Scholar
  20. 20.
    Guo B., Song S., Chacko J., Ghalambor A.: Offshore Pipelines. Elsevier, Oxford (2005)Google Scholar
  21. 21.
    Szczotka M., Maczyński A., Wojciech S.: Mathematical model of a pipelay spread. Arch. Mech. Eng. LIV 1, 27–46 (2007)Google Scholar
  22. 22.
    Szczotka M.: Pipe laying simulation with an active reel drive. Ocean Eng. 37, 539–548 (2010)CrossRefGoogle Scholar
  23. 23.
    Chai Y.T., Varyani K.S.: An absolute coordinate formulation for three-dimensional flexible pipe analysis. Ocean Eng. 33, 23–58 (2006)CrossRefGoogle Scholar
  24. 24.
    Vogel H., Natvig B.J.: Dynamics of flexible hose riser systems. J. Offshore Mech. Arct. 109, 244–248 (1987)CrossRefGoogle Scholar
  25. 25.
    Vlahopoulos N., Bernitsas M.M.: Three-dimensional nonlinear dynamics of pipelaying. Appl. Ocean Res. 12, 112–125 (1990)CrossRefGoogle Scholar
  26. 26.
    Kalliontzis C., Andrianis E., Spyropoulos K., Soikas S.: Nonlinear static stress analysis of submarine high pressure pipelines. Comp. Struct. 63, 397–411 (1997)CrossRefGoogle Scholar
  27. 27.
    Pasqualino I.P., Estefen S.F.: A nonlinear analysis of the buckle propagation problem in deepwater pipelines. Int. J. Solids Struct. 38, 8481–8502 (2001)MATHCrossRefGoogle Scholar
  28. 28.
    Nakajima, T., Motora, S., Fujino, M.: On the dynamic analysis of multi-component mooring lines. In: 14th Offshore Technology Conference, OTC-4309, pp. 105–121 (1982)Google Scholar
  29. 29.
    Palmer A.: Touchdown indentation of the seabed. Appl. Ocean Res. 30, 235–238 (2008)CrossRefGoogle Scholar
  30. 30.
    Rienstra, S.W.: Analytical approximations for offshore pipelaying problems. In: Proceedings IClAM 87, pp. 99–108. Paris-La Villette (1987)Google Scholar
  31. 31.
    Zhu D.S., Cheung Y.K.: Optimisation of bouyancy of an articulated stringer on submerged pipelines laid with a barge. Ocean Eng. 24, 301–311 (1997)MATHCrossRefGoogle Scholar
  32. 32.
    Lenci S., Callegari M.: Simple analytical models for the J-lay problem. Acta Mech. 178, 23–39 (2005)MATHCrossRefGoogle Scholar
  33. 33.
    Liu G.R., Quek S.S.: The Finite Element Method: A Practical Course. Butterworth-Heinemann, Oxford (2003)MATHGoogle Scholar
  34. 34.
    Chapman B., Jost G., van der Pas R.: Using OpenMP: Portable Shared Memory Parallel. MIT Press, Cambridge (2008)Google Scholar
  35. 35.
    Szczotka M., Wojciech S.: Application of joint coordinates and homogeneous transformations to modeling of vehicle dynamics. Nonlinear Dyn. 52(4), 377–393 (2008)MATHCrossRefGoogle Scholar
  36. 36.
    Morison J.R., O’Brien M.P., Johnson J.W., Schaaf S.A.: The force exerted by surface waves on piles. Pet. Trans. 189, 149–154 (1950)Google Scholar
  37. 37.
    DNV-RP-F105: Free Spanning Pipelines. Det Norske Veritas, Høvik, Norway (2006)Google Scholar
  38. 38.
    Verley, R., Lund, K.M.: A soil resistance model for pipelines placed on clay soils. In: 14th International Conference on Offshore Mechanics & Arctic Engineering, Copenhagen (1995)Google Scholar
  39. 39.
    Chakrabarti S.K.: Handbook of Offshore Engineering. Elsevier, Oxford (2005)Google Scholar
  40. 40.
    Ansys Documentation: Release 12. SAS IP (2009)Google Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Department of Applied Computer SciencesUniversity of Bielsko-BiałaBielsko-BiałaPoland

Personalised recommendations