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Multibody System Dynamics

, Volume 34, Issue 1, pp 23–51 | Cite as

The simplest 3-, 6- and 8-noded fully-parameterized ANCF plate elements using only transverse slopes

  • Alexander Olshevskiy
  • Oleg Dmitrochenko
  • Mai D. Dai
  • Chang-Wan Kim
Article

Abstract

In this paper, the simplest kinematical models of triangular plate finite elements using the absolute nodal coordinate formulation (ANCF) are considered. The ANCF is the finite element approach for simulating large displacements and rotations, in which the nodal position vectors and their derivatives are described in the inertial frame only. This leads to linear kinematics of elements, constant mass matrix and simple expressions for inertia terms in the equations of motion. The elastic forces appear in the ANCF in highly nonlinear form due to using the Green–Lagrange strain tensor. This fact compels researchers to find possibilities of reducing the computational complexity in using the ANCF. One of the ways in this direction is to use simplest fully-parameterized plate elements employing transverse slopes only, without using longitudinal slopes.

Keywords

Finite element method Absolute nodal coordinate formulation Flexible multibody system dynamics Large displacements Fully parameterized plate elements 

Notes

Acknowledgements

This research was supported by Basic Science Research Program through Korea NRF (2012R1A2A2A04047240 and 2012R1A1A2008870), Defense Acquisition Program Administration and Agency for Defense Development under the contract UD120037CD, and 2012 KU Brain Pool of Konkuk University.

References

  1. 1.
    Shabana, A.A.: Definition of the slopes and the finite element absolute nodal coordinate formulation. Multibody Syst. Dyn. 1(3#5), 339–348 (1997) CrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    Dibold, M., Gerstmayr, J., Irschik, H.: On the accuracy and computational costs of the absolute nodal coordinate and the floating frame of reference formulation in deformable multibody systems. In: Proceedings of the IDETC/CIE 2007, ASME 2007 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, Paper Number DETC2007-34756, Las Vegas (NV), USA, 4–7 September 2007 Google Scholar
  3. 3.
    Gerstmayr, J., Shabana, A.A.: Analysis of thin beams and cables using the absolute nodal co-ordinate formulation. Nonlinear Dyn. 45(1#A), 109–130 (2006) CrossRefMATHGoogle Scholar
  4. 4.
    Kerkkänen, K., García-Vallejo, D., Mikkola, A.: Modeling of belt-drives using a large deformation finite element formulation. Nonlinear Dyn. 43(3#2), 239–256 (2006) CrossRefMATHGoogle Scholar
  5. 5.
    Sugiyama, H., Escalona, J.L., Shabana, A.A.: Formulation of three-dimensional joint constraints using the absolute nodal coordinates. Nonlinear Dyn. 31(2#4), 167–195 (2003) CrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    Matikainen, M., Dmitrochenko, O., Mikkola, A.: Beam elements with trapezoidal cross-section deformation modes based on the absolute nodal coordinate formulation. In: Proc. of the 8th Int. Conf. of Num. Analysis & Appl. Math., Rhodes, Greece. American Inst. of Physics Conf. Proc., vol. 1281, pp. 1262–1265 (2010) Google Scholar
  7. 7.
    Dmitrochenko, O., Mikkola, A.: Extended digital nomenclature code for description of complex finite elements and generation of new elements. Mech. Based Des. Struct. Mach. 39(2#5), 229–252 (2011) CrossRefGoogle Scholar
  8. 8.
    Sanborn, G., Choi, J., Choi, J.H.: Curve-induced distortion of polynomial space curves, flat-mapped extension modeling, and their impact on ANCF thin-plate finite elements. Multibody Syst. Dyn. 26, 191–211 (2011) CrossRefMATHMathSciNetGoogle Scholar
  9. 9.
    Dmitrochenko, O., Mikkola, A.: Digital nomenclature code for topology and kinematics of finite elements based on the absolute nodal coordinate formulation. Proc. Inst. Mech. Eng., Proc., Part K, J. Multi-Body Dyn. 225(1#3), 34–51 (2011) Google Scholar
  10. 10.
    Sopanen, J.T., Mikkola, A.M.: Description of elastic forces in absolute nodal coordinate formulation. Nonlinear Dyn. 34(1#3), 53–74 (2004) Google Scholar
  11. 11.
    Schwab, A., Meijaard, J.: Comparison of three-dimensional flexible beam elements for dynamic analysis: finite element method and absolute nodal coordinate formulation. In: Proceedings of the IDEC/CIE 2005, ASME 2005 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, Paper Number DETC2005-85104, Long Beach (CA), USA, 24–28 September 2005 Google Scholar
  12. 12.
    Gerstmayr, J., Matikainen, M.K., Mikkola, A.M.: A geometrically exact beam element based on the absolute nodal coordinate formulation. Multibody Syst. Dyn. 20(4#4), 359–384 (2008) CrossRefMATHMathSciNetGoogle Scholar
  13. 13.
    Kreyszig, E.: Differential Geometry, p. 119. Dover, New York (1991) Google Scholar
  14. 14.
    Gere, J.M., Timoshenko, S.P.: Mechanics of Materials, 4th edn. PWS, Boston (1997), 912 pp Google Scholar
  15. 15.
    Nachbagauer, K., Pechstein, A.S., Irschik, H., Gerstmayr, J.: A new locking-free formulation for planar, shear deformable, linear and quadratic beam finite elements based on the absolute nodal coordinate formulation. Multibody Syst. Dyn. 26, 245–263 (2011) CrossRefMATHGoogle Scholar
  16. 16.
    Dmitrochenko, O., Mikkola, A.: Two simple triangular plate elements based on the absolute nodal coordinate formulation. J. Comput. Nonlinear Dyn. 3(4#C), 041012-1-8 (2008) Google Scholar
  17. 17.
    Matikainen, M.K., von Hertzen, R., Mikkola, A., Gerstmayr, J.: Elimination of high frequencies in the absolute nodal coordinate formulation. Proc. Inst. Mech. Eng., Proc., Part K, J. Multi-Body Dyn. 224(1#7), 103–116 (2009) Google Scholar
  18. 18.
    Olshevskiy, A.A., Dmitrochenko, O.N., Lee, S., Kim, C.W.: A triangular plate element 2343 using second-order absolute-nodal-coordinate slopes: numerical computation of shape functions. Nonlinear Dyn. 74(3), 769–781 (2013) CrossRefMATHMathSciNetGoogle Scholar
  19. 19.
    Dmitrochenko, O., Mikkola, A.: Two simple triangular plate elements based on the absolute nodal coordinate formulation. J. Comput. Nonlinear Dyn. 3(4#C), 041012-1-8 (2008) Google Scholar
  20. 20.
    Mikkola, A.M., Shabana, A.A.: A non-incremental finite element procedure for the analysis of large deformation of plates and shells in mechanical system applications. Multibody Syst. Dyn. 9(3#4), 283–309 (2003) CrossRefMATHMathSciNetGoogle Scholar
  21. 21.
    Dmitrochenko, O.N., Pogorelov, D.Yu.: Generalization of plate finite elements for absolute nodal coordinate formulation. Multibody Syst. Dyn. 10(1#2), 17–43 (2003) CrossRefMATHGoogle Scholar
  22. 22.
    Matikainen, M.K., Valkeapää, A.I., Mikkola, A.M., Schwab, A.L.: A study of moderately thick quadrilateral plate elements based on the absolute nodal coordinate formulation. Multibody Syst. Dyn. (2013). doi: 10.1007/s11044-013-9383-6 Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Alexander Olshevskiy
    • 1
  • Oleg Dmitrochenko
    • 2
  • Mai D. Dai
    • 1
  • Chang-Wan Kim
    • 1
  1. 1.School of Mechanical EngineeringKonkuk UniversitySeoulKorea
  2. 2.Department of Mechanical EngineeringLappeenranta University of TechnologyLappeenrantaFinland

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