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Acta Mechanica Sinica

, Volume 34, Issue 4, pp 769–780 | Cite as

Multibody dynamic analysis using a rotation-free shell element with corotational frame

Research Paper
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Abstract

Rotation-free shell formulation is a simple and effective method to model a shell with large deformation. Moreover, it can be compatible with the existing theories of finite element method. However, a rotation-free shell is seldom employed in multibody systems. Using a derivative of rigid body motion, an efficient nonlinear shell model is proposed based on the rotation-free shell element and corotational frame. The bending and membrane strains of the shell have been simplified by isolating deformational displacements from the detailed description of rigid body motion. The consistent stiffness matrix can be obtained easily in this form of shell model. To model the multibody system consisting of the presented shells, joint kinematic constraints including translational and rotational constraints are deduced in the context of geometric nonlinear rotation-free element. A simple node-to-surface contact discretization and penalty method are adopted for contacts between shells. A series of analyses for multibody system dynamics are presented to validate the proposed formulation. Furthermore, the deployment of a large scaled solar array is presented to verify the comprehensive performance of the nonlinear shell model.

Keywords

Flexible multibody dynamics Rotation-free shell Corotational frame Geometric nonlinearity 

Notes

Acknowledgements

This research was supported by the National Natural Science Foundation of China (Grants 11772188, 11132007).

References

  1. 1.
    Bauchau, O.A., Choi, Y., Bottasso, C.L.: On the modeling of shells in multibody dynamics. Multibody Syst. Dyn. 8, 459–489 (2002)CrossRefMATHGoogle Scholar
  2. 2.
    Pappalardo, C.M., Wallin, M., Shabana, A.A.: A new ANCF/CRBF fully parameterized plate finite element. J. Comput. Nonlinear Dyn. 12(3), 031008 (2016)CrossRefGoogle Scholar
  3. 3.
    Ren, H.: A simple absolute nodal coordinate formulation for thin beams with large deformations and large rotations. J. Comput. Nonlinear Dyn. 10(6), 061005 (2015)CrossRefGoogle Scholar
  4. 4.
    Pavan, G.S., Nanjunda Rao, K.S.: Bending analysis of laminated composite plates using isogeometric collocation method. Compos. Struct. 176, 715–728 (2017)CrossRefGoogle Scholar
  5. 5.
    Liu, Z.Y., Liu, J.Y.: Experimental validation of rigid-flexible coupling dynamic formulation for hub-beam system. Multibody Syst. Dyn. 40(3), 303–326 (2017)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Wempner, G.: Finite elements, finite rotations and small strains of flexible shells. Int. J. Solids Struct. 5(15), 117–153 (1969)CrossRefMATHGoogle Scholar
  7. 7.
    Belytschko, T., Schwer, L., Klein, M.J.: Large displacement, transient analysis of space frames. Int. J. Numer. Methods Eng. 1, 65–84 (1977)CrossRefMATHGoogle Scholar
  8. 8.
    Rankin, C.C., Brogan, F.A.: An element independent corotational procedure for the treatment of large rotations. J. Press. Vessel Technol. 108, 165–174 (1986)CrossRefGoogle Scholar
  9. 9.
    Chimakurthi, S.K., Cesnik, C.E.S., Stanford, B.K.: Flapping-wing structural dynamics formulation based on a corotational shell finite element. AIAA J. 49(1), 128–142 (2011)CrossRefGoogle Scholar
  10. 10.
    Cho, H., Shin, S.J., Yoh, J.J.: Geometrically nonlinear quadratic solid/solid-shell element based on consistent corotational approach for structural analysis under prescribed motion. Int. J. Numer. Methods Eng. 112(5), 434–458 (2017)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Faroughi, S., Eriksson, A.: Co-rotational formulation for dynamic analysis of space membranes based on triangular elements. Int. J. Mech. Mater. Des. 13(2), 229–241 (2017)CrossRefGoogle Scholar
  12. 12.
    Sabourin, F., Brunet, M.: Detailed formulation of the rotation-free triangular element S3 for general purpose shell analysis. Eng. Comput. 23(5), 469–502 (2006)CrossRefMATHGoogle Scholar
  13. 13.
    Guo, Y.Q., Gati, W., Naceur, H., et al.: An efficient DKT rotation free shell element for springback simulation in sheet metal forming. Compos. Struct. 80, 2299–2312 (2002)CrossRefGoogle Scholar
  14. 14.
    Oñate, E., Cervera, M.: Derivation of thin plate bending elements with one degree of freedom per node: a simple three node triangle. Eng. Comput. 10(6), 543–561 (1993)CrossRefGoogle Scholar
  15. 15.
    Flores, F.G., Oñate, E.: Wrinkling and folding analysis of elastic membranes using an enhanced rotation-free thin shell triangular element. Finite Elem. Anal. Des. 47(9), 982–990 (2011)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Phaal, R., Calladine, C.R.: Simple class of finite elements for plate and shell problems. II: an element for thin shells, with only translational degrees of freedom. Int. J. Numer. Methods Eng. 35(5), 979–996 (1992)CrossRefMATHGoogle Scholar
  17. 17.
    Zhou, Y.X., Sze, K.Y.: A geometric nonlinear rotation-free triangle and its application to drape simulation. Int. J. Numer. Methods Eng. 89, 509–536 (2011)CrossRefMATHGoogle Scholar
  18. 18.
    Das, M., Barut, A., Madenci, E.: Analysis of multibody systems experiencing large elastic deformations. Multibody Syst. Dyn. 23(1), 1–31 (2009)MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    Liu, C., Tian, Q., Hu, H.Y.: Dynamics of a large scale rigid-flexible multibody system composed of composite laminated plates. Multibody Syst. Dyn. 26(3), 283–305 (2011)CrossRefMATHGoogle Scholar
  20. 20.
    Nour-Omid, B., Rankin, C.C.: Finite rotation analysis and consistent linearization using projectors. Comput. Methods Appl. Mech. Eng. 93(3), 353–384 (1991)CrossRefMATHGoogle Scholar
  21. 21.
    Battini, J.: A modified corotational framework for triangular shell elements. Comput. Methods Appl. Mech. Eng. 196(13–16), 1905–1914 (2007)CrossRefMATHGoogle Scholar
  22. 22.
    Shabana, A.A.: Dynamics of Multibody Systems, 3rd edn. Cambridge University Press, Cambridge (2005)CrossRefMATHGoogle Scholar
  23. 23.
    Felippa, C.A., Haugen, B.: A unified formulation of small-strain corotational finite elements: I. Theory. Comput. Methods Appl. Mech. Eng. 194(21–24), 2285–2335 (2005)CrossRefMATHGoogle Scholar
  24. 24.
    Wriggers, P.: Computational Contact Mechanics. Springer, Berlin, Heidelberg (2006)CrossRefMATHGoogle Scholar
  25. 25.
    Liu, C., Tian, Q., Hu, H.Y.: New spatial curved beam and cylindrical shell elements of gradient-deficient Absolute Nodal Coordinate Formulation. Nonlinear Dyn. 70(3), 1903–1918 (2012)MathSciNetCrossRefGoogle Scholar
  26. 26.
    Xie, Q., Sze, K.Y., Zhou, Y.X.: Drape simulation using solid-shell elements and adaptive mesh subdivision. Finite Elem. Anal. Des. 106, 85–102 (2015)CrossRefGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Naval Architecture, Ocean and Civil EngineeringShanghai Jiao Tong UniversityShanghaiChina

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