Skip to main content
SpringerLink
Log in

A model reduction technique for laminated solids of revolution with a curved cross-section

  • Original
  • Published:
Archive of Applied Mechanics Aims and scope Submit manuscript

Abstract

This paper presents an extension of the numerical reduction method, which has been proposed in Lejeunes et al. (Arch Appl Mech, 76:311–326, 2006), for modeling curved laminated structures of revolution such as for instance rubber bearings. This method based on high-order finite elements is developed in the context of nearly incompressible hyperelastic behavior. The displacement is approximated with a sum of independent functions, leading to a separation of variables. Therefore, a one-dimensional finite element can be formulated, which represents a 3-dimensional solid in a general loading case. Comparisons with classical finite element models are provided and show the reliability of this model reduction. An important decrease in the model size and a greatly reduced computing time, compared to standard models, is observed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Babuška I., Narasimhan R.: The babuška-brezzi condition and the patch test: an example. Comput. Methods Appl. Mech. Eng. 140, 183–199 (1997)

    Article  MATH  Google Scholar 

  2. Babuška I., Ogden J.T.: Verification and validation in computational engineering and science: basic concepts. Comput. Methods Appl. Mech. Eng. 193, 4057–4066 (2004)

    Article  MATH  Google Scholar 

  3. Boukamel, A.: Etude théorique et expérimentale d’un stratifié caoutchouc-acier en grandes déformations. Ph.D thesis, Université d’Aix-Marseille II (1988)

  4. Chang C.H.: Modeling of laminated rubber bearings using an analytical stiffness matrix. Int. J. Solids Struct. 39, 6055–6078 (2002)

    Article  MATH  Google Scholar 

  5. Cheung Y., Au F.: Isoparametric spline finite strip for degenerate shells. Thin-Walled Struct. 21, 65–92 (1995)

    Article  Google Scholar 

  6. Cheung Y., Jiang C.: Finite layer method in analyses of piezoelectric composite laminates. Comput. Methods Appl. Mech. Eng. 191, 879–901 (2001)

    Article  MATH  Google Scholar 

  7. Cheung Y., Kong J.: The application of a new finite strip to the free vibration of rectangular plates of varying complexity. J. Sound Vib. 181, 341–353 (1995)

    Article  Google Scholar 

  8. Cheung Y.K.: Finite strip method in structural analysis. Pergamon Press, Oxford (1976)

    MATH  Google Scholar 

  9. Devries F.: Homogenization of elastomer matrix composites: method and validation. Compos. Part B Eng. 29, 753–762 (1998)

    Article  Google Scholar 

  10. Dumontet, H.: Homogénéisation et effets de bords dans les matériaux composites. Thèse d’état, Université Pierre et Marie Curie Paris 6 (1990)

  11. Foerch R., Besson J., Cailletaud G., Pivlin P.: Polymorphic constitutive equations in finite element codes. Comput. Methods Appl. Mech. Eng. 141, 355–372 (1996)

    Article  Google Scholar 

  12. Fu, Y., Ogden, R. (eds.): Nonlinear Elasticity: Theory and Applications. Cambridge University Press, London Mathematical Society Lecture Note Series, 283 (2001)

  13. Heisserer S.Y.Z., Hartmann U., Düster A.: On volumetric locking-free behavior of p-version finite elements under finite deformations. Commun. Numer. Methods Eng. 24, 1019–1032 (2008)

    Article  MATH  Google Scholar 

  14. Holzapfel G.: Nonlinear Solid Mechanics. Wiley, London (2004)

    Google Scholar 

  15. Lejeunes, S.: Modeling of laminated rubber-like/metal structures with a numerical reduction method. Ph.D thesis, University of Aix-Marseille II, (2006): http://tel.archives-ouvertes.fr/tel-00090600/fr/

  16. Lejeunes S., Boukamel A., Cochelin B.: Analysis of laminated rubber bearings with a numerical reduction model method. Arch. Appl. Mech. 76, 311–326 (2006)

    Article  MATH  Google Scholar 

  17. Léné F., Rey C.: Some strategies to compute elastomeric lamified composite structures. Compos. Struct. 54, 231–241 (2001)

    Article  Google Scholar 

  18. Marusak R., Becker E.: A finite element procedure for axisymmetric elastomeric solids under general loading. Int. J. Numer. Methods Eng. 36, 2031–2048 (1993)

    Article  MATH  Google Scholar 

  19. Tsai H.C.: Compression stiffness of infinite-strip bearings of laminated elastic material interleaving with flexible reinforcements. Int. J. Solids Struct. 41, 6647–6660 (2004)

    Article  MATH  Google Scholar 

  20. Zhong W., Cheung Y., Li Y.: The precise finite strip method. Comput. Struct. 69, 773–783 (1998)

    Article  MATH  Google Scholar 

  21. Zienkiewicz, O., Taylor, R.: The Finite Element Method, vol. 2, 5th edn. Butterworth–Heinemann, Oxford (2000)

Download references

Author information

Authors and Affiliations

  1. Laboratoire de Mécanique et d’Acoustique, CNRS UPR-7051, 31 chemin Joseph-Aiguier, 13402, Marseille Cedex 20, France

    S. Lejeunes, A. Boukamel & F. Khedimi

  2. Ecole Centrale de Marseille, IMT/Technopôle Chateau-Gombert, 13451, Marseille Cedex 20, France

    A. Boukamel

Authors
  1. S. Lejeunes
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Boukamel
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. F. Khedimi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. Lejeunes.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lejeunes, S., Boukamel, A. & Khedimi, F. A model reduction technique for laminated solids of revolution with a curved cross-section. Arch Appl Mech 80, 1085–1102 (2010). https://doi.org/10.1007/s00419-010-0427-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00419-010-0427-6

Keywords

Search

Navigation