Skip to main content
Log in

Analysis of Laminated Rubber Bearings with a Numerical Reduction Model Method

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

Abstract

In this paper, we present a reduction method for modeling slender laminated elastomeric structures, which is developed in the context of nearly incompressible hyperelasticity. This method, based on a finite element formulation, consists in projecting the unknown fields onto a polynomial basis in order to reduce the dimension of the problem and the model size. Two types of finite elements are used, one for plane-strain and the other for 3D structures. Comparisons with classical finite element models on single layers show the reliability of the present method. The method proposed successfully predicts the global and local behavior and since it reduces both the model size and the computing time. It can be used to model slender bearing consisting of several layers.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

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

    Article  MathSciNet  Google Scholar 

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

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

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

  7. Ciarlet, P.: Elasticité tridimensionnelle. Masson (1986)

  8. Cugnon, F.: Automatisation des calculs éléments finis dans le cadre de la méthode-p. PhD thesis, Université de Liège (2000)

  9. Devries F. (1998). Homogenization of elastomer matrix composites: method and validation. Composite 29:753–762

    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. (1996). Polymorphic constitutive equations in finite element codes. Comput Methods Appl Mech Engrg 141:355–372

    Article  Google Scholar 

  12. Fu Y., Ogden R. (eds) (2001). Nonlinear elasticity: theory and applications. Cambridge university press, London Mathematical Society Lecture Note Series, PP 283

    Google Scholar 

  13. Hartmann S., Neff P. (2003). Polyconvexity of generalized polynomial-type hyperelastic strain energy functions for near incompressibility. Int J Solids Struct 40:2767–2791

    Article  MATH  MathSciNet  Google Scholar 

  14. Holzapfel G. (2004). Nonlinear solid mechanics. Wiley, Newyork

    MATH  Google Scholar 

  15. Iizuka M. (2000). A macroscopic model for predicting large-deformation behaviors of laminated rubber bearings. Engg Struct 22:323–334

    Article  Google Scholar 

  16. Kelly, J.: Tension buckling in multilayer elastomeric bearings. In: 16th Engineering mechanics conference, American Society of Civil Engineers, Seattle (2003)

  17. Koo G., Lee J., Yoo B., Ohtori Y. (1999). Evaluation of laminated rubber bearing for seismic isolation using modified macro-model with parameter equations of instantaneous apparent shear modulus. Engg Struct 21:594–602

    Article  Google Scholar 

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

    Article  Google Scholar 

  19. Malkus D., Hughes T. (1978). Mixed finite element methods– reduced and selective integration techniques: a unification of concepts. Comp Meth Appl Mech Engg 15:63–81

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  21. Miehe C. (1994). Aspects of the formulation and finite element implementation of large strain isotropic elasticity. Int J Numer Methods Engg 37:1981–2004

    Article  MATH  MathSciNet  Google Scholar 

  22. Rüter M., Stein E. (2000). Analysis, finite element computation and error estimation in transversly isotropic nearly incompressible finite elasticity. Comput Methods Appl Mech Engrg 190:519–541

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  Google Scholar 

  24. Tsai H.C., Kelly J.M. (2005). Buckling load of seismic isolators affected by flexibility of reinforcement. Int J of Solids Struct 42:255–269

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  26. Zienkiewicz O., Taylor R. (2000). The finite element method, 5th edn. Butterworth-Heinemann, Oxford

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to S. Lejeunes.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lejeunes, S., Boukamel, A. & Cochelin, B. Analysis of Laminated Rubber Bearings with a Numerical Reduction Model Method. Arch Appl Mech 76, 311–326 (2006). https://doi.org/10.1007/s00419-006-0030-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00419-006-0030-z

Keywords

Navigation