Towards the convergence of 3D and shell finite elements?

  • D. Chapelle
Conference paper


We present an approach for formulating efficient “3D-shell elements”, which are shell finite elements that feature the same external characteristics (geometry, shape functions) as standard 3D isoparametric elements. This makes the coupling with elements sharing the same outer surfaces straightforward. In addition, these 3D-shell elements can be used with a 3D variational formulation without modifying the constitutive equation, and they are much better adapted to large strain analysis than classical shell elements.


Shape Function Shell Model Shell Element Finite Element Solution Finite Element Procedure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Bathe, K.-J. (1996): Finite element procedures. Prentice Hall, Englewood Cliffs, NJGoogle Scholar
  2. [2]
    Bathe, K.-J., Iosilevich. A., Chapelle, D. (2000): An evaluation of the MITC shell elements. Comput. & Structures 75, 1–30MathSciNetCrossRefGoogle Scholar
  3. [3]
    Bernadou, M. (1996): Finite element methods for thin shell problems. Wiley, ChichesterMATHGoogle Scholar
  4. [4]
    Bischoff, M., Ramm, E. (2000): On the physical significance of higher order kinematic and static variables in a three-dimensional shell formulation. Internat. J. Solids Structures 37, 6933–6960MATHCrossRefGoogle Scholar
  5. [5]
    Brezzi, F, Fortin. M. (1991): Mixed and hybrid finite element methods. Springer, BerlinMATHCrossRefGoogle Scholar
  6. [6]
    Chapelle, D. (2001): Some new results and current challenges in the finite element analysis of shells. In: Iserles, A. (ed.): Acta Numerica 2001. Vol. 10. Cambridge University Press, Cambridge, pp. 215–250Google Scholar
  7. [7]
    Chapelle, D., Bathe, K.-J. (1998): Fundamental considerations for the finite element analysis of shell structures. Comput. & Structures 66, 19–36MATHCrossRefGoogle Scholar
  8. [8]
    Chapelle, D., Bathe, K.-J. (2000): The mathematical shell model underlying general shell elements. Internat. J. Numer. Methods Engrg. 48, 289–313MathSciNetMATHCrossRefGoogle Scholar
  9. [9]
    Chapelle, D., Bathe, K.-J. (2001): Optimal consistency errors for general shell elements. C. R. Acad. Sci. Paris Sér. I Math. 332, 771–776MathSciNetMATHCrossRefGoogle Scholar
  10. [10]
    Chapelle, D., Bathe, K.-J. (2003): The finite element analysis of shells. Fundamentals. Springer, Berlin, in pressGoogle Scholar
  11. [11]
    Chapelle, D., Ferent, A., Bathe, K.-J.: 3D-shell finite elements and their underlying model, in preparationGoogle Scholar
  12. [12]
    Chapelle, D., Ferent, A., Le Tallec, R (2003): The treatment of pinching locking in 3D-shell elements. M2AN Math. Model. Numer. Anal, in pressGoogle Scholar
  13. [13]
    Delfour, M.C. (1999): Intrinsic P(2, 1) thin shell model and Naghdi’s models without a priori assumption on the stress tensor. In: Hoffmann, K.-H. et al. (eds.): Optimal control of partial differential equations. Birkhäuser, Basel, pp. 99–113CrossRefGoogle Scholar
  14. [14]
    Havu, V., Pitkäranta, J. (2002): Analysis of a bilinear finite element for shallow shells. I: Approximation of inextensional deformations. Math. Comp. 71, 923–943MathSciNetMATHCrossRefGoogle Scholar
  15. [15]
    Malinen, M.: On refined 2D shell models taking into account transverse deformations, to appearGoogle Scholar
  16. [16]
    Malinen, M. (2001): On the classical shell model underlying bilinear degenerated shell finite elements. Internat. J. Numer. Methods Engrg. 52, 389–416MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Italia 2003

Authors and Affiliations

  • D. Chapelle
    • 1
  1. 1.INRIA-RocquencourtLe ChesnayFrance

Personalised recommendations