Skip to main content
SpringerLink
Log in

Energy estimates for shell problems

  • Conference paper
Numerical Mathematics and Advanced Applications

  • 1175 Accesses

Summary

We consider the behavior of a general Koiter shell in the framework of linear elasticity. We investigate the asymptotics (for the thickness tending to zero) of the energy functional and of the percentage of the energy which is stored in the bending term. Such an analysis is motivated by the need to understand better how to design a reliable finite element scheme for arbitrary thin shell.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Arnold, D. N., Brezzi, E (1997): Locking-free finite element methods for shells. Math. Comp. 66, 1–14

    Article  MathSciNet  MATH  Google Scholar 

  2. Baiocchi, C., Lovadina, C. (2002): A shell classification by interpolation. Math. Models Methods Appl. Sci. 12, 1359–1380

    Article  MathSciNet  MATH  Google Scholar 

  3. Baiocchi, C., Savaré, G. (1994): Singular perturbation and interpolation. Math. Models Methods Appl. Sci. 4, 557–570

    Article  MathSciNet  MATH  Google Scholar 

  4. Bathe, K.-J. (1996): Finite element procedures. Prentice Hall, Englewood Cliffs, NJ

    Google Scholar 

  5. Bathe, K.-J., Iosilevich, A., Chapelle, D. (2000): An evaluation of the MITC shell elements. Comput. & Structures 75, 1–30

    Article  MathSciNet  Google Scholar 

  6. Beirão da Veiga, L.: Theoretical and numerical study of shell intermediate states on particular toroidal and cylindrical problems. Istit. Lombardo Accad. Sci. Lett. Rend. A, to appear

    Google Scholar 

  7. Beirão da Veiga, L.: Uniform error estimates for a class of intermediate cylindrical shell problems. Numer. Math., to appear

    Google Scholar 

  8. Bergh, J., Löfström, J. (1976): Interpolation spaces. An introduction. Springer, Berlin

    Google Scholar 

  9. Bernadou, M., Ciarlet, P. G. (1976): Sur l'ellipticité du modèle linéaire de W. T. Koiter. In: Glowinski, R., Lions, J.-L. (eds): Computing methods in applied sciences and engineering. Part I. (Lecture Notes in Economics and Mathematical Systems, vol. 134). Springer, Berlin, pp. 89–136

    Chapter  Google Scholar 

  10. Blouza, A., Brezzi, E, Lovadina, C. (1999): A New classification for shell problems. Technical Report IAN-CNR-1128. Istituto di Analisi Numerica — Consiglio Nazionale delle Richerche, Pavia

    Google Scholar 

  11. Blouza, A., Brezzi, E, Lovadina, C. (1999): Sur la classification des coques linéairement élastiques, C. R. Acad. Sci. Paris Sér, I Math. 328, 831–836

    Article  MathSciNet  MATH  Google Scholar 

  12. Blouza, A., Le Dret, H. (1999): Existence and uniqueness for the linear Koiter model for shells with little regularity. Quart. Appl. Math. 57, 317–337

    MathSciNet  MATH  Google Scholar 

  13. 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. 215–250

    Google Scholar 

  14. Chapelle, D., Bathe, K.-J. (1998): Fundamental considerations for the finite element analysis of shell structures. Comput. & Structures 66, 19–36

    Article  MATH  Google Scholar 

  15. Chapelle, D., Stenberg, R. (1999): Stabilized finite element formulations for shells in a bending dominated state. SIAM J. Numer. Anal. 36, 32–73

    Article  MathSciNet  Google Scholar 

  16. Chenais, D., Paumier, J. C. (1994): On the locking phenomenon for a class of elliptic problems. Numer. Math. 67, 427–440

    Article  MathSciNet  MATH  Google Scholar 

  17. Ciarlet, P. G. (1998): Introduction to linear shell theory. (Series in Applied Mathematics, vol. 1). Gauthier-Villars, Paris

    MATH  Google Scholar 

  18. Ciarlet, P. G. (2001): Mathematical modelling of linearly elastic shells. In: Iserles, A. (ed.): Acta Numerica 2001. Cambridge University Press, Cambridge, pp. 103–214

    Google Scholar 

  19. Lee, P.-S., Bathe, K.-J. (2002): On the asymptotic behavior of shell structures and the evaluation in finite element solutions. Comput. & Structures 80, 235–255

    Article  Google Scholar 

  20. Lions, J.-L., Peetre, J. (1964): Sur une classe d’espaces d’interpolation. Inst. Hautes Études Sci. Publ. Math. No. 19, 5–68

    Article  MathSciNet  MATH  Google Scholar 

  21. Lions, J.-L., Sanchez-Palencia, E. (1996): Problèmes sensitifs et coques élastiques minces. In: Cea, J. et al. (eds.): Partial differential equations and functional analysis. Birkhäuser Boston, Boston, MA, pp. 207–220

    Chapter  Google Scholar 

  22. Piila, J., Leino, Y., Ovaskainen, O., Pitkäranta, J. (1995): Shell deformation states and the finite element method: a benchmark study of cylindrical shells. Comput. Methods Appl. Mech. Engrg. 128, 81–121

    Article  MathSciNet  MATH  Google Scholar 

  23. Sanchez-Palencia, E. (1989): Statique et dynamique des coques minces. II. Cas de flexion pure inhibée. Approximation membranaire. C. R. Acad. Sci. Paris Sér. I Math. 309, 531–537

    MathSciNet  MATH  Google Scholar 

  24. Sanchez-Palencia, E. (1989): Statique et dynamique des coques minces. I. Cas de flexion pure non inhibée, C. R. Acad. Sci. Paris Sér. I Math. 309, 411–417

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Matematica, Università di Pavia, Pavia, Italy

    C. Lovadina

Authors
  1. C. Lovadina
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. e Tecnologie Informatiche IMATI-CNR, Università di Pavia and Istituto di Matematica Applicata, Pavia, Italy

    Franco Brezzi

  2. e Tecnologie Informatiche IMATI-CNR, Istituto di Matematica Applicata, Pavia, Italy

    Annalisa Buffa

  3. e Reti ad Alte Prestazioni ICAR-CNR, Istituto per il Calcolo, Napoli, Italy

    Stefania Corsaro

  4. e Reti ad Alte Prestazioni ICAR-CNR, Università di Napoli and Istituto per il Calcolo, Napoli, Italy

    Almerico Murli

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Italia

About this paper

Cite this paper

Lovadina, C. (2003). Energy estimates for shell problems. In: Brezzi, F., Buffa, A., Corsaro, S., Murli, A. (eds) Numerical Mathematics and Advanced Applications. Springer, Milano. https://doi.org/10.1007/978-88-470-2089-4_36

Download citation

  • DOI: https://doi.org/10.1007/978-88-470-2089-4_36

  • Publisher Name: Springer, Milano

  • Print ISBN: 978-88-470-2167-9

  • Online ISBN: 978-88-470-2089-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation