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Numerische Mathematik

, Volume 96, Issue 4, pp 661–689 | Cite as

Uniform error estimates for a class of intermediate cylindrical shell problems

  • L. Beirão da VeigaEmail author
Article

Summary.

A uniform in thickness error estimate is obtained for a particular class of intermediate Koiter shell problems, solved with a classical conforming finite element method. The model problem is that of a cylinder under a class of irregular loads which, due to particular symmetries, allow a simplified reformulation on a one dimensional domain. The result is an almost h s error behavior in the H −1 dual norm, were s>0 depends on the load regularity. Such estimate is believable to be sharp (this additional claim is supported by some numerical tests).

Keywords

Finite Element Method Error Estimate Cylindrical Shell Model Problem Numerical Test 
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.

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References

  1. 1.
    Auricchio, F., Beirão da Veiga, L., Lovadina, C.: Remarks on the asymptotic behaviour of Koiter shells. Computers and Structures 80, 735–745 (2002)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Baiocchi, C., Lovadina, C.: Interpolation theory and shell problems. Appl. Math. Lett. 13(7), 33–37 (2000)CrossRefzbMATHGoogle Scholar
  3. 3.
    Baiocchi, C., Lovadina, C.: A shell classification by interpolation. Math. Models and Methods Appl. Sci. (to appear)Google Scholar
  4. 4.
    Beirão da Veiga, L.: Theoretical and numerical study of shell intermediate states on particular toroidal and cylindrical problems. Ist. Lomb. Cad. Sci. Let. Rend. (A) 134, 133–161 (2000)Google Scholar
  5. 5.
    Bathe, K.J., Lee, P.S.: On the asymptotic behavior of shell structures and the evaluation in finite element solutions. Computer & Structures 80, 235–255 (2002)Google Scholar
  6. 6.
    Bergh, J., Löfstrom, J.: Interpolation Spaces: An Introduction. Springer, 1976Google Scholar
  7. 7.
    Bernadou, M.: Finite Element Methods for Thin Shell Problems. John Wiley & Sons 1996Google Scholar
  8. 8.
    Blouza, A., Brezzi, F., Lovadina, C.: A new classification for Shell Problems. Pubbl. I.A.N. Tech. Reports 1128, 1999Google Scholar
  9. 9.
    Blouza, A., Brezzi, F., Lovadina, C.: Sur la classification des coques linéarment élastiques. C.R. Acad. Sci. Paris., t.328 I, 831–836 (1999)Google Scholar
  10. 10.
    Brezzi, F., Fortin, M.: Mixed and Hybrid Finite Element Methods. Springer-Verlag 1991Google Scholar
  11. 11.
    Brenner, S.C., Scott, L.R.: The Mathematical Theory of Finite Element Methods. Springer-Verlag 1994Google Scholar
  12. 12.
    Chapelle, D., Bathe, K.J.: Fundamental consideration for the Finite Element analysis of shell structures. Computer & Structures 66, 19–36 (1998)Google Scholar
  13. 13.
    Chenais, D., Paumier, J.C.: On the locking phenomenon for a class of elliptic problems. Numer. Math. 67(4), 427–440 (1994)CrossRefzbMATHGoogle Scholar
  14. 14.
    Choi, D., Palma, F.J., Sanches-Palencia, E., Vilariño, M.A.: Membrane locking in the finite element computation of very thin elastic shells. Rairo Model. Math. Anal. Numer. 32(2), 131–152 (1998)zbMATHGoogle Scholar
  15. 15.
    Ciarlet, P.G.: Introduction to linear Shell Theory, Series in Applied Mathematics. Gauthiers-Villairs 1998Google Scholar
  16. 16.
    Hakula, H., Leino, Y., Pitkäranta, J.: Scale resolution, locking, and high order finite element modelling of shells. Comp. Meth. Appl. Mech. Engrg 133, 157–182 (1996)CrossRefzbMATHGoogle Scholar
  17. 17.
    Leino, Y., Ovaskien, O., Pitkäranta, J.: Shell deformation states and the finite element method: a benchmark study of cylindrical shells. Comp. Meth. Appl. Mech. Engrg 127, 81–121 (1995)MathSciNetGoogle Scholar
  18. 18.
    Lions, J.L.: Perturbations singulieres dans les problemes aux limites non linéaires. Lecture Notes in Math. 323, Springer, Berlin 1973Google Scholar
  19. 19.
    Lions, J.L., Peetre, J.: Sur une classe d’espaces d’interpolation. Publ. I.H.E.S. 19, 5–68 (1964)zbMATHGoogle Scholar
  20. 20.
    Pitkäranta, J.: The problem of membrane locking in finite element analysis of cylindrical shells. Numer. Math. 61(4), 523–542 (1992)Google Scholar
  21. 21.
    Sanchez-Palencia, E.: Asymptotic and spectral properties of a class of singular-stiff problems. J. Math. Pures Appl. 71, 379–406 (1992)MathSciNetzbMATHGoogle Scholar
  22. 22.
    Schwab, C., Suri, M., Xenophontos, C.: The hp finite element method for problems in mechanics with boundary layers. Comput. Methods Appl. Mech. Engrg 157, 311–333 (1998)CrossRefMathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità di PaviaPaviaItaly

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