Free access
Volume 38, Number 6, November-December 2004
Page(s) 1055 - 1070
Published online 15 December 2004
  1. S.M. Alessandrini, D.N. Arnold, R.S. Falk and A.L. Madureira, Derivation and justification of plate models by variational methods, in Plates and Shells, M. Fortin Ed., AMS, Providence, CRM Proc. Lect. Notes Ser. 21 (1999) 1–20.
  2. D.N. Arnold and R.S. Falk, A uniformly accurate finite element method for the Reissner-Mindlin plate. SIAM J. Numer. Anal. 26 (1989) 1276–1290. [CrossRef] [MathSciNet]
  3. K.J. Bathe and F. Brezzi, On the convergence of a four-node plate bending element based on Mindlin/Reissner plate theory and a mixed interpolation in Mathematics of Finite Elements an Applications V, J.R. Whiteman Ed., Academic Press, London (1985) 491–503.
  4. K.J. Bathe and E.N. Dvorkin, A four-node plate bending element based on Mindlin/Reissner plate theory and a mixed interpolation. Int. J. Numer. Methods Eng. 21 (1985) 367–383. [CrossRef]
  5. A. Bermúdez and R. Rodríguez, Finite element computation of the vibration modes of a fluid-solid system. Comp. Methods Appl. Mech. Eng. 119 (1994) 355–370. [CrossRef]
  6. A. Bermúdez, P. Gamallo and R. Rodríguez, An hexahedral face element for elastoacoustic vibration problems. J. Comp. Acoust. 119 (1994) 355–370.
  7. A. Bermúdez, R. Durán, M.A. Muschietti, R. Rodríguez and J. Solomin, Finite element vibration analysis of fluid-solid systems without spurious modes. SIAM J. Numer. Anal. 32 (1995) 1280–1295. [CrossRef] [MathSciNet]
  8. F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods. Springer-Verlag, New York (1991).
  9. F. Brezzi, M. Fortin and R. Stenberg, Quasi-optimal error bounds for approximation of shear-stresses in Mindlin-Reissner plate models. Math. Models Methods Appl. Sci. 1 (1991) 125–151. [CrossRef] [MathSciNet]
  10. R. Durán and E. Liberman, On mixed finite element methods for the Reissner-Mindlin plate model. Math. Comp. 58 (1992) 561–573. [CrossRef] [MathSciNet]
  11. R. Durán, L. Hervella-Nieto, E. Liberman, R. Rodríguez and J. Solomin, Approximation of the vibration modes of a plate by Reissner-Mindlin equations. Math. Comp. 68 (1999) 1447–1463. [CrossRef] [MathSciNet]
  12. R. Durán, L. Hervella-Nieto, E. Liberman, R. Rodríguez and J. Solomin, Finite element analysis of the vibration problem of a plate coupled with a fluid. Numer. Math. 86 (2000) 591–616. [CrossRef] [MathSciNet]
  13. R. Durán, E. Hernández, L. Hervella-Nieto, E. Liberman and R. Rodríguez, Computation of the vibration modes of plates and shells by low-order MITC quadrilateral finite elements. SIAM J. Numer. Anal. 41 (2003) 1751–1772. [CrossRef] [MathSciNet]
  14. P. Gamallo, Métodos numéricos de elementos finitos en problemas de interacción fluido-estructura. Ph.D. Thesis, U. de Santiago de Compostela, Spain (2002).
  15. V. Girault and P.A. Raviart, Finite Element Methods for Navier-Stokes Equations. Springer-Verlag, Berlin, Heidelberg, New York, Tokyo (1986).
  16. T.J.R. Hughes, The Finite Element Method: Linear Static and Dinamic Finite Element Analysis. Prentice-Hall, Englewood Cliffs, NJ (1987).
  17. H.J.-P. Morand and R. Ohayon, Fluid-structure interactions. John Wiley & Sons, New York (1995).
  18. R. Rodríguez and J. Solomin, The order of convergence of eigenfrequencies in finite element approximations of fluid-structure interaction problems. Math. Comp. 65 (1996) 1463–1475. [CrossRef] [MathSciNet]
  19. P.A. Raviart and J.M. Thomas, A mixed finite element method for second order elliptic problems, in Mathematical Aspects of Finite Element Methods, Springer-Verlag, Berlin, Heidelberg, New York. Lect. Notes Math. 606 (1977) 292–315. [CrossRef]
  20. R. Stenberg and M. Suri, An hp error analysis of MITC plate elements. SIAM J. Numer. Anal. 34 (1997) 544–568. [CrossRef] [MathSciNet]
  21. J.M. Thomas, Sur l'analyse numérique des méthodes d'éléments finis hybrides et mixtes. Thèse de Doctorat d'Etat, Université Pierre et Marie Curie, Paris 6, France (1977).

Recommended for you