Free access
Issue
ESAIM: M2AN
Volume 40, Number 2, March-April 2006
Page(s) 269 - 294
DOI http://dx.doi.org/10.1051/m2an:2006014
Published online 21 June 2006
  1. S.M. Alessandrini, D.N. Arnold, R.S. Falk and A.L. Madureira, Derivation and justification of plate models by variational methods, Centre de Recherches Math., CRM Proc. Lecture Notes (1999).
  2. D.N. Arnold and R.S. Falk, Asymptotic analysis of the boundary layer for the Reissner-Mindlin plate model. SIAM J. Math. Anal. 27 (1996) 486–514. [CrossRef] [MathSciNet]
  3. D.N. Arnold and A. Mardureira, Asymptotic estimates of hierarchical modeling. Math. Mod. Meth. Appl. S. 13 (2003).
  4. D.N. Arnold, A. Mardureira and S. Zhang, On the range of applicability of the Reissner–Mindlin and Kirchhoff–Love plate bending models, J. Elasticity 67 (2002) 171–185.
  5. J. Bergh and J. Lofstrom, Interpolation space: An introduction, Springer-Verlag (1976).
  6. C. Chen, Asymptotic convergence rates for the Kirchhoff plate model, Ph.D. Thesis, Pennsylvania State University (1995).
  7. P.G. Ciarlet, Mathematical elasticity, Vol II: Theory of plates. North-Holland (1997).
  8. M. Dauge, I. Djurdjevic and A. Rössle, Full Asymptotic expansions for thin elastic free plates, C.R. Acad. Sci. Paris Sér. I. 326 (1998) 1243–1248.
  9. M. Dauge, I. Gruais and A. Rössle, The influence of lateral boundary conditions on the asymptotics in thin elastic plates. SIAM J. Math. Anal. 31 (1999) 305–345. [CrossRef] [MathSciNet]
  10. M. Dauge, E. Faou and Z. Yosibash, Plates and shells: Asymptotic expansions and hierarchical models, in Encyclopedia of computational mechanics, E. Stein, R. de Borst, T.J.R. Hughes Eds., John Wiley & Sons, Ltd. (2004).
  11. K.O. Friedrichs and R.F. Dressler, A boundary-layer theory for elastic plates. Comm. Pure Appl. Math. XIV (1961) 1–33.
  12. T.J.R. Hughes, The finite element method: Linear static and dynamic finite element analysis. Prentice-Hall, Englewood Cliffs (1987).
  13. W.T. Koiter, On the foundations of linear theory of thin elastic shells. Proc. Kon. Ned. Akad. Wetensch. B73 (1970) 169–195.
  14. A.E.H. Love, A treatise on the mathematical theory of elasticity. Cambridge University Press (1934).
  15. D. Morgenstern, Herleitung der Plattentheorie aus der dreidimensionalen Elastizitatstheorie. Arch. Rational Mech. Anal. 4 (1959) 145–152. [CrossRef] [MathSciNet]
  16. P.M. Naghdi, The theory of shells and plates, in Handbuch der Physik, Springer-Verlag, Berlin, VIa/2 (1972) 425–640.
  17. W. Prager and J.L. Synge, Approximations in elasticity based on the concept of function space. Q. J. Math. 5 (1947) 241–269.
  18. E. Reissner, Reflections on the theory of elastic plates. Appl. Mech. Rev. 38 (1985) 1453–1464. [CrossRef]
  19. A. Rössle, M. Bischoff, W. Wendland and E. Ramm, On the mathematical foundation of the (1,1,2)-plate model. Int. J. Solids Structures 36 (1999) 2143–2168. [CrossRef]
  20. J. Sanchez-Hubert and E. Sanchez-Palencia, Coques élastiques minces: Propriétés asymptotiques, Recherches en mathématiques appliquées, Masson, Paris (1997).
  21. B. Szabó, I. Babuska, Finite Element analysis. Wiley, New York (1991).
  22. F.Y.M. Wan, Stress boundary conditions for plate bending. Int. J. Solids Structures 40 (2003) 4107–4123. [CrossRef]
  23. S. Zhang, Equivalence estimates for a class of singular perturbation problems. C.R. Acad. Sci. Paris, Ser. I 342 (2006) 285–288.

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