Une modification du modèle de Mindlin pour les plaques minces en flexion présentant un bord libre

Philippe Destuynder; Thierry Nevers

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1988)

  • Volume: 22, Issue: 2, page 217-242
  • ISSN: 0764-583X

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Destuynder, Philippe, and Nevers, Thierry. "Une modification du modèle de Mindlin pour les plaques minces en flexion présentant un bord libre." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 22.2 (1988): 217-242. <http://eudml.org/doc/193528>.

@article{Destuynder1988,
author = {Destuynder, Philippe, Nevers, Thierry},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {Modified Mindlin Model; thin plates; bending; mixed formulation; deflection; rotation; transverse shear stress; multiplier unknowns; surface Helmholtz theorem; existence; uniqueness; convergence; compatibility conditions; augmented Lagrangean; penalty parameter; edge effects},
language = {fre},
number = {2},
pages = {217-242},
publisher = {Dunod},
title = {Une modification du modèle de Mindlin pour les plaques minces en flexion présentant un bord libre},
url = {http://eudml.org/doc/193528},
volume = {22},
year = {1988},
}

TY - JOUR
AU - Destuynder, Philippe
AU - Nevers, Thierry
TI - Une modification du modèle de Mindlin pour les plaques minces en flexion présentant un bord libre
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1988
PB - Dunod
VL - 22
IS - 2
SP - 217
EP - 242
LA - fre
KW - Modified Mindlin Model; thin plates; bending; mixed formulation; deflection; rotation; transverse shear stress; multiplier unknowns; surface Helmholtz theorem; existence; uniqueness; convergence; compatibility conditions; augmented Lagrangean; penalty parameter; edge effects
UR - http://eudml.org/doc/193528
ER -

References

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  1. [1] I. RAJU, J. CREWS, Interlaminar stress singularities at the free edge in composites laminates. Comp. Struc. Vol. 14 n° 1, pp. 21-28 (1981). 
  2. [2] R. ZWIERS, T. TING, R. SPILKER, On the logarithmic singularity of free-edges stress in laminated composite under uniform extension. J. Appl. Mechan., Vol. 49, pp. 561-569 (1982). Zbl0522.73056
  3. [3] A. S. D. WANG, F. CROSSMAN, Some new results on edge effects in symmetric composite laminates. J. Comp. Mat., Vol. 11, pp. 92-106 (1977). 
  4. [4] J. L. DAVET, Ph. DESTUYNDER, Singularités logarithmiques dans les effets de bord d'une plaque en matériaux composites. J.M.T.A., Vol. 4, pp. 357-373 (1985). Zbl0564.73066MR800024
  5. [5] R. D. MINDLIN, Influence of rotary inertia and shear on flexural motion of isotropic elastic plates. J. Appl. Mech., Vol. 18, pp. 31-38 (1951). Zbl0044.40101
  6. [6] Ph. DESTUYNDER, Thèse université P. M. Curie, Paris (1980). 
  7. [7] R. TEMAM, Navier Stokes equations. North Holland Studies in Mathematics and its application. Vol. 2 (1979). Zbl0426.35003MR603444
  8. [8] F. BREZZI, K. J. BATHE, Article à paraître et communication personnelle de F. Brezzi au colloque d'Analyse Numérique, Puy-Saint-Vincent (1985). 
  9. [9] Ph. DESTUYNDER, J. C. NEDELEC, Approximation numérique du cisaillement transverse dans les plaques minces en flexion. Numér. Math., pp. 1-22, n° 876 (1985). Zbl0613.73066MR826470
  10. [10] G. DUVAUT, J. L. LIONS, Les inéquations en mécanique et en physique. Vol. 21. Travaux et recherches mathématiques. Dunod 1972. Zbl0298.73001MR464857
  11. [11] K. YOSIDA, Functional Analysis. 4th edition. Springer Verlag, Berlin (1975). 
  12. [12] P. G. CIARLET, The finite element method for elliptic problems. Stud. Math. Appl. Amsterdam North Holland (1978). Zbl0383.65058MR520174
  13. [13] D. BERTSEKAS, An penalty and multiplier method for constrained minimization. E.E.S. Departement working paper. Standford university. August (1973). Zbl0324.49029MR407692
  14. [14] V. GIRAULT, P. A. RAVIART, Finite Element Methods for Navier-Stokes Equations. Springer-Verlag, 1986. Zbl0585.65077MR851383

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