Modeling and justification of an eigenvalue problem for a plate inserted in a three-dimensional support

V. Lods

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1996)

  • Volume: 30, Issue: 4, page 413-444
  • ISSN: 0764-583X

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Lods, V.. "Modeling and justification of an eigenvalue problem for a plate inserted in a three-dimensional support." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 30.4 (1996): 413-444. <http://eudml.org/doc/193810>.

@article{Lods1996,
author = {Lods, V.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {convergence of eigenvalues; limit eigenvalue problems; three-dimensional linearized elasticity; Lamé constants},
language = {eng},
number = {4},
pages = {413-444},
publisher = {Dunod},
title = {Modeling and justification of an eigenvalue problem for a plate inserted in a three-dimensional support},
url = {http://eudml.org/doc/193810},
volume = {30},
year = {1996},
}

TY - JOUR
AU - Lods, V.
TI - Modeling and justification of an eigenvalue problem for a plate inserted in a three-dimensional support
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1996
PB - Dunod
VL - 30
IS - 4
SP - 413
EP - 444
LA - eng
KW - convergence of eigenvalues; limit eigenvalue problems; three-dimensional linearized elasticity; Lamé constants
UR - http://eudml.org/doc/193810
ER -

References

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  1. [1] F. BOURQUIN and P. G. CIARLET, 1989, Modeling and Justification of Eigenvalue Problems for Jonctions between Elastic Structures, J. Funct. Anal., 87, pp. 392-427. Zbl0699.73010MR1026860
  2. [2] P. G. CIARLET, 1990, Plates and Junctions in Elastic Multi Structures : An asymptotic Analysis, Masson, Paris and Springer-Verlag, Heidelberg. Zbl0706.73046MR1071376
  3. [3] P. G. CIARLET and P. DESTUYNDER, 1979, A justification of the two-dimensional plate model, J. Mécanique, 18, pp. 315-344. Zbl0415.73072MR533827
  4. [4] P. G. CIARLET and S. KESAVAN, 1981, Modélisation de la jonction entre un corps élastique tri-dimensionnel et une plaque, C. R.Acad. Sci. Paris, Série I 305,pp 55-58. Zbl0632.73015MR902275
  5. [5] P. G. CIARLET and H. LE DRET, 1989, Justification of boundary conditions of a clamped plate by an asymptotic analysis, Asymptotic Analysis, 2, pp. 257-277. Zbl0699.73011MR1030351
  6. [6] P. G. CIARLET, H. LE DRET and R. NZENGWA, 1987, Two dimensional approximations of three-dimensional eigenvalue problems in plate theory, Comp. Methods Appl. Mech. Engrg., 26, pp. 149-172. Zbl0489.73057MR626720
  7. [7] P. G. CIARLET, H. LE DRET and R. NZENGWA, 1989, Junctions between three-dimensional and two-dimensional liearly elastic structures, J. Math. Pures Appl.,68, pp. 261-295. Zbl0661.73013MR1025905
  8. [8] P. G. CIARLET and J. C. PAUMIER, 1986, A justification of the Marguerre von Karman equations, Comput, Mech, I, pp. 177-202. Zbl0633.73069
  9. [9] R. COURANT and D. HILBERT, 1953, Methods of Mathematical Physics, Vol. 1, Interscience, New York. Zbl0051.28802MR65391
  10. [10] P. DESTUYNDER, 1980, Sur une Justification des Modèles de Plaques et de Coques par les Méthodes Asymptotiques, Thèse d'état, Université Pierre et Marie Curie, Paris (1980). 
  11. [11] P. DESTUYNDER, 1986, Une Théorie Asymptotique des Plaques Minces en Élasticité Linéarisée, Masson, Paris. Zbl0627.73064MR830660
  12. [12] G. DUVAUT and J. L. LIONS, 1972, Les Inéquations en Mécanique et en Physique, Dunod, Paris. Zbl0298.73001MR464857
  13. [13] W. T. KOITER, 1970, On the foundation of the linear theory of thin elastic shells, Proc. Kon. Nederl. Akad Wetensch., B 73, pp. 169-195. Zbl0213.27002MR280050
  14. [14] J. NECAS, 1967, Les méthodes Directes en Théorie des Équations Elliptiques, Masson, Paris. MR227584
  15. [15] A. RAOULT, 1990, Asymptotic modeling of the elastodynamics of a multi-structure, Asymptotic Analysis, 6, 73-108. Zbl0777.73033MR1188078

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