Existence and convergence of the expansion in the asymptotic theory of elastic thin plates

J.-C. Paumier

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1991)

  • Volume: 25, Issue: 3, page 371-391
  • ISSN: 0764-583X

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Paumier, J.-C.. "Existence and convergence of the expansion in the asymptotic theory of elastic thin plates." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 25.3 (1991): 371-391. <http://eudml.org/doc/193632>.

@article{Paumier1991,
author = {Paumier, J.-C.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {linearly elastic plate; periodicity condition; trigonometric polynomials; Sobolev space},
language = {eng},
number = {3},
pages = {371-391},
publisher = {Dunod},
title = {Existence and convergence of the expansion in the asymptotic theory of elastic thin plates},
url = {http://eudml.org/doc/193632},
volume = {25},
year = {1991},
}

TY - JOUR
AU - Paumier, J.-C.
TI - Existence and convergence of the expansion in the asymptotic theory of elastic thin plates
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1991
PB - Dunod
VL - 25
IS - 3
SP - 371
EP - 391
LA - eng
KW - linearly elastic plate; periodicity condition; trigonometric polynomials; Sobolev space
UR - http://eudml.org/doc/193632
ER -

References

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  1. [1] F. BREZZI (1974) : On the existence uniqueness and approximation of saddle point problems arising from Lagrangian multipliers, R.A.I.R.O., R2, 129-151. Zbl0338.90047MR365287
  2. [2] P. G. CIARLET (1980) : A justification of the von Kármán equations. Arch. Rat. Mech. Anal. 73, 349-389. Zbl0443.73034MR569597
  3. [3] P. G. CIARLET, P. DESTUYNDER (1979) : A justification of the two-dimensional linear plate model. J. Mécanique 18, 315-344. Zbl0415.73072MR533827
  4. [4] P. G. CIARLET, S. KESAVAN (1980) : Two dimensional approximations of three dimensional eigenvalues in plate theory. Comp. Methods Appl. Mech. Eng. 26, 149-172. Zbl0489.73057MR626720
  5. [5] P. G. CIARLET, J.-C. PAUMIER (1986) : A justification of the Marguerre - von Kármán equations. Comp. mech. 1, 177-202. Zbl0633.73069
  6. [6] P. DESTUYNDER (1980) Sur une justification des modèles de plaques et de coques par les méthodes asymptotiques. Thesis, Université P. et M. Curie, Paris. 
  7. [7] P. DESTUYNDER (1981) Comparaison entre les modèles tridimensionnels et bidimensionnels de plaques en élasticité. RAIRO An. Num. 15, 331-369. Zbl0479.73042MR642497
  8. [8] J.-L. LIONS (1973) Perturbation singulière dans les problèmes aux limites et en contrôle optimal. Lecture notes in maths 323, Berlin, Heidelberg, New-York : Springer. Zbl0268.49001MR600331
  9. [9] J. C. PAUMIER (1985) Analyse de certains problèmes non linéaires, modèles de plaques et de coques. Thesis, Université P. et M. Curie 
  10. [10] J. C. PAUMIER (1990) Existence Theorems for Non Linear Elastic Plates with Periodic Boundary Conditions, Journal of Elasticity, 23, 233-252. Zbl0738.73038MR1074678
  11. [11] A. RAOULT (1985) Constructiond'un modèle d'évolution de plaques, Annali di Matematica Pura et Applicata CXXXIX, 361-400. Zbl0596.73033MR798182
  12. [12] K. O. FRIEDRICHS, R. F. DRESSLER (1961) A boundary-layer theory for elastic plates, Comm. Pure Appl. Maths. 14, 1-33. Zbl0096.40001MR122117
  13. [13] A. L. GOLDENVEIZERDerivation of an approximate theory of bending of a plate by the method of asymptotic integration of the equations of the theory of elasticity, Prikl. Mat. Mech. 26, 668-686 (English translation J. Appl. Math. Mech. (1964), 1000-1025). Zbl0118.41603MR170523

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