Existence of a solution for a nonlinearly elastic plane membrane “under tension”

Daniel Coutand

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1999)

  • Volume: 33, Issue: 5, page 1019-1032
  • ISSN: 0764-583X

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Coutand, Daniel. "Existence of a solution for a nonlinearly elastic plane membrane “under tension”." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 33.5 (1999): 1019-1032. <http://eudml.org/doc/193952>.

@article{Coutand1999,
author = {Coutand, Daniel},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {coercive non-lower semi-continuous energy functional; existence; nonlinear membrane-plate equations},
language = {eng},
number = {5},
pages = {1019-1032},
publisher = {Dunod},
title = {Existence of a solution for a nonlinearly elastic plane membrane “under tension”},
url = {http://eudml.org/doc/193952},
volume = {33},
year = {1999},
}

TY - JOUR
AU - Coutand, Daniel
TI - Existence of a solution for a nonlinearly elastic plane membrane “under tension”
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1999
PB - Dunod
VL - 33
IS - 5
SP - 1019
EP - 1032
LA - eng
KW - coercive non-lower semi-continuous energy functional; existence; nonlinear membrane-plate equations
UR - http://eudml.org/doc/193952
ER -

References

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  2. [2] P.G. Ciarlet, Mathematical Elasticity, I, Three-Dimensional Elasticity. North Holland, Amsterdam (1988). Zbl0953.74004MR936420
  3. [3] P.G. Ciarlet, Mathematical Elasticity, II, Theory of Plates. North Holland, Amsterdam (1997). Zbl0953.74004MR1477663
  4. [4] P.G. Ciarlet and P. Destuynder, A justification of a nonlinear model in plate theory. Comput. Methods Appl. Mech. Engrg. 17/18 (1979) 227-258. Zbl0405.73050MR533827
  5. [5] D. Coutand, Existence d'un minimiseur pour le modèle "proprement invariant" de plaque "en flexion" non linéairement élastique. C.R. Acad. Sci. Paris Sér. I 324 (1997) 245-248. Zbl0873.73078MR1438393
  6. [6] D. Coutand, Théorèmes d'existence pour un modèle "proprement invariant" de plaque membranaire non linéairement élastique. C.R. Acad. Sci. Paris Sér. I 324 (1997) 1181-1184. Zbl0882.73035MR1451944
  7. [7] D. Coutand, Existence of a solution for a nonlinearly elastic plane membrane subject to plane forces. J. Elasticity 53 (1999) 147-159. Zbl1083.74530MR1705408
  8. [8] J. Diestel and J.J.Jr. Uhl, Vector Measures. Math. Surveys, AMS 15 (1977). Zbl0369.46039MR453964
  9. [9] D. Fox, A. Raoult and J.C. Simo, A justification of nonlinear properly invariant plate theories. Arch. Rational Mech. Anal 124 (1993) 157-199. Zbl0789.73039MR1237909
  10. [10] G. Geymonat, Sui problemi ai limiti per i sistemi lineari ellitici. Ann. Mat Pura Appl. 69 (1965) 207-284 Zbl0152.11102MR196262
  11. [11] A.E. Green and W. Zerna, Theoretical Elasticity. Oxford University Press (1968). Zbl0155.51801MR245245
  12. [12] H. Le Dret and A. Raoult, The nonlinear membrane model as variational limit of nonlinear three dimensional elasticity. J. Math. Pures Appl. 74 (1995) 549-578. Zbl0847.73025MR1365259
  13. [13] J. Nečas, Les Méthodes Directes en Théorie des Equations Elliptiques. Masson, Paris (1967). MR227584

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