Justification de modèles de plaques non linéaires pour des lois de comportement générales. (Justification of nonlinear models of plates for general constitutive laws). (French) Zbl 0634.73048

(Author’s summary.) Two-dimensional models in nonlinear elastic plate theory have been justified by asymptotic expansion methods, under the assumption that the three-dimensional constitutive equation was linear with respect to the “full” strain tensor (St. Venant-Kirchhoff material). It is shown that the same models can actually be obtained for any nonlinear three-dimensional constitutive law.
Reviewer: V.Goincu


74K20 Plates
74A20 Theory of constitutive functions in solid mechanics
74B20 Nonlinear elasticity
Full Text: DOI EuDML


[1] J. M. BALL (1977), Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rational Mech. Anal. 63, 337-403. Zbl0368.73040 MR475169 · Zbl 0368.73040
[2] D. BLANCHARD, P. G. CIARLET (1983), A remark on the von Karman equations, Comput. Methods Appl. Mech. Engrg. 37, 79-92. Zbl0486.73051 MR699016 · Zbl 0486.73051
[3] P. G. CIARLET (1980), A justification of the von Karman equations, Arch. Rational Mech. Anal. 73, 349-389. Zbl0443.73034 MR569597 · Zbl 0443.73034
[4] P. G. CIARLET (1981), Two dimensional approximations of three-dimensional models in nonlinear plate theory, Proc. IUTAM, Symposium on Finite Elasticity, Martinus Nijhoff Pub. The Hague/ Boston/London. Zbl0515.73059 MR676663 · Zbl 0515.73059
[5] P. G. CIARLET (1984), Lectures on Three-dimensional Elasticity (Notes by S. Kesavan); Tata Institute Lectures on Mathematics, Springer-Verlag, Berlin. Zbl0542.73046 MR730027 · Zbl 0542.73046
[6] P. G. CIARLET, G. GEYMONAT (1982), Sur les lois de comportement en élasticité non linéaire compressible, C.R. Acad. Sci. Paris, Série A. Zbl0497.73017 MR695540 · Zbl 0497.73017
[7] P. G. CIARLET, P. DESTUYNDER (1979), A justification of a nonlinear model in plate theory, Comput. Methods Appl. Mech. Engrg. 17/18, 227-258. Zbl0405.73050 MR533827 · Zbl 0405.73050
[8] J. L. DAVET (1982), Détermination expérimentale des densités d’énergie en élasticité non linéaire, Rapport D.E.A., Laboratoire Analyse Numérique, Université Pierre et Marie Curie, Paris 6.
[9] J. L. DAVET (1985), Thèse Université Pierre et Marie Curie, Paris, à paraître.
[10] P. DESTUYNDER (1984), Théorie Asymptotique des Plaques Minces, Masson, Paris, à paraître.
[11] J. E. MARSDEN, T. J. R. HUGUES (1978), Topics in the mathematical foundations of elasticity, in Nonlinear Analysis and Mechanics: Heriot-Wyatt Symposium, Vol. 2, pp. 30-285, Pitman, Londres. Zbl0402.73003 MR576233 · Zbl 0402.73003
[12] T. VALENT (1979), Teoremi di esistenza e unicita in elastostatica finita, Rend. Sem. Mat. Univ. Padova 60, 165-181. Zbl0425.73011 · Zbl 0425.73011
[13] C. C. WANG, C. TRUESDELL (1973), Introduction to Rational Elasticity, Nordhoff, Groningen. Zbl0308.73001 MR468442 · Zbl 0308.73001
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