×

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

MSC:

74K20 Plates
74A20 Theory of constitutive functions in solid mechanics
74B20 Nonlinear elasticity

References:

[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 · doi:10.1007/BF00279992
[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 · doi:10.1016/0045-7825(83)90142-1
[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 · doi:10.1007/BF00247674
[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 · doi:10.1016/0045-7825(79)90089-6
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.