×

Homogénéisation de structures minces en béton armé. (French) Zbl 0592.73097

Starting from the three-dimensional elastic model of a reinforced concrete plate, the thickness of the plate is considered as a small parameter (with respect to other dimensions). A transformation is given to obtain a plate of uniform thickness. For the periodic structure with period \(\epsilon\) of the iron of the reinforced concrete, the authors use a local variable to describe the behaviour in one period. In the framework of homogenization theory, the problem is transformed to a multiscale problem with small parameter \(\epsilon\). Applications to various kinds of reinforcements are then discussed, from which practical rules are deduced.
Reviewer: M.Codegone

MSC:

74E30 Composite and mixture properties
74K20 Plates
74E05 Inhomogeneity in solid mechanics
PDF BibTeX XML Cite
Full Text: DOI EuDML

References:

[1] G. LACOMBRE, Cours de Génie Civil,Ecole Centrale, Paris 1983.
[2] P. G. CIARLET, Ph. DESTUYNDER: A justification of the two dimensional linear plate model, Journal de Mécanique 18 (1979), 315-344. Zbl0415.73072 MR533827 · Zbl 0415.73072
[3] Ph. DESTUYNDER, Sur une Justification Mathématique des Théories de Plaques et de Coques en Elasticité Linéaire,Thèse d’Etat, Université Pierre et Marie Curie, Paris, 1980.
[4] D. CAILLERIE, The effect of a thin inclusion of high rigidity in an elastic body,Math. Meths.Appl.Sci.2 (1980,251-270. Zbl0446.73014 MR581205 · Zbl 0446.73014
[5] Th. NEVERS, Rapport de recherche STCN, Marine Nationale, Paris (à paraître).
[6] C. THEODORY, Thèse de troisième cycle, Département MMN-EDF-DER, I.S.T.N., 1984.
[7] E. SANCHEZ-PALENCIA, Non Homogeneous Media and Vibration Theory, Lecture Notes in Physics 127, Springer-Verlag, Heidelberg, 1980. Zbl0432.70002 MR578345 · Zbl 0432.70002
[8] A. BENSOUSSAN, J.L. LIONS, G. PAPANICOLAOU, Asymptotic Analysis for Periodic Structures,North Holland, Amsterdam, 1978. Zbl0404.35001 MR503330 · Zbl 0404.35001
[9] G. DUVAUT, Comportement macroscopique d’une plaque perforée périodiquement,dans Singular Perturbations and Boundary Layer Theory,pp.131-145,Lecture Notes in Mathematics 554, Springert-Verlag, Heidelberg, 1977. Zbl0363.35001 MR462086 · Zbl 0363.35001
[10] K. WASHIZU, Variational Methods in Elasticity and Plasticity,Pergamon, Oxford, 1975. Zbl0339.73035 MR391680 · Zbl 0339.73035
[11] R. VALIDLa Mécanique des Milieux Continus et le Calcul des Structures, Eyrolles,Paris, 1977. Zbl0454.73003 · Zbl 0454.73003
[12] S. TIMOSHENKO, W. WOINOWSKY-KRIEGER, Theory of Plates and shells.McGraw-Hill, 1959. · Zbl 0114.40801
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.