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On the Asymptotic Analys of a Non-Symmetric Bar

Published online by Cambridge University Press:  15 April 2002

Abderrazzak Majd*
Affiliation:
Équipe d'analyse numérique Lyon - Saint-Etienne, UMR 5585, Université Jean Monnet, 23 rue P. Michelon, 42023 Saint-Etienne Cedex 02, France. (majd@iris.univ-lyon1.fr)
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Abstract

We study the 3-D elasticity problem in the case of a non-symmetric heterogeneous rod. The asymptotic expansion of the solution is constructed. The coercitivity of the homogenized equation is proved. Estimates are derived for the difference between the truncated series and the exact solution.

Type
Research Article
Copyright
© EDP Sciences, SMAI, 2000

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References

N.S. Bakhvalov and G.P. Panasenko, Homogenization: Averaging Processes in Periodic Media. Nauka, Moscow (1984) (Russian). Kluwer, Dordrecht, Boston and London (1989) (English).
G. Fichera, Existence theorems in elasticity. Handbuch der Physic, Band 6a/2, Springer-Verlag, Berlin-Heidelberg-New York (1972).
G.A. Iosifían, O.A. Oleinik and A.S. Shamaev, Mathematical Problems in elasticity and homogenization. Studies Math. Appl. 26, Elsevier, Amsterdam (1992).
S.M. Kozlov, O.A. Oleinik and V.V. Zhikov, Homogenization of Partial Differential Operators and Integral Functionals. Springer-Verlag, Berlin (1992).
Murat, F. and Sili, A., Comportement asymptotique des solutions du système de l'élasticité linéarisée anisotrope hétérogène dans des cylindres minces. C. R. Acad. Sci. Ser. I 328 (1999) 179-184.
S.A. Nazarov, Justification of asymptotic theory of thin rods. Integral and pointwise estimates, in Problems of Mathematical Physics and Theory of Functions, St-Petersbourg University Publishers (1997) 101-152.
Panasenko, G.P., Asymptotics of higher orders of solutions of equations with rapidly oscillating coefficients. U.S.S.R Doklady 6 (1978) 1293-1296.
Panasenko, G.P., Asymptotic analysis of bar systems. I. Russian J. Math. Phys. 2 (1994) 325-352.
Panasenko, G.P., Asymptotic analysis of bar systems. II. Russian J. Math. Phys. 4 (1996) 87-116.
G.P. Panasenko and J. Saint Jean Paulin, An asymptotic analysis of junctions of non-homogeneous elastic rods: boundary layers and asymptotics expansions, touch junctions. Moscow, Metz, Comp. Math. Phys. 33 (1993) 1483-1508.
J. Sanchez-Hubert and E. Sanchez-Palencia, Introduction aux méthodes asymptotiques et à l'homogénisation. Masson, Paris, Milan, Barcelone, Bonne (1992).
Sanchez-Hubert, J. and Sanchez-Palencia, E., Statics of curved rods on account of torsion and flexion. Eur. J. Mech. A/Solids 18 (1999) 365-390. CrossRef