On the Asymptotic Analys of a Non-Symmetric Bar

Abderrazzak Majd

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 34, Issue: 5, page 1069-1085
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Majd, Abderrazzak. "On the Asymptotic Analys of a Non-Symmetric Bar." ESAIM: Mathematical Modelling and Numerical Analysis 34.5 (2010): 1069-1085. <http://eudml.org/doc/197435>.

@article{Majd2010,
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. },
author = {Majd, Abderrazzak},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Elastic bar homogenization.; error estimate; three-dimensional elasticity; non-symmetric heterogeneous rod; asymptotic expansion; coercitivity; homogenized equation; truncated series},
language = {eng},
month = {3},
number = {5},
pages = {1069-1085},
publisher = {EDP Sciences},
title = {On the Asymptotic Analys of a Non-Symmetric Bar},
url = {http://eudml.org/doc/197435},
volume = {34},
year = {2010},
}

TY - JOUR
AU - Majd, Abderrazzak
TI - On the Asymptotic Analys of a Non-Symmetric Bar
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 34
IS - 5
SP - 1069
EP - 1085
AB - 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.
LA - eng
KW - Elastic bar homogenization.; error estimate; three-dimensional elasticity; non-symmetric heterogeneous rod; asymptotic expansion; coercitivity; homogenized equation; truncated series
UR - http://eudml.org/doc/197435
ER -

References

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  1. N.S. Bakhvalov and G.P. Panasenko, Homogenization: Averaging Processes in Periodic Media. Nauka, Moscow (1984) (Russian). Kluwer, Dordrecht, Boston and London (1989) (English).  
  2. G. Fichera, Existence theorems in elasticity. Handbuch der Physic, Band 6a/2, Springer-Verlag, Berlin-Heidelberg-New York (1972).  
  3. G.A. Iosifían, O.A. Oleinik and A.S. Shamaev, Mathematical Problems in elasticity and homogenization. Studies Math. Appl.26, Elsevier, Amsterdam (1992).  
  4. S.M. Kozlov, O.A. Oleinik and V.V. Zhikov, Homogenization of Partial Differential Operators and Integral Functionals. Springer-Verlag, Berlin (1992).  
  5. F. Murat and A. Sili, Comportement asymptotique des solutions du système de l'élasticité linéarisée anisotrope hétérogène dans des cylindres minces. C. R. Acad. Sci. Ser. I328 (1999) 179-184.  
  6. 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.  Zbl0917.35029
  7. G.P. Panasenko, Asymptotics of higher orders of solutions of equations with rapidly oscillating coefficients. U.S.S.R Doklady6 (1978) 1293-1296.  
  8. G.P. Panasenko, Asymptotic analysis of bar systems. I. Russian J. Math. Phys.2 (1994) 325-352.  Zbl0924.73020
  9. G.P. Panasenko, Asymptotic analysis of bar systems. II. Russian J. Math. Phys.4 (1996) 87-116.  Zbl0924.73021
  10. 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.  Zbl0816.73025
  11. J. Sanchez-Hubert and E. Sanchez-Palencia, Introduction aux méthodes asymptotiques et à l'homogénisation. Masson, Paris, Milan, Barcelone, Bonne (1992).  
  12. J. Sanchez-Hubert and E. Sanchez-Palencia, Statics of curved rods on account of torsion and flexion. Eur. J. Mech. A/Solids18 (1999) 365-390.  Zbl0938.74040

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