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Homogenization of the anisotropic heterogeneous linearized elasticity system in thin reticulated structures

Published online by Cambridge University Press:  12 July 2007

J. Casado-Díaz  and
M. Luna-Laynez
J. Casado-Díaz
Affiliation:
Dpto. de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Fac. de Matemáticas, C/Tarfia s/n, 41012 Sevilla, Spain ([email protected])
M. Luna-Laynez
Affiliation:
Dpto. de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Fac. de Matemáticas, C/Tarfia s/n, 41012 Sevilla, Spain ([email protected])
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Abstract

The aim of this paper is to study the asymptotic behaviour of the solutions of the linearized elasticity system, posed on thin reticulated structures involving several small parameters. We show that this behaviour depends on the relative size of the parameters. In each case, we obtain a limit system where the microstructure and macrostructure appear simultaneously. From it, we get a suitable approximation in L2 of the displacements and the linearized strain tensor.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 134 , Issue 6 , December 2004 , pp. 1041 - 1083
Copyright
Copyright © Royal Society of Edinburgh 2004

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