Homogenization of the linearized system of elasticity in anisotropic heterogeneous thin cylinders

✍ Scribed by Ali Sili

• Publisher: John Wiley and Sons
• Year: 2002
• Tongue: English
• Weight: 213 KB
• Volume: 25
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/mma.264

✦ Synopsis

Abstract

This paper is the second of the two announced in our Note (Sili A, [16]). It generalizes to the linearized system of elasticity the results of our previous work (Sili, 2000 [15]) on the heat equation. We study the asymptotic analysis, as ϵ tends to zero, of the solution u^ϵ^ of the linearized system of elasticity posed on a composite elastic cylindrical domain Ω^ϵ^ with radius ϵ and height L. The heterogeneities of the material are assumed to be periodic with a period ϵ along the cylinder axis and with a period ϵ^2^ along the sections of the cylinder. It is shown that the limit problem is a system in which appear two entities: the first one (u, v, w) corresponds to the reduction of dimension 3d–1d while the second one (û, v̂, ŵ) takes into account the homogenization process. Moreover, a corrector result is given. Copyright © 2002 John Wiley & Sons, Ltd.