Homogenization of the linearized system of elasticity in anisotropic heterogeneous thin cylinders
Ali Sili · Mathematical Methods in the Applied Sciences · 2002
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.