Asymptotic Analysis - Volume 56, issue 1

Authors: Blanchard, Dominique | Griso, Georges

Article Type: Research Article

Abstract: This paper is devoted to investigate a few microscopic effects in the homogenization process of the junction of a periodic family of rods with a thin plate in elasticity. We focus on the case where the thickness of the plate tends to zero faster than the periodicity. As a consequence of the studied microscopic effects, the elastic coefficients of the membrane and bending limit problems for the plate are modified. Moreover, we observe a torsion in the homogenized “continuum” of rods which depends on the curl of the membrane displacement of the plate.

Keywords: linear elasticity, rods, plates, rough boundary, homogenization

Citation: Asymptotic Analysis, vol. 56, no. 1, pp. 1-36, 2008

Authors: Mercaldo, Anna | Mossino, Jacqueline | Prignet, Alain

Article Type: Research Article

Abstract: We study the asymptotic behaviour, as ε goes to zero, of the entropy solution uε to a class of nonlinear elliptic problems whose prototype is −div((δε )p−1 |∇uε |p−2 ∇uε )=fε in Ωε , uε =0 on ∂Ωε , where 1<p<N, $\varOmega^{\varepsilon}=\overline{\varOmega}\cup\Sigma^{\varepsilon}$ , Ω⊂RN is a bounded domain of class C1,1 , surrounded along its boundary by a layer Σε of small thickness ε, δε =1 in Ω, δε =ε in Σε , and fε belongs to L1 (Ωε ). The solutions uε also satisfies natural transmission conditions on ∂Ω.

Citation: Asymptotic Analysis, vol. 56, no. 1, pp. 37-59, 2008