Antonio Gaudiello

Junction of a periodic family of elastic rods with a 3d plate. Part I

In this second paper, we consider again a set of elastic rods periodically distributed over an elastic plate whose thickness tends here to 0. This work is then devoted to describe the homogenization process for the junction of the rods and a thin plate. We use a technique based on two decompositions of the displacement field in each rod and in the plate. We obtain a priori estimates on each term of the two decompositions which permit to exhibit a few critical cases that distinguish the different possible limit behaviors. Then, we completely investigate one of these critical case which leads to a coupled bending-bending model for the rods and the 2d plate. Résumé Dans ce deuxième article, nous reprenons un ensemble de poutres élastiques périodiquement distribuées sur une plaque élastique dont l’épaisseur tend maintenant vers 0. Il s’agit donc de décrire des modèles d’homogénéisation pour la jonction de poutres et d’une plaque mince. Nous utilisons une technique de décomposition du champ de déplacement à la fois dans chaque poutre et dans la plaque. On obtient des estimations a priori sur chacun des termes de ces décompositions qui mettent en particulier en évidence les cas critiques qui séparent les différents modèles limites possibles. Ensuite, nous analysons en détail un de ces cas critiques pour lequel on obtient un modèle de couplage flexion-flexion entre les poutres et la plaque 2d.

Asymptotic Approximation of the Solution of the Laplace Equation in a Domain with Highly Oscillating Boundary

We study the asymptotic behavior of the solution of the Laplace equation in a domain, a part of whose boundary is highly oscillating. The motivation comes from the study of a longitudinal flow in an infinite horizontal domain bounded at the bottom by a wall and at the top by a rugose wall. The latter is a plane covered with periodic asperities whose size depends on a small parameter,

BOUNDARY HOMOGENIZATION AND REDUCTION OF DIMENSION IN A KIRCHHOFF-LOVE PLATE

\varepsilon >0.

Optimal control for a parabolic problem in a domain with highly oscillating boundary

The assumption of sharp asperities is made; that is, the height of the asperities is fixed. Using a boundary layer corrector, we derive and analyze a nonoscillating approximation of the solution at order

On the junction of elastic plates and beams

{\cal O}(\varepsilon^{3/2})

Asymptotic analysis of the eigenvalues of an elliptic problem in an anisotropic thin multidomain

for the H1 -norm.

HOMOGENIZATION OF HIGHLY OSCILLATING BOUNDARIES WITH STRONGLY CONTRASTING DIFFUSIVITY

We investigate the asymptotic behavior, as

Asymptotic analysis and domain decomposition for a biharmonic problem in a thin multi-structure

\varepsilon

Ferromagnetic thin multi-structures

tends to

HOMOGENIZATION OF AN ELLIPTIC SECOND-ORDER PROBLEM WITH L log L DATA IN A DOMAIN WITH OSCILLATING BOUNDARY

0^+