3D-2D Asymptotic Analysis for Inhomogeneous Thin Films
Andrea Braides, Irene Fonseca, Gilles A. Francfort · Indiana University Mathematics Journal · 2000
A dimension reduction analysis is undertaken using Γ -convergence techniques within a relaxation theory for 3D nonlinear elastic thin domains of the formwhere ω is a bounded domain of R 2 and f ε is an ε-dependent profile.An abstract representation of the effective 2D energy is obtained, and specific characterizations are found for nonhomogeneous plate models, periodic profiles, and within the context of optimal design for thin films.CONTENTS 1. Introduction 1367 2. A compactness result in a general setting 1371 3. First application -Nonhomogeneous plate models 1381 4. Second application -The periodic case 1388 5. Third application -Optimal design of a thin film 1392 6.