Derivation of a Hierarchy of Nonlinear Two-dimensional Models For Heterogeneous Plates
Erick Pruchnicki · Mathematics and Mechanics of Solids · 2009
This paper is concerned with the asymptotic analysis of plates with periodically rapidly varying heterogeneities. The formal asymptotic procedure is performed when both the periods of changes of the material properties and the thickness of the plate are of the same orders of magnitude. Our approach is based on a sequence of recursive minimization problems. We consider a plate made of Ciarlet—Geymonat type materials. Depending on the order of magnitude of the applied loads, we obtain a nonlinear membrane model and a nonlinear membrane inextensional bending model as announced by Pruchnicki.