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Derivation of a Hierarchy of Nonlinear Two-dimensional Models For Heterogeneous Plates

type de publication      article dans une revue internationale avec comité de lecture
date de publication 2009
auteur(s) Pruchnicki Erick
journal (abréviation) Mathematics and Mechanics of Solids (Math Mech Solid)
volume (numéro) 16 (1)
pages 77 – 108
résumé 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.
mots clés Asymptotic analysis, plates, nonlinear elasticity, minimization problem
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