Analise Assimptotica de Modelos Hierarquicos em Dominios Finos

Abstract: In this talk we propose a way to analyze certain classes of dimension reduction models for elliptic problems in thin domains.  We consider Poisson equations in thin plates,  and develop asymptotic expansions for the exact and model solutions,  having the thickness as small parameter. The modeling error is then estimated by comparing the respective expansions, and the upper bounds obtained make clear the influence of the order of the model and the thickness on the convergence rates. The techniques developed here allows for estimates in several norms and semi-norms, and also interior estimates (which disregards boundary layers).  Finally, we present several low order dimension reduction models  for a clamped linearly elastic plates,  the simplest ones being variants of the Reissner-Mindlin models.  Unlike many of the previous works on the subject, we impose no restrictive assumptions on the loads and tractions.