ESAIM: Mathematical Modelling and Numerical Analysis

An asymptotically optimal model for isotropic heterogeneous linearly elastic plates

a1 Dipartimento di Meccanica Strutturale, Università di Pavia, Via Ferrata 1, 27100 Pavia, Italy. auricchio@unipv.it.

a2 Dipartimento di Matematica, Università di Pavia, Via Ferrata 1, 27100 Pavia, Italy. lovadina@dimat.unipv.it.

a3 Departamento de Matemática Aplicada e Computacional, Laboratório Nacional de Computação Científica, Av. Getúlio Vargas 333, Petrópolis - RJ, Brazil. alm@lncc.br.

Abstract

In this paper, we derive and analyze a Reissner-Mindlin-like model for isotropic heterogeneous linearly elastic plates. The modeling procedure is based on a Hellinger-Reissner principle, which we modify to derive consistent models. Due to the material heterogeneity, the classical polynomial profiles for the plate shear stress are replaced by more sophisticated choices, that are asymptotically correct. In the homogeneous case we recover a Reissner-Mindlin model with 5/6 as shear correction factor. Asymptotic expansions are used to estimate the modeling error. We remark that our derivation is not based on asymptotic arguments only. Thus, the model obtained is more sophisticated (and accurate) than simply taking the asymptotic limit of the three dimensional problem. Moreover, we do not assume periodicity of the heterogeneities.

(Revised August 31 2004)

(Online publication October 15 2004)

Key Words:

• Reissner;
• Mindlin;
• plate;
• heterogeneous plates;
• asymptotic analysis.

Mathematics Subject Classification:

• 35B40;
• 74K20
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