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 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.
Mots clés : Reissner, Mindlin, plate, heterogeneous plates, asymptotic analysis
@article{M2AN_2004__38_5_877_0,
author = {Auricchio, Ferdinando and Lovadina, Carlo and Madureira, Alexandre L.},
title = {An asymptotically optimal model for isotropic heterogeneous linearly elastic plates},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {877--897},
publisher = {EDP-Sciences},
volume = {38},
number = {5},
year = {2004},
doi = {10.1051/m2an:2004042},
mrnumber = {2104433},
zbl = {1130.74403},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an:2004042/}
}
TY - JOUR AU - Auricchio, Ferdinando AU - Lovadina, Carlo AU - Madureira, Alexandre L. TI - An asymptotically optimal model for isotropic heterogeneous linearly elastic plates JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2004 SP - 877 EP - 897 VL - 38 IS - 5 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2004042/ DO - 10.1051/m2an:2004042 LA - en ID - M2AN_2004__38_5_877_0 ER -
%0 Journal Article %A Auricchio, Ferdinando %A Lovadina, Carlo %A Madureira, Alexandre L. %T An asymptotically optimal model for isotropic heterogeneous linearly elastic plates %J ESAIM: Modélisation mathématique et analyse numérique %D 2004 %P 877-897 %V 38 %N 5 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2004042/ %R 10.1051/m2an:2004042 %G en %F M2AN_2004__38_5_877_0
Auricchio, Ferdinando; Lovadina, Carlo; Madureira, Alexandre L. An asymptotically optimal model for isotropic heterogeneous linearly elastic plates. ESAIM: Modélisation mathématique et analyse numérique, Tome 38 (2004) no. 5, pp. 877-897. doi : 10.1051/m2an:2004042. http://www.numdam.org/articles/10.1051/m2an:2004042/
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