An asymptotically optimal model for isotropic heterogeneous linearly elastic plates
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 38 (2004) no. 5, p. 877-897

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.

DOI : https://doi.org/10.1051/m2an:2004042
Classification:  35B40,  74K20
Keywords: Reissner, Mindlin, plate, heterogeneous plates, asymptotic analysis
@article{M2AN_2004__38_5_877_0,
title = {An asymptotically optimal model for isotropic heterogeneous linearly elastic plates},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {38},
number = {5},
year = {2004},
pages = {877-897},
doi = {10.1051/m2an:2004042},
zbl = {1130.74403},
mrnumber = {2104433},
language = {en},
url = {http://www.numdam.org/item/M2AN_2004__38_5_877_0}
}
Auricchio, Ferdinando; Lovadina, Carlo; Madureira, Alexandre L. An asymptotically optimal model for isotropic heterogeneous linearly elastic plates. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 38 (2004) no. 5, pp. 877-897. doi : 10.1051/m2an:2004042. http://www.numdam.org/item/M2AN_2004__38_5_877_0/

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