An asymptotically optimal model for isotropic heterogeneous linearly elastic plates

Ferdinando Auricchio; Carlo Lovadina; Alexandre L. Madureira

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 38, Issue: 5, page 877-897
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Auricchio, Ferdinando, Lovadina, Carlo, and Madureira, Alexandre L.. "An asymptotically optimal model for isotropic heterogeneous linearly elastic plates." ESAIM: Mathematical Modelling and Numerical Analysis 38.5 (2010): 877-897. <http://eudml.org/doc/194244>.

@article{Auricchio2010,
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. },
author = {Auricchio, Ferdinando, Lovadina, Carlo, Madureira, Alexandre L.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Reissner; Mindlin; plate; heterogeneous plates; asymptotic analysis.},
language = {eng},
month = {3},
number = {5},
pages = {877-897},
publisher = {EDP Sciences},
title = {An asymptotically optimal model for isotropic heterogeneous linearly elastic plates},
url = {http://eudml.org/doc/194244},
volume = {38},
year = {2010},
}

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: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 38
IS - 5
SP - 877
EP - 897
AB - 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.
LA - eng
KW - Reissner; Mindlin; plate; heterogeneous plates; asymptotic analysis.
UR - http://eudml.org/doc/194244
ER -

References

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