# 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

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topAuricchio, 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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- P. Destuynder, Sur une justification des modèles de plaques et de coques par les méthodes asymptotiques. Ph.D. thesis, Université Pierre et Marie Curie - Paris, France (1980).
- K.H. Lo, R.M. Christensen and E.M. Wu, A high-order theory of plate deformation. J. Appl. Mech.46 (1977) 663–676. Zbl0369.73052
- O.V. Motygin and S.A. Nazarov, Justification of the Kirchhoff hypotheses and error estimation for two-dimensional models of anisotropic and inhomogeneous plates, including laminated plates. IMA J. Appl. Math.65 (2000) 1–28. Zbl0985.74037
- J.C. Paumier and A. Raoult, Asymptotic consistency of the polynomial approximation in the linearized plate theory application to the Reissner-Mindlin model. ESAIM: Proc.2 (1997) 203-213. Zbl0897.73033
- J. Sanchez Hubert and E. Sanchez Palencia, Introduction aux méthodes asymptotiques et à l'homogénéisation, Masson, Paris (1992).

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