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An asymptotically optimal model for isotropic heterogeneous linearly elastic plates

Published online by Cambridge University Press:  15 October 2004

Ferdinando Auricchio ,
Carlo Lovadina  and
Alexandre L. Madureira
Ferdinando Auricchio
Affiliation:
Dipartimento di Meccanica Strutturale, Università di Pavia, Via Ferrata 1, 27100 Pavia, Italy. [email protected].
Carlo Lovadina
Affiliation:
Dipartimento di Matematica, Università di Pavia, Via Ferrata 1, 27100 Pavia, Italy. [email protected].
Alexandre L. Madureira
Affiliation:
Departamento de Matemática Aplicada e Computacional, Laboratório Nacional de Computação Científica, Av. Getúlio Vargas 333, Petrópolis - RJ, Brazil. [email protected].
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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.

Keywords

ReissnerMindlinplateheterogeneous platesasymptotic analysis.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 38 , Issue 5 , September 2004 , pp. 877 - 897
Copyright
© EDP Sciences, SMAI, 2004

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References

S.M. Alessandrini, D.N. Arnold, R.S. Falk and A.L. Madureira, Derivation and Justification of Plate Models by Variational Methods. Centre de Recherches Mathematiques, CRM Proceedings and Lecture Notes (1999).
Arnold, D.N. and Falk, R.S., Asymptotic analysis of the boundary layer for the Reissner Mindlin plate model. SIAM J. Math. Anal. 27 (1996) 486–514. CrossRef
Arnold, D.N., Madureira, A.L. and Zhang, S., On the range of applicability of the Reissner-Mindlin and Kirchhoff-Love plate bending models. J. Elasticity 67 (2002) 171–185. CrossRef
Auricchio, F. and Sacco, E., Partial-mixed formulation and refined models for the analysis of composite laminates within FSDT. Composite Structures 46 (1999) 103–113. CrossRef
Caillerie, D., Thin elastic and periodic plates. Math. Meth. Appl. Sci. 6 (1984) 159–191. CrossRef
P.G. Ciarlet, Mathematical Elasticity, volume II: Theory of Plates, North-Holland Publishing Co., Amsterdam. Stud. Math. Appl. 27 (1997).
Ciarlet, P.G. and Destuynder, Ph., A justification of the two dimensional linear plate model. J. Mécanique 18 (1979) 315–344.
Dauge, M. and Gruais, I., Asymptotics of arbitrary order for a thin elastic clamped plate, I. Optimal error estimates. Asymptotic Anal. 13 (1996) 167–197.
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).
Lo, K.H., Christensen, R.M. and Wu, E.M., A high-order theory of plate deformation. J. Appl. Mech. 46 (1977) 663–676. CrossRef
Motygin, O.V. and Nazarov, S.A., 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. CrossRef
Paumier, J.C. and Raoult, A., Asymptotic consistency of the polynomial approximation in the linearized plate theory application to the Reissner-Mindlin model. ESAIM: Proc. 2 (1997) 203-213. CrossRef
J. Sanchez Hubert and E. Sanchez Palencia, Introduction aux méthodes asymptotiques et à l'homogénéisation, Masson, Paris (1992).