Geodesic
Asymptotic consistency of the polynomial approximation in the linearized plate theory
Jean-Claude Paumier1 ; Annie Raoult1
1 LMC-IMAG, Université Joseph Fourier BP 53 38041 Grenoble Cedex 9, France
ESAIM. Proceedings, Tome 2 (1997), pp. 203-213.

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We establish a partial link between two standard methods for deriving plate models from linearized three-dimensional elasticity: the asymptotic method, known to justify the Kirchhoff-Love model, and the polynomial reduction method. In the polynomial method, the reduced model is obtained by projecting the three-dimensional displacement on a closed subspace of admissible displacements, namely displacements that are polynomial with respect to the thickness variable. Our procedure characterizes minimal polynomial subspaces that are consistent with the Kirchhoff-Love model. In the same time, if a singular perturbation term is dropped in the equations of the lower degree model, we recover a Reissner-Mindlin model.
DOI : 10.1051/proc:1997018

Jean-Claude Paumier 1 ; Annie Raoult 1

1 LMC-IMAG, Université Joseph Fourier BP 53 38041 Grenoble Cedex 9, France 
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Jean-Claude Paumier; Annie Raoult. Asymptotic consistency of the polynomial approximation in the linearized plate theory. ESAIM. Proceedings, Tome 2 (1997), pp. 203-213. doi : 10.1051/proc:1997018. http://geodesic.mathdoc.fr/articles/10.1051/proc:1997018/

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