Asymptotic consistency of the polynomial approximation in the linearized plate theory

LMC-IMAG, Université Joseph Fourier BP 53 38041 Grenoble Cedex 9, France

Abstract

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.