Homogenization of an active distributed network coupled with a continuous medium

Abstract

In this paper we state the homogenized model of a periodic electro-piezo-mechanical thin shells. The electrical network is including resistive devices, tension sources, current sources and voltage to voltage amplifiers. It is distributed evenly on the surface of the shell. The model derivation is based on a two-scale convergence which is based on the two- scale transform introduced by T. Arbogast, J. Douglas and U. Hornung. The present work is based on some results of two- scale convergence of gradients which leads to the same results than the usual two-scale convergence introduced by G. Allaire. We apply these results and those introduced in the framework of M. Lenczner and G. Senouci-Bereksi for the electrical network, to derive the two-dimensional electro-piezo- mechanical thin shell model applying Reisner-Mindlin kinematic.