Modelling of thin isotropic elastic plates with small piezoelectric inclusions and distributed electric circuits. Models for inclusions larger or comparable to the thickness of the plate

2013/11/04 by Eric Canon, Canon, Eric, Michel Lenczner +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1311.0904

arxiv created 2013/11/04 · arxiv updated 2013/11/06

Abstract

This paper is the second part of a work devoted to the modelling of thin elastic plates with small, periodically distributed piezoelectric inclusions. We consider the equations of linear elasticity coupled with the electrostatic equation, with various kinds of electric boundary conditions. We derive the corresponding effective models when the thickness a of the plate and the characteristic dimension ε of the inclusions tend together to zero, in the two following situations: first when a ≃ ε, second when a/ε tends to zero.

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