Premium
Modeling of thin isotropic elastic plates with small piezoelectric inclusions and distributed electric circuits
Author(s) -
Ca Éric,
Lenczner Michel
Publication year - 2013
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3050
Subject(s) - piezoelectricity , isotropy , elasticity (physics) , zero (linguistics) , transverse isotropy , work (physics) , dimension (graph theory) , boundary value problem , mathematical analysis , materials science , physics , mathematics , composite material , optics , thermodynamics , pure mathematics , linguistics , philosophy
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 , and second, when a ∕ ϵ tends to zero. Copyright © 2013 John Wiley & Sons, Ltd.