The purpose of this paper is to derive and study a new asymptotic model for the equilibrium state of a thin anisotropic piezoelectric plate in frictional contact with a rigid obstacle. In the asymptotic process, the thickness of the piezoelectric plate is driven to zero and the convergence of the unknowns is studied. This leads to two-dimensional Kirchhoff-Love plate equations, in which mechanical displacement and electric potential are partly decoupled. Based on this model numerical examples are presented that illustrate the mutual interaction between the mechanical displacement and the electric potential. We observe that, compared to purely elastic materials, piezoelectric bodies yield a significantly different contact behavior.
Classification : 74K20, 78M35, 74M15, 74M10, 74F15
Mots clés : contact, friction, asymptotic analysis, anisotropic material, piezoelectricity, plate
@article{COCV_2009__15_1_149_0,
author = {Figueiredo, Isabel N. and Stadler, Georg},
title = {Frictional contact of an anisotropic piezoelectric plate},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {149--172},
publisher = {EDP-Sciences},
volume = {15},
number = {1},
year = {2009},
doi = {10.1051/cocv:2008022},
zbl = {1155.74031},
mrnumber = {2488573},
language = {en},
url = {www.numdam.org/item/COCV_2009__15_1_149_0/}
}
Figueiredo, Isabel N.; Stadler, Georg. Frictional contact of an anisotropic piezoelectric plate. ESAIM: Control, Optimisation and Calculus of Variations, Tome 15 (2009) no. 1, pp. 149-172. doi : 10.1051/cocv:2008022. http://www.numdam.org/item/COCV_2009__15_1_149_0/
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