# Homogenization of thin piezoelectric perforated shells

Marius Ghergu; Georges Griso; Houari Mechkour; Bernadette Miara

ESAIM: Mathematical Modelling and Numerical Analysis (2007)

- Volume: 41, Issue: 5, page 875-895
- ISSN: 0764-583X

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topGhergu, Marius, et al. "Homogenization of thin piezoelectric perforated shells." ESAIM: Mathematical Modelling and Numerical Analysis 41.5 (2007): 875-895. <http://eudml.org/doc/250048>.

@article{Ghergu2007,

abstract = {
We rigorously establish the existence of the limit
homogeneous constitutive law of a piezoelectric composite made of
periodically
perforated microstructures and whose reference configuration is a
thin shell with fixed thickness. We deal with an extension of the
Koiter shell model in which the three curvilinear coordinates of
the elastic displacement field and the electric potential are
coupled. By letting the size of the
microstructure going to zero and by using the periodic
unfolding method combined with the Korn's inequality in perforated
domains, we obtain the limit model.
},

author = {Ghergu, Marius, Griso, Georges, Mechkour, Houari, Miara, Bernadette},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Computational solid mechanics; homogenization; perforations;
piezoelectricity; shells.; existence; Koiter shell model; Korn's inequality; periodic unfolding method},

language = {eng},

month = {10},

number = {5},

pages = {875-895},

publisher = {EDP Sciences},

title = {Homogenization of thin piezoelectric perforated shells},

url = {http://eudml.org/doc/250048},

volume = {41},

year = {2007},

}

TY - JOUR

AU - Ghergu, Marius

AU - Griso, Georges

AU - Mechkour, Houari

AU - Miara, Bernadette

TI - Homogenization of thin piezoelectric perforated shells

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2007/10//

PB - EDP Sciences

VL - 41

IS - 5

SP - 875

EP - 895

AB -
We rigorously establish the existence of the limit
homogeneous constitutive law of a piezoelectric composite made of
periodically
perforated microstructures and whose reference configuration is a
thin shell with fixed thickness. We deal with an extension of the
Koiter shell model in which the three curvilinear coordinates of
the elastic displacement field and the electric potential are
coupled. By letting the size of the
microstructure going to zero and by using the periodic
unfolding method combined with the Korn's inequality in perforated
domains, we obtain the limit model.

LA - eng

KW - Computational solid mechanics; homogenization; perforations;
piezoelectricity; shells.; existence; Koiter shell model; Korn's inequality; periodic unfolding method

UR - http://eudml.org/doc/250048

ER -

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