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

Abstract

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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.

How to cite

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Ghergu, 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 -

References

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