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Homogenization of thin piezoelectric perforated shells. (English) Zbl 1138.74039
Summary: We establish the existence of limit homogeneous constitutive law for 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 Koiter shell model in which 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 Korn’s inequality in perforated domains, we obtain the limit model.

MSC:
74Q05 Homogenization in equilibrium problems of solid mechanics
74K25 Shells
74F15 Electromagnetic effects in solid mechanics
35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
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