Abstract
The object of this paper is to present new intrinsic linear models of thin and asymptotic piezoelectric shells starting from a three-dimensional model of piezoelectric material. It is based on the completely intrinsic methods developed and used in [2, 6] to obtain linear models of thin and asymptotic mechanical shells without local coordinates or Christoffel symbols. The thin shell approximation is achieved via an extended version of the P(2, 1) model studied in [2] and a scalar P(2, 1)-approximation of the electrical potential. This type of approximation yields models of the Naghdi’s type without the standard assumption on the stress tensor. We also present a new completely uncoupled system of two equations for the asymptotic model. The decoupling results from the choice of the scalar product used to define the projection. It is different from the one used in [2] where the second equation is coupled with the first one through a term which is zero for the plate and in the bending dominated case. Effective mechanical and electrical constitutive laws are obtained from arbitrary three-dimensional mechanical and electrical constitutive laws.
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© 2001 Birkhãuser Verlag Basel/Switzerland
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Delfour, M.C., Bernadou, M. (2001). Intrinsic Asymptotic Model of Piezoelectric Shells. In: Hoffmann, KH., Lasiecka, I., Leugering, G., Sprekels, J., Tröltzsch, F. (eds) Optimal Control of Complex Structures. ISNM International Series of Numerical Mathematics, vol 139. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8148-7_5
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DOI: https://doi.org/10.1007/978-3-0348-8148-7_5
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