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On the Deformation of Chiral Piezoelectric Plates

  • Dorin Ieşan
  • Ramon Quintanilla
Chapter
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 89)

Abstract

The paper is concerned with the linear theory of piezoelectricity for isotropic chiral Cosserat elastic solids. The behavior of chiral bodies is of interest for the investigation of auxetic materials, carbon nanotubes, bones, honeycomb structures, as well as composites with inclusions. First, we establish the basic equations which govern the behavior of thin plates. It is shown that, in contrast with the theory of achiral plates, the stretching and flexure cannot be treated independently of each other. Then, we present a uniqueness result with no definiteness assumption on elastic constitutive coefficients. A reciprocity theorem is also established. Then, we present the conditions on the constitutive coefficients which guarantee that the energy of the system is positive definite and we give a continuous dependence result. In the case of stationary theory we derive a uniqueness result for the Neumann problem. Finally, the effects of a concentrated charge density in an unbounded plate are investigated.

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Notes

Acknowledgements

R.Q. is supported by the Project “Análisis Matemático de Problemas de la Termomecánica“(MTM2016-74934-P) (AEI/FEDER, UE) of the Spanish Ministry of Economy and Competitiveness.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsAl. I. Cuza University and Octav Mayer Institute of Mathematics (Romanian Academy)IaşiRomania
  2. 2.Department of MathematicsESEIAAT, Polytechnic University of CataloniaTerrassa, BarcelonaSpain

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