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Pure bending of a piezoelectric layer in second gradient electroelasticity theory

  • Yury SolyaevEmail author
  • Sergey Lurie
Original Paper
  • 31 Downloads

Abstract

The semi-inverse analytical solution of a pure bending problem for a piezoelectric layer is developed in the framework of linear electroelasticity theory with strain gradient and electric field gradient effects. The simplified gradient theory of transversely isotropic material with a single additional length scale parameter is considered. A two-dimensional solution is derived assuming plane strain state of a layer (cylindrical bending of a plate) and low dielectric properties of the surrounding medium. The electromechanical response of a layer is found under conditions of prescribed bending moments at the end faces. Boundary conditions on the top and bottom surfaces of a layer are satisfied exactly. The analytical solution is validated based on numerical finite element modeling. It is shown that the obtained solutions can be used for the validation of size-dependent beam and plate models in the second gradient electroelasticity theory.

Mathematics Subject Classification

74F15 74G05 74A30 

Notes

Funding

This work was supported by the Russian Science Foundation under Grant 17-79-20105 issued to the Moscow Aviation Institute.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute of Applied Mechanics of the Russian Academy of SciencesMoscowRussia
  2. 2.Moscow Aviation InstituteMoscowRussia

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