Pure bending of a piezoelectric layer in second gradient electroelasticity theory

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 addition...

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Bibliographic Details
Published in:Acta mechanica 2019-12, Vol.230 (12), p.4197-4211
Main Authors: Solyaev, Yury, Lurie, Sergey
Format: Article
Language:English
Subjects:
Analysis
Bending moments
Boundary conditions
Classical and Continuum Physics
Control
Dielectric properties
Dielectrics
Dynamical Systems
Electric fields
Electrical conductivity
Engineering
Engineering Fluid Dynamics
Engineering Thermodynamics
Exact solutions
Finite element method
Heat and Mass Transfer
Isotropic material
Mathematical models
Original Paper
Piezoelectricity
Plane strain
Solid Mechanics
Theoretical and Applied Mechanics
Vibration
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Description
Summary: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.
ISSN:0001-5970
1619-6937
DOI:10.1007/s00707-019-02484-x