The Mindlin-Medick Plate Theory and Its Application Under Flexoelectricity and Temperature Effects

LU Shuang; LI Dongbo; CHEN Jingbo; XI Bo

doi:10.21656/1000-0887.440017

Volume 44 Issue 9

Sep. 2023

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Article Navigation > Applied Mathematics and Mechanics > 2023 > 44(9): 1122-1133

LU Shuang, LI Dongbo, CHEN Jingbo, XI Bo. The Mindlin-Medick Plate Theory and Its Application Under Flexoelectricity and Temperature Effects[J]. Applied Mathematics and Mechanics, 2023, 44(9): 1122-1133. doi: 10.21656/1000-0887.440017

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The Mindlin-Medick Plate Theory and Its Application Under Flexoelectricity and Temperature Effects

doi: 10.21656/1000-0887.440017

School of Science, Xi'an University of Architecture and Technology, Xi'an 710055, P.R.China

Received Date: 2023-01-20
Rev Recd Date: 2023-05-05
Publish Date: 2023-09-01

Abstract

Abstract

Based on the Hamiltonian variational principle, the 2D field equations and boundary conditions for flexoelectricity were derived, and the corresponding governing equations were obtained through substitution of the constitutive relation and geometric equations into the field equation. The in-plane tensile deformation, thickness-stretch deformation, symmetric thickness-shear deformation, and their coupled flexoelectric polarization of flexoelectric nanoplates caused by inhomogeneous temperature changes, were studied. The displacement fields and electric potential fields were solved with the double Fourier series method. The results demonstrate that, all fields are sensitive to the temperature load, which raises the prospect of controlling the mechanical and electrical behaviors of flexoelectric nanoplates by means of the temperature field. The effects of the thermal field and mechanical field on the displacement field were compared and examined. The work extends the Mindlin-Medick plate structure analysis theory in view of the flexoelectric and temperature effects, and provides a reference for the structural design of micro- and nano-scale devices.
- Mindlin-Medick theory,
- flexoelectric effect,
- temperature effect,
- temperature control,
- mechanical control

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References(33)

References

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