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A Transversely Isotropic Magneto-Electro-Elastic Circular Kirchhoff Plate Model Incorporating Microstructure Effect

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Abstract

A non-classical model for transversely isotropic magneto-electro-elastic circular Kirchhoff plates is established based on the extended modified couple stress theory. The Gibbs-type variational principle is used to obtain the governing equations and boundary conditions. To illustrate the newly derived model, the static bending problem of a clamped circular plate subjected to a uniformly distributed constant load is solved numerically by Fourier–Bessel series. The numerical results show that the values of transverse displacement, electric and magnetic potentials predicted by the current model are always smaller than those of the classical model, and the differences are diminishing as the plate thickness increases. In addition, it is shown that the magneto-electro-elastic coupling effect plays an important role in the transverse displacement, electric potential and magnetic potential of the magneto-electro-elastic circular Kirchhoff plates. Furthermore, several reduced specific models are provided for simpler cases.

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Acknowledgements

The work reported here is funded by the National Natural Science Foundation of China [Grant Numbers 12002086 and 11672099]. These supports are gratefully acknowledged.

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Authors and Affiliations

  1. School of Civil Engineering, Chongqing University, Chongqing, 400044, China

    Wei Shen & Shuitao Gu

  2. Jiangsu Key Laboratory of Engineering Mechanics, School of Civil Engineering, Southeast University, Nanjing, 210096, China

    Gongye Zhang

  3. LMEE, University Paris-Saclay, Univ Evry, 91020,, Evry, France

    Yu Cong

Authors
  1. Wei Shen
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  2. Gongye Zhang
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  3. Shuitao Gu
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  4. Yu Cong
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Correspondence to Gongye Zhang or Shuitao Gu.

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Shen, W., Zhang, G., Gu, S. et al. A Transversely Isotropic Magneto-Electro-Elastic Circular Kirchhoff Plate Model Incorporating Microstructure Effect. Acta Mech. Solida Sin. 35, 185–197 (2022). https://doi.org/10.1007/s10338-021-00271-7

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  • DOI: https://doi.org/10.1007/s10338-021-00271-7

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