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Nonlinear bending analysis of magnetoelectroelastic rectangular plates using higher order shear deformation theory

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Abstract

Nonlinear bending analysis was performed of magnetoelectroelastic (MEE) composite plates under a mechanical and magnetoelectric (ME) load by using von Karman’s nonlinear geometric equation and the higher order shear deformation theory (HSDT). Nonlinear higher order partial differential equations for MEE plates were derived by using Hamiltonian equilibrium equation. The MEE plate is considered to have clamped boundary condition. The nonlinear high-order equations can turn into algebraic equations through Galerkin method. Then the effects of scale effect of MEE plate (for instance, the aspect ratio) and external load (for instance, mechanical) on the displacement of the considered MEE plate were investigated.

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Abbreviations

a :

MEE plate length

b :

MEE plate width

h :

MEE plate thickness

σ ij :

Stress vector

D i :

Electric displacement vector

B i :

Magnetic flux vector

C ij :

Elastic coefficient

η ij :

Dielectric coefficient

μ ij :

Magnetic permeability coefficient

e ij :

Piezoelectric coefficient

q ij :

Piezomagnetic coefficient

d ij :

Magnetoelectric coefficient

ϕ :

Electric potential

ψ :

Magnetic potential

q :

Distributed transverse load

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Acknowledgments

The project was supported by the National Natural Science Foundation of China (Grant No. 51778551), the Major Science and Technology Project of Fujian Province, China (Grant No. 2019HZ07011).

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Authors and Affiliations

  1. College of Civil Engineering, Fuzhou University, Fuzhou, Fujian, 350116, China

    Yu-fang Zheng & Liang-liang Xu

  2. Department of Civil Engineering and Architecture, Xiamen University of Technology, Xiamen, Fujian, 361024, China

    Chang-ping Chen

Authors
  1. Yu-fang Zheng
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  2. Liang-liang Xu
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  3. Chang-ping Chen
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Corresponding author

Correspondence to Liang-liang Xu.

Additional information

Recommended by Editor Seungjae Min

Yu-fang Zheng is a Professor of College of Civil Engineering at Fuzhou University, Fujian, China. She received her Ph.D. in Mechanical Engineering from Hunan University, Hunan, China. Her research interests include smart structures mechanics, microstructure mechanics and mechanics of composite structures.

Liang-liang Xu is a Master’s candidate in the College of Civil Engineering at Fuzhou University, Fujian, China. His research interests include smart structures mechanics and mechanics of composite structures.

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Zheng, Yf., Xu, Ll. & Chen, Cp. Nonlinear bending analysis of magnetoelectroelastic rectangular plates using higher order shear deformation theory. J Mech Sci Technol 35, 1099–1108 (2021). https://doi.org/10.1007/s12206-021-0223-y

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  • DOI: https://doi.org/10.1007/s12206-021-0223-y

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