Acta Mechanica Solida Sinica

, Volume 31, Issue 5, pp 652–671 | Cite as

A Three-Dimensional Size-Dependent Layered Model for Simply-Supported and Functionally Graded Magnetoelectroelastic Plates

  • Junhong Guo
  • Jiangyi Chen
  • Ernian PanEmail author


A three-dimensional size-dependent layered model for simply-supported and functionally graded magnetoelectroelastic plates is presented based on the modified couple-stress theory. The functionally graded material is assumed to be exponential in the thickness direction of the plate. The final governing equations are reduced to an eigensystem by expressing the extended displacements in terms of two-dimensional Fourier series. Using the propagator matrix method, the exact solutions of the magnetic, electric and mechanical fields of sandwich nanoplates with couple-stress effect and under the surface loads are derived. Numerical examples for two functionally graded sandwich plates made of piezoelectric \(\hbox {BaTiO}_{{3}}\) and magnetostrictive \(\hbox {CoFe}_{{2}}\hbox {O}_{{4}}\) materials are presented to demonstrate the effect of the functional gradient factor and material length-scale parameter on the induced fields. The exact solutions presented in this work can also serve as benchmarks to various numerical methods for analyzing the size-dependent features in layered systems.


Functionally graded Magnetoelectroelastic Modified couple stress Layered plate Three-dimensional solution 



This work was supported by the National Natural Science Foundation of China (Grant Nos. 11262012, 11502123, 11172273) and the Natural Science Foundation of Inner Mongolia Autonomous Region of China (Grant No. 2015JQ01).


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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics 2018

Authors and Affiliations

  1. 1.Department of MechanicsInner Mongolia University of TechnologyHohhotChina
  2. 2.School of Mechanical EngineeringZhengzhou UniversityZhengzhouChina
  3. 3.Department of Civil Engineering and Department of MathematicsThe University of AkronAkronUSA

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