Buckling of piezoelectric sandwich microplates with arbitrary in-plane BCs rested on foundation: effect of hygro-thermo-electro-elastic field

  • Yukang Yang
  • Youheng DongEmail author
  • Yinghui LiEmail author
Regular Article


Buckling and post-buckling behaviors of simply supported microplates in complex environment are studied, where elastic foundation and hygro-thermal-electro-mechanical loads are considered. The first-order shear deformation theory is used to establish basic equations of the microplate considering the von Kármán’s nonlinearity. The size-dependent effect is characterized by the modified couple stress theory. A unified boundary condition model is introduced to discuss various in-plane boundary conditions (BCs). Analytical solutions for critical mechanical/hygrothermal buckling loads and post-buckling paths of the microplate under different in-plane BCs are obtained by using the perturbation method and the Galerkin method, respectively. Results reveal that size-dependent effect and elastic foundation enhance the stiffness of the microplate. Transverse displacement of the microplate in the post-buckling stage increases with the external compressive load, temperature and moisture concentration, expressing a nonlinear curve. When the displacement constraint in the normal direction is applied on the microplate edge, the critical mechanical/hygrothermal buckling load decreases. These results can be utilized in the optimization design of the micro-electro-mechanical systems.

Graphical abstract



Yinghui Li was supported by National Natural Science Foundation of China (Grant no. 11872319).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Società Italiana di Fisica (SIF) and Springer-Verlag GmbH Germany, part of Springer Nature 2020

Authors and Affiliations

  1. 1.School of Mechanics and EngineeringSouthwest Jiaotong UniversityChengduPeople’s Republic of China

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