Thermo-electro-mechanical bending of FG piezoelectric microplates on Pasternak foundation based on a four-variable plate model and the modified couple stress theory

In this paper, the size-dependent bending response of functionally graded piezoelectric (FGP) microplates resting on two-parameter elastic foundations and subjected to an external mechanical load, electric voltage and elevated temperature is investigated. The thermo-electro-mechanical loads are presumed uniformly distributed on the upper surface of the plate. To capture the size effect, the modified couple stress theory is employed. In this theory, the couple stress tensor is symmetric and it contains only one material length scale parameter. Based on a four-variable shear deformation plate theory, the governing equations are derived from Hamilton principle, which does not involve only the strain tensor but also the curvature tensor and electric field. The electrical and elastic properties of the microplate are assumed to be graded through the thickness of the plate according to a power law distribution as a function of the volume fraction of the constituents. The effects of the geometrical parameters (material length scale parameter, side-to-thickness ratio and plate aspect ratio), gradient index, electric voltage, elastic foundation stiffness and temperature parameters on the deflection, electric potential, stresses and electric displacements of the FGP microplates are all presented and discussed.