An extension of Carrera’s unified formulation via the modified couple stress theory to electromechanical analysis of thick functionally graded piezoelectric microplates using the generalized differential quadrature method

In this paper, an electromechanical analysis of thick functionally graded piezoelectric (FGP) microplates has been investigated, considering size effects and through-thickness stretching of the microplate, for the first time. For this purpose, employing the modified couple stress theory (MCST), the Carrera’s unified formulation (CUF) has been extended to the micro scale to capture size effects. In fact, the CUF is a robust model that allows achieving many theories that can differ by the order of expansion and the variables description in the thickness direction. The governing differential equations of the problem, incorporating the electromechanical coupling effects of the piezoelectric material, have discretized and solved using the generalized differential quadrature (GDQ) numerical method. Some benchmarks have been presented for electromechanical analysis of the FGP microplates with different electrical boundary conditions. An interesting finding of the results is that, the size effects have a significant influence on the out of plane electric displacement of the FGP microplate, which has not been reported so far. The reason for this fact is the through–thickness stretching of the thick microplate. In this regard, some novel results have been presented by investigating the influence of different size effect parameters, various power-law indices material gradient, and different boundary conditions of the FGP microplates.