Thickness-stretch analysis of functionally graded magneto-electro-elastic microplates based on the Mindlin-Medick theory

A new functionally graded magneto-electro-elastic (FG-MEE) composite microplate model is developed with the aid of the Mindlin-Medick (M-M) theory and an extended modified couple stress theory (MCST). This new model accounts for both symmetric thickness-shear and thickness-stretch deformations in the plate and is capable of capturing the size effect that is dependent on microstructure. Then, the governing equations and complete boundary conditions are obtained simultaneously based on the basic assumption of displacement, electric and magnetic fields, and Hamilton’s principle. As an application of the proposed model, the thickness-stretch deformation of a simply supported plate subjected to equal and opposite local normal loads is analytically solved. The numerical analysis results indicate that the magnitudes of the displacement, electric, and magnetic fields are lower than those forecasted by classical theory. Moreover, functionally graded (FG) parameters are found to be significant and can be utilized to regulate the electric and magnetic fields. These results guide the design of a Micro-Electrical-Mechanical System (MEMS) fabricated from FG-MEE materials.