Size dependent thermo-electro-mechanical nonlinear bending analysis of flexoelectric nano-plate in the presence of magnetic field

Abstract

The present paper studies the thermo-electro-magnetic mechanical behavior of a flexoelectric nano-plate using a modified flexoelectric theory and application of classical Kirchhoff plate theory. Size and flexoelectric effects are considered. Using the variation method and the principle of minimum potential energy in the coupling form, for the first time, the nonlinear governing differential equations of the nano-plate and the relevant boundary conditions are obtained. The nano-plate is subjected to mechanical, electrical, magnetic and thermal loadings and is simply supported on all edges. Moreover, in the present study, analytical solutions are presented to investigate the effects of length scale parameters, geometric parameters, mechanical loading, and temperature rise of the nano-plate lower surface, the external electric potential, and the external static magnetic flux density on the magneto-thermo-electro-elastic behavior of the nano-plate. In order to verify the presented formulations, the results are compared to analytical results found in the literature. Due to high stain gradients in nano-scales, the results indicate that the flexoelectricity has a larger influence in plates with smaller thicknesses. The results also show that, in the presence of flexoelectricity and static magnetic field, the rigidity of the nano-plate increases. Also, the deflection and the generated electric potential along nano-plate thickness decrease.