Static analysis of functionally graded anisotropic nanoplates using nonlocal strain gradient theory

We study functionally graded nanoplates made of (hexagonal) beryllium crystals. Therefore, a five-variable refined plate theory in conjunction with the nonlocal strain gradient theory is developed. From the best knowledge of authors, it is the first time that mentioned theories are developed for hexagonal materials. The governing equations are obtained using Hamilton's principle where an analytical technique based on Navier's series is utilized to solve the static problem for simply-supported boundary conditions. To simplify the equations, the number of unknowns and governing equations are reduced by dividing the transverse displacement into bending, shear, and thickness stretching parts. The obtained results of the displacements are compared with those predicted by other 2D and quasi-3D plate theories available in the literature. We show that the bending characteristics of FG anisotropic nanoplates are influenced by the nonlocal parameter, strain gradient parameter, length-to-thickness ratio, length-to-width ratio and exponential factor. This study offers benchmark results for the static analysis of functionally graded anisotropic nanoplates which could for instance be used for other computational approaches. We also quantify the accuracy of replacing an anisotropic model with an isotropic one and show that the differences in the stresses can grow up to 10% in some conditions.