Bending analysis of functionally graded nanoplates based on a higher-order shear deformation theory using dynamic relaxation method

In this paper, bending analysis of rectangular functionally graded nanoplates under a uniform transverse load has been considered based on the modified couple stress theory. Using Hamilton’s principle, governing equations are derived based on a higher-order shear deformation theory. The set of coupled equations are solved using the dynamic relaxation method combined with finite difference discretization technique for clamped and simply supported boundary conditions. Finally, the effects of aspect ratio, thickness-to-length ratio, boundary conditions, transverse load, and length scale parameter are studied in detail. The results showed that by rising the length scale-to-thickness ratio, the influence of the grading index on the deflection decreased