Stability of size dependent functionally graded nanoplate based on nonlocal elasticity and higher order plate theories and different boundary conditions

Abstract

This article presents a nonlocal higher order plate theory for stability analysis of nanoplates subjected to biaxial in plane loadings. It is assumed that the properties of the FG nanoplate follow a power law form through the thickness. Governing equations and corresponding boundary conditions are derived by using the principle of minimum potential energy. Generalized differential quadrature (GDQ) method is implemented to solve the size dependent buckling analysis according to the higher order shear deformation plate theories where highly coupled equations exist for various boundary conditions of rectangular plates. Some numerical results are presented to study the effects of the material length scale parameter, plate thickness, Poisson’s ratio, side to thickness ratio and aspect ratio on size dependent buckling load. It is observed that buckling load predicted by higher order theory significantly deviates from classical ones, especially for thick plates. Also comparing the results obtained from different theories shows that as the material length scale parameter take higher values, the difference between the buckling load resulting from the first order shear deformation plate theory (FSDT), classical theory and higher order plate theory declines.