Buckling analysis of functionally graded rectangular nano-plate based on nonlocal exponential shear deformation theory

Abstract

In this article, buckling response of functionally graded nano-plate based on exponential shear deformation theory is presented. The theory presented herein is built upon the classical plate theory.In this displacement-based, refined shear deformation theory, an exponential functions are used in terms of thickness co-ordinate to include the effect of transverse shear deformation and rotary inertia. The number of unknown displacement variables in the proposed theory are same as that in first order shear deformation theory. Nonlocal elasticity theory is employed to investigate effects of small scale on buckling of the functionally graded rectangular nano-plate. The material properties of the plate are assumed to vary according to the Power Law form in the thickness direction. The governing equations and corresponding boundary conditions are derived by implementing Hamilton's principle. To show the accuracy of the formulations, our research results in specific cases are compared with available results in the literature and a good agreement will be observed. Finally, the effect of various parameters such as nonlocal parameter, Power Law indexes, aspect ratio, and the thickness ratio on the non-dimensional critical buckling load of rectangular FG nano-plates are presented and discussed in detail.