Nonlocal Buckling Characteristics of Functionally Graded Nano-Plates Subjected to Thermal Loads and Biaxial Linearly Varying Forces

Abstract

The buckling characteristics of thin functionally graded (FG) nano-plates subjected to both thermal loads and biaxial linearly varying forces is investigated. Eringen’s nonlocal elasticity theory is employed to account for the nano-scale phenomena in the plates. Hamilton’s principle and the constitutive relations are used to derive the partial differential governing equations of motion for the thin plates that are modeled using Kirchhoff’s plate theory. The mechanical properties of the FG nano-plates are assumed to vary smoothly across the thickness of the plate following a power law. Three types of thermal loads are presented and the spectral collocation method is utilized to solve for the critical buckling loads. The accuracy of the numerical solution of the proposed model is verified by comparing the results with those available in the literature. A comprehensive parametric study is carried out, and the effects of the nonlocal scale parameter, power law index, aspect ratio, slopes of the axial loads, boundary conditions, assumed temperature distributions, and the difference between the ceramic-rich and metal-rich surfaces on the nonlocal critical buckling loads of the nano-plates are examined. The results reveal that these parameters have significant influence on the stability behavior of the FG nano-plates.