Nonlocal buckling analysis of functionally graded nano-plates subjected to biaxial linearly varying forces

The buckling problem of a thin, rectangular, functionally graded (FG) nano-plate with varying boundary conditions subjected to biaxial linearly varying forces is investigated utilizing the Eringen’s nonlocal theory. The plates are modeled using Kirchoff’s classical plate theory and the mechanical properties of the FG nano-plates vary continuously through the thickness of the plate following a power law model. The governing differential equations of motion of the nano-plates subjected to linearly varying biaxial loads is derived using the Hamilton’s principle, along with the constitutive relations. The Chebyshev spectral collocation method is then utilized to solve for the critical buckling loads. A parametric study is then performed to examine the impacts of varying the nonlocal parameter, power law index, aspect ratio, slopes of the axial loads, and varying boundary conditions on the nonlocal critical buckling loads of the nano-plates. It is shown that these parameters have significant influence on the stability characteristics of the FG nano-plates.