Analysis of the buckling of rectangular nanoplates by use of finite-difference method

Abstract

In recent years nanostructures have been widely used in industry, for example in nanoelectromechanical systems (NEMS); knowledge of the mechanical behavior of nanostructured materials is therefore important. In the work discussed in this paper, the non-dimensional buckling load of rectangular nano-plates was determined for general boundary conditions. Non-local theory was used to derive the governing equation, and this equation was then solved, by use of the finite-difference method, by applying different combinations of boundary conditions. To verify the proposed method, the non-dimensional buckling load determined for a simply supported plate was compared with results obtained by use of local theory and with results reported in the literature. When the method was used to calculate the buckling load of nano-beams, results were in good agreement with literature results. As a novel contribution of the work, non-symmetric boundary conditions were also studied. The non-dimensional buckling load was obtained for several values of aspect ratio, non-local variables, and different types of boundary condition. For better understanding, mode shapes are also depicted. The finite-difference method could be a powerful means of determination of the mechanical behavior of nanostructures, with little computational effort, and the results could be as reliable as those obtained by use of other methods. The ability to deal with a combination of boundary conditions illustrates the advantages of this method compared with other methods.