Nonlocal Effect on Buckling of Triangular Nano-composite Plates

Abstract

In the present study, small scale effect on critical buckling loads of triangular nano- composite plates under uniform in-plane compression is studied. Since at nano-scale the structure of the plate is discrete, the size dependent nonlocal elasticity theory is employed to develop an equivalent continuum plate model for this nanostructure incorporating the changes in its mechanical behavior. The two-parameter, Winkler-Pasternak, elastic medium is used for precisely modelling the behavior of matrix surrounding the nano-plate. The governing stability equations are then derived using the classical plate theory and the principle of virtual work for a perfect uniform triangular nano-plate composite. The well-known numerical Galerkin method in conjunction with the areal coordinates system is used as the basis for the solution. The solution procedure views the entire nano-composite plate as a single super-continuum element. Effects of nonlocal parameter, length, aspect ratio, mode number, anisotropy, edge supports and elastic medium on the buckling loads are rigorously investigated. All of these parameters are seen to have significant effect on the stability of nano-composite plate. It is shown that the results depend obviously on the non-locality of buckled nano-composite plate, especially at very small dimensions, small aspect ratios, higher mode numbers, higher anisotropy degree, stiffer edge supports and softer elastic mediums. Also, it is seen that the classical continuum mechanics overestimates the buckling results which can lead to deficient design and analysis of these widely used nanostructures.