Nonlocal Effect on Buckling of Triangular Nano-composite Plates

In the present study, small scale effect on critical buckling loads of triangular nano-composite platesunder uniform in-plane compression is studied. Since at nano-scale the structure of the plate is discreteand the long-range cohesive forces become important, the size dependent nonlocal elasticity theory isemployed to develop an equivalent continuum plate model for this nanostructure incorporating thechange in its mechanical behavior. Two parameter Winkler-Pasternak elastic medium is used toprecisely model the elastic behavior of the matrix surrounding the nano-plate. The governing stabilityequations are then derived using the classical plate theory and the principle of virtual work for a perfectuniform triangular nano-plate composite system. The well-known numerical Galerkin method is thenused as the basis for the solution in conjunction with the areal coordinates system. The solutionprocedure views the entire nano-composite plate as a single super element which can be of generalshape. Effects of nonlocal parameter, length, aspect ratio, mode number, anisotropy, edge supports andelastic medium on buckling loads are investigated. All of these parameters are seen to have significanteffect on the stability characteristics of nano-composite plate. It is shown that the results dependobviously on the non-locality of buckled nano-composite plate, especially at very small dimensions,small aspect ratios, higher mode numbers, higher anisotropy and stiffer edge supports. Also it is seenthat the medium parameters, especially the Winkler parameter, have significant influence on the smallscale effect and can decrease or increase it. Also, it is seen that the classical continuum mechanicsoverestimates the results which can lead to deficient design and analysis of these widely usednanostructures. The results from current study can be used in design, analysis and optimization ofdifferent nano-devices such as nano-electro-mechanical systems (NEMS) utilizing nano-compositeplates as load-bearing components. Although it is seen that nano-fillers, here the nano-plates, increasethe stiffness of the whole nano-composite, by increasing the bending rigidities, on the other hand it isshown in this study that the small scale effect or the nonlocal effect decreases the critical loads of thenano-composite system. Thus, the nonlocal effect plays a key role in the design of these nanostructuresand must be attended and comprehensively studied to avoid the failure of the nanostructure. Further,the solution employed here is general and can be applied to nano-composite plates with arbitraryshapes which is an asset in structural optimization.