Buckling response of functionally graded nanoplates under combined thermal and mechanical loadings

This effort focuses on a buckling analysis of a functionally graded (FG), thin, rectangular nanoplate subjected to biaxial linearly varying mechanical loads and various temperature distributions through the thickness of the nanoplate. On the basis of the Eringen’s nonlocal elasticity theory and Kirchhoff’s classical plate theory, the governing equations are obtained for functionally graded rectangular nanoplates using the minimum total potential energy principle. In the proposed model, it is assumed that the mechanical and thermal properties of nanoplates are position-dependent and that they vary through the thickness via a power rule of the volume fraction of the constituents. The governing equation and boundary conditions are discretized for the rectangular nanoplate by adopting the Chebyshev spectral collocation method, and the resulting eigenvalue problem is solved to obtain the critical buckling loads. Finally, numerical results are presented to show the impact of various thermal loadings and boundary conditions on the buckling behaviors of size-dependent functionally graded nanoplates. Moreover, the influences of varying different parameters, such as the nonlocal parameter, power law index, temperature rise, aspect ratio, and slopes of the linearly varying axial mechanical forces, are investigated and discussed in detail. The study of each of these parameters highlights phenomena present at the nanoscale from a theoretical point of view.