Buckling analysis of Nano composite plates based on combination of the incremental load technique and dynamic relaxation method

Document Type: Research Paper


1 Department of Mechanical Engineering, Mashhad branch, Azad University, Mashhad, Iran

2 Department of Mechanical Engineering, Mashhad Branch, Azad University, Mashhad, Iran



In this paper, a different method, incremental load technique in conjunction with dynamic relaxation (DR) method, is employed to analyze the buckling behavior of composite plates reinforced with functionally graded (FG) distributions of single-walled carbon nanotubes (SWCNTs) along the thickness direction. The properties of carbon-nanotubes reinforced composite (CNTRC) plate were determined through modified rule of mixture. The nonlinear governing relations are obtained incrementally in the form of partial differential equations (PDEs) based on first-order shear deformation theory (FSDT) and Von Karman nonlinear strain. In the proposed method, for finding the critical buckling load, the mechanical loads are applied to the CNTRC plate incrementally so that in each load step the incremental form of PDEs are solved by the DR method combined with the finite difference (FD) discretization technique. Finally, the critical buckling load is determined from the load-displacement curve. In order to verify the accuracy of the present method, the results are compared with those available in the literatures. Finally, a detailed parametric study is carried out and results demonstrate that the change of carbon nanotube volume fraction, plate width-to-thickness ratio, plate aspect ratio, boundary condition and loading condition have pronounced effects on the buckling strength of CNTRC plates. It is seen that for all types of loading, boundary conditions and both cases of with and without presence of elastic foundation the FG-X and FG-O have the highest and lowest values of buckling loads.