Mechanics of Advanced Composite Structures 8 (2021) 132 –148 Semnan University Mechanics of Advanced Composite Structures journal homepage: http://MACS.journals.semnan.ac.ir * Corresponding author. Tel.: +98-51-36625046; Fax: +98-51-36612960 E-mail address: m.e.golmakani@mshdiau.ac.ir DOI: 10.22075/macs.2020.19884.1244 Received 2020-02-21; Received in revised form 2020-05-14; Accepted 2020-06-19 © 2021 Published by Semnan University Press. All rights reserved. Buckling Analysis of Nano Composite Plates Based on Combination of the Incremental Load Technique and Dynamic Relaxation Method V. Zeighami a , M.E. Golmakani a* a Department of Mechanical Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran KEYWORDS ABSTRACT CNTRC plate Buckling Incremental loading DR method 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. 1. Introduction Carbon nanotubes (CNTs) have been widely accepted owing to their remarkable mechanical, electrical and thermal properties and the applications of CNTs are thus drawing much attention currently. Conventional fiber- reinforced composite materials are normally made of stiff and strong fillers with microscale diameters embedded into various matrix phases. The discovery of CNTs may lead to a new way to improve the properties of resulting composites by changing reinforcement phases to nano-scaled fillers [1]. Carbon nanotubes are considered as a potential candidate for the reinforcement of polymer composites, provided that good interfacial bonding between CNTs and polymer and proper dispersion of the individual CNTs in the polymeric matrix can be guaranteed [2]. Since the load transfer between the nanotube and the matrix is less than perfect, several micromechanical models have been developed to predict properties of CNT-reinforced nanocomposites. Fidelus et al. [3] examined thermo-mechanical properties of epoxy-based nanocomposites with low weight fractions of randomly oriented single- and multi-walled carbon nanotubes with a rule-of-mixture type prediction of the modulus. Based on the rule of mixture, Anumandla and Gibson [4] presented a comprehensive closed form micromechanics model for estimating the elastic modulus of nanotube-reinforced composites. Han and Elliot [5] presented classical molecular dynamics (MD) simulations to model polymer/CNT composites constructed by embedding a single wall (10, 10) CNT into two different amorphous polymer matrices. The CNT–polymer interfacial shear