Postbuckling analysis of axially compressed CNT reinforced functionally graded composite plates resting on Pasternak foundations using an element-free approach

A postbuckling analysis of functionally graded carbon nanotube (FG-CNT) reinforced composite plates resting on Pasternak foundations is presented. The plate under consideration is subjected to axial compression. The improved moving least-squares (IMLS) approximations are employed for the field variables in the Ritz method to derive the discretized governing equations. The plates are reinforced by single-walled carbon nanotubes (SWCNTs) which are assumed to be graded through the thickness direction with different types of distributions. The effective material properties of FG-CNT plates are estimated through a micromechanical model based on the extended rule of mixture. The bending stiffness is evaluated using the stabilized conforming nodal integration scheme. The membrane and shear terms in the governing equation are determined using the direct nodal integration technique. The postbuckling path is traced using the arc-length method combined with the modified Newton-Raphson technique. Parametric studies are conducted to examine the effects of CNT volume fraction, plate thickness-to-width ratio, plate aspect ratio and elastic foundation modulus on the postbuckling behaviors of FG-CNT plates under various boundary conditions.