An element-free IMLS-Ritz framework for buckling analysis of FG–CNT reinforced composite thick plates resting on Winkler foundations

An element-free based improved moving least squares-Ritz (IMLS-Ritz) method is proposed to study the buckling behavior of functionally graded nanocomposite plates reinforced by single-walled carbon nanotubes (SWCNTs) resting on Winkler foundations. The first-order shear deformation theory (FSDT) is employed to account for the effect of shear deformation of plates. The IMLS is used for construction of the two-dimensional displacement field. We derive the energy functional for moderately thick plates. By minimizing the energy functional via the Ritz method, solutions for the critical buckling load of the functionally graded carbon nanotube (FG–CNT) reinforced composite plates on elastic matrix are obtained. Numerical experiments are carried out to examine the effect of the Winkler modulus parameter on the critical buckling loads. The influences of boundary condition, plate thickness-to-width ratio, plate aspect ratio on the critical buckling loads are also investigated. It is found that FG–CNT reinforced composite plates with top and bottom surfaces of CNT-rich have the highest critical buckling loads.