Buckling of FG-CNT reinforced composite thick skew plates resting on Pasternak foundations based on an element-free approach

Abstract

Buckling behavior of functionally graded carbon nanotube (FG-CNT) reinforced composite thick skew plates is studied. The element-free IMLS-Ritz method is used to obtain the buckling solutions to this problem. The first-order shear deformation theory (FSDT) is employed for formulation of the energy functional to incorporate the effects of transverse shear deformation and rotary inertia. Using the IMLS approximation in the field variables and minimizing the energy functional via the Ritz procedure, a discretized eigenvalue equation of the problem is derived. The buckling solution can be obtained through solving this eigenvalue problem. The numerical stability of the IMLS-Ritz method is validated through convergence studies. The accuracy of the IMLS-Ritz results is examined by comparing with the known solutions. Close agreement is found from the comparison study. Besides, parametric studies are conducted for various types of CNTs distributions, CNT ratios, aspect ratios, plate geometries and thickness-to-height ratios under different boundary conditions.