Postbuckling of carbon nanotube reinforced functionally graded plates with edges elastically restrained against translation and rotation under axial compression

This paper presents, to the authors' knowledge, a first known postbuckling analysis of carbon nanotube (CNT) reinforced functionally graded plates with edges elastically restrained against translation and rotation. The plate considered is of moderate thickness and, hence, the first-order shear deformation theory (FSDT) and von Kármán assumption are adopted to incorporate the effects of transverse shear strains, rotary inertia and moderate rotations. The element-free IMLS-Ritz method is employed. The cubic spline weight function and linear basis are utilized in the approximation. In this study, the bending stiffness is evaluated through the nodal integration scheme. The postbuckling path is traced using the arc-length method combined with the modified Newton-Raphson technique. Parametric studies on the postbuckling behavior of CNT reinforced functionally graded plates are conducted to examine the effects of CNT content by volume, plate width-to-thickness ratio and plate aspect ratio by varying the elastically restrained parameters of translation and rotation on the boundaries. The results of the present study are obtained for simplified cases so that comparison studies can be undertaken using the values reported in the literature.