Static and Free Vibration Analyses of Functionally Graded Nano-composite Plates Reinforced by Wavy Carbon Nanotubes Resting on a Pasternak Elastic Foundation

Abstract

In this study, static and free vibration analyses of functionally graded (FG) nanocomposite plates, reinforced by wavy single-walled carbon nanotubes (SWCNTs) resting on a Pasternak elastic foundation, were investigated based on a mesh-free method and modified first-order shear deformation theory (FSDT). Three linear types of FG nanocomposite plate distributions and a uniform distribution of wavy carbon nanotubes (CNTs) were considered, in addition to plate thickness. The mechanical properties were by an extended rule of mixture. In the mesh-free analysis, moving least squares (MLS) shape functions were used for approximation of the displacement field in the weak form of a motion equation, and the transformation method was used for imposition of essential boundary conditions. Effects of geometric dimensions, boundary conditions, the type of applied force, and the waviness index, aspect ratio, volume fraction, and distribution pattern of CNTs were examined for their effects on the static and frequency behaviors of FG carbon nanotube reinforced composite (CNTRC) plates. Waviness and the distribution pattern of CNTs had a significant effect on the mechanical behaviors of FG-CNTRC plates, even more than the effect of the CNT volume fraction.