Static and dynamic stability responses of multilayer functionally graded carbon nanotubes reinforced composite nanoplates via quasi 3D nonlocal strain gradient theory

This manuscript presents the comprehensive study of thickness stretching effects on the free vibration, static stability and bending of multilayer functionally graded (FG) carbon nanotubes reinforced composite (CNTRC) nanoplates. The nanoscale and microstructure influences are considered through a modified nonlocal strain gradient continuum model. Based on power-law functions, four different patterns of CNTs distribution are considered in this analysis, a uniform distribution UD, FG-V CNTRC, FG-X CNTRC, and FG-O CNTRC. A 3D kinematic shear deformation theory is proposed to include the stretching influence, which is neglected in classical theories. Hamilton's principle is applied to derive the governing equations of motion and associated boundary conditions. Analytical solutions are developed based on Galerkin method to solve the governing equilibrium equations based on the generalized higher-order shear deformation theory and the nonlocal strain gradient theory and get the static bending, buckling loads, and natural frequencies of nanoplates. Verification with previous works is presented. A detailed parametric analysis is carried out to highlight the impact of thickness stretching, length scale parameter (nonlocal), material scale parameter (gradient), CNTs distribution pattern, geometry of the plate, various boundary conditions and the total number of layers on the stresses, deformation, critical buckling loads and vibration frequencies. Many new results are also reported in the current study, which will serve as a benchmark for future research.