Size-dependent analysis of functionally graded carbon nanotube-reinforced composite nanoshells with double curvature based on nonlocal strain gradient theory

As initial endeavors, this paper presents an in-depth study to investigate the influence of nanoscale parameters on bending and free vibration responses of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) nanoshells with double curvature. Carbon nanotubes (CNTs) are considered as reinforcements that are distributed across the shell thickness with two different distributions, namely the UD and FG-X. First of all, the mathematical formulas are built on the nonlocal strain gradient theory which, as a critical point of this study, considers both nonlocal and strain gradient parameters simultaneously. Additionally, toward using the Navier solution, the simply supported boundary condition is established to obtain the deflection and natural frequency of FG-CNTRC nanoshells. Furthermore, some specific numerical results are shown and compared with the results reported in the literature. Most importantly, the new findings are given and discussed deeply to show the effect of nanoscale parameters and material property and shape of shells on the deflection and fundamental frequency parameters of the FG-CNTRC nanoshells. From the obtained results, it is shown that the small length-scale has a significant effect on frequencies and deflection of FG-CNTRC nanoshells.