Stability analysis and visual design of carbon nanotube-reinforced spherical shells products using higher-order theories and HDQM

This paper presents an in-depth investigation concerning the stability, temporary position, and visual design of spherical shells having functional graded carbon nanotube (FG-CNT) reinforced composites (FG-CNTRC) is investigated in this study. The analysis is based on Higher-order theories, in particular, the 12-variable displacement field (HOST12), which adequately describes the kinematic behavior of the shell. The material properties of FG-CNTRC were based on the Rule of Mixtures, thus the geometrically and materially nonlinear distribution and interaction of carbon nanotubes with matrix was described and incorporated. The stability of the FG-CNTRC spherical shells are investigated by developing the governing equations of motion via Hamilton's principle, thus accounting for material and geometrical parameters. To discretize the governing equations a hyperbolic differential quadrature method (HDQM) is employed based on Chebyshev–Gauss–Lobatto grid points, ensuring high accuracy and convergence in the results. Complete stability analyses are carried out by varying the effects of the volume fraction of the carbon nanotube and the geometry of the shell for visual design. The results point out the critical buckling loads and two deformation characteristics, along with the improvements in performance for FG-CNTRC shells versus typical materials. The findings are also compared to results reported by other authors in the literature showing the improved accuracy and reliability of the proposed approach. This study both reinforces the move toward sophisticated higher-order theories for the design of nanoreinforced structures and addresses an emerging field of knowledge related to the topic of nanocomposites for use in structural engineering.