Static and thermal instability analysis of embedded functionally graded carbon nanotube-reinforced composite plates based on HSDT via GDQM and validated modeling by neural network

In this research, the stability, and vibrational characteristics of functionally graded single-walled carbon nanotube-reinforced composite (FG-SWCNTRC) plates resting on a Visco-Hetenyi medium are perused based on a 12 unknown higher-order shear deformation theory (HSDT). The system is subjected to hygro-thermal environments and both compressive and tensile in-plane loads in both x- and y-direction. In addition to both linear and nonlinear thermal conditions, a two-dimensional (2D) magnetic field's effects on the stability of the system are studied. The governing equations of motion are solved numerically by means of the generalized differential quadrature method (GDQM) due to its capability to consider the various geometric boundary conditions (BCs). In order to validate the current work, a comparative study is accomplished between the present outcomes and reported ones in the open literature. The impact of the carbon nanotube (CNT) volume fraction, patterns of CNT distribution, environmental attacks, magnetic field strength and direction, structure aspect ratios, BCs, and foundation types on the vibrational behavior of the considered structure are scrutinized. Obtained results represent that considering the impacts of in-plane tensile forces and the magnetic field in modeling improves the system's vibrational behavior. While imposing the hygro-thermal effects similar to the axial compressive loads have destabilizing influences on the system and make the structure more vulnerable to static instability. Moreover, uncertain conditions are assessed for sensitive parameters which have effects on the performance of the system. Finally, using a supervised neural network (NN) learning approach, the accuracy of the model is proved.