Vibrational and elastic stability responses of functionally graded carbon nanotube reinforced nanocomposite beams via a new Quasi-3D finite element model

A new finite element model is formulated and implemented in this analysis to assess the free vibration and elastic stability behaviors of functionally graded carbon nanotube-reinforced (FG-CNTRC) nanocomposite beams. The developed model is founded on an efficient Quasi-3D shear deformation beam theory. The traction-free boundary conditions are guaranteed with no shear correction factors by integrating the hyperbolic warping function for transverse shear deformation and stress through the thickness coordinate. The suggested two-node beam element has four degrees of freedom per node, and the discrete model maintains inter-element continuity by using both C1 and C0 continuities for the kinematics variables. As a result, the isoparametric coordinate system is used to produce the elementary stiffness, geometric, and mass matrices to improve the current formulation. The weak form of the variational principle is used to generate the governing equations. Following the distribution patterns and CNT volume fraction, the mechanical characteristics of used FG-CNTRC beams change gradually over the beam thickness. The high performance of the present beam element is demonstrated by comparing current results to those predicted by previous theories and solution procedures. In addition, detailed numerical research is conducted to investigate the effects of boundary conditions, distribution patterns, and slenderness ratio on the free vibration and buckling responses of FGCNTRC beams. An appropriate reinforcement technique based on optimum distribution patterns can significantly improve computational efficiencies. The developed finite element beam model is computationally efficient and can be explored as a helpful design and optimization tool for CNT-reinforced nanocomposite structures.