Mechanical Behavior Analysis of FG-CNT-Reinforced Polymer Composite Beams via a Hyperbolic Shear Deformation Theory

This paper presents a hyperbolic shear deformation theory and discusses its application to investigate the bending and buckling behavior of functionally graded carbon nanotubes-reinforced composite (FG-CNTRC) beams. The proposed theory satisfies the parabolic variation of shear stress distribution throughout the thickness and fulfills the zero condition of shear stress on the upper and bottom surfaces of the FG-CNTRC beams. Therefore, there is no need to use any correction factor concerning conventional equivalent single-layer theories. Five different types of CNTs reinforcement distribution are considered for the analysis while assuming a power-law function variation of the material properties in the thickness direction. The governing equations are solved using a finite element method, where several new numerical results are presented to demonstrate the robustness and reliability of the proposed model. The compartive study shows that the proposed element model is: (a) accurate and comparable with the literature; (b) of a faster rate of convergence to the reference solution; (c) excellent in terms of numerical stability; (d) valid for both symmetric and non-symmetric FG-CNTRC beams. Results also show the validity of the proposed formulation for both thin and thick FG-CNTRC beams. In addition, the effect of various material and geometric parameters such as the CNTs volume fraction, distribution patterns of CNTs, boundary conditions, and the length-to-thickness ratio is investigated on the bending and buckling responses of FG-CNTRC beam structures. Several new referential results are also reported for the first time, which will serve as a benchmark for future studies in a similar direction.