A three-unknown refined shear beam model for the bending of randomly oriented FG-CNT/fiber-reinforced composite laminated beams rested on a new variable elastic foundation

Advanced composite materials are widely employed in several industrial structures such as turbine blades, cutting tools, and aircraft engines. Given the need for analytical and numerical analysis of these complex structures, a mathematical model of novel structures is presented in this paper. The main aim of the present work is to analyze the static bending response of laminated composite beams reinforced by both functionally graded (FG) fibers and randomly oriented single-walled carbon nanotubes rested on a new variable elastic foundation (EF). The fibers volume fraction is changed along the beam thickness from layer to layer in a linear manner, whereas the CNTs volume fraction is uniformly distributed. Three distribution patterns, namely FG-V, FG-O, and FG-X, are considered here to define the fiber-reinforced elements distribution in addition to the uniform distribution UD. A new shear deformation theory is proposed to depict the kinematic displacement field and the requirement of zero transverse shear stresses at the upper and the lower surfaces of the FG beam are satisfied. Further, the present theory obviates the use to shear correction factors as it satisfies the parabolic variation of through-thickness shear stress distribution. Three types of EFs (including linear, trigonometric and reverse trigonometric) are selected here for the analysis. Virtual work principle is exploited to derive the equilibrium equations and Fourier series is employed to get a numerical solution. A detailed parametric analysis was carried out to highlight the impact of various schemes of material distributions, volume fractions and the EF parameters on the deflection of FG CNTs/Fiber reinforced composite beam.