Geometric non-linear analysis of auxetic hybrid laminated beams containing CNT reinforced composite materials

In the current work, a novel hybrid laminate with negative Poisson's ratio (NPR) is developed by considering auxetic laminate which is composed of carbon nanotube-reinforced composite (CNTRC) and fiber-reinforced composite (FRC) materials. The maximum magnitude of out-of-plane NPR is identified in the case of (20 F/20 C/-20 C/20 C) S laminate as well. Meanwhile, a method for the geometric non-linear analysis of hybrid laminated beam with NPR including the non-linear bending, free, and forced vibrations is proposed. The beam deformation is modeled by combining higher-order shear-deformation theory (HSDT) and large deflection theory. Based on a two-step perturbation approach, the asymptotic solutions of the governing equations are obtained to capture the linear and non-linear frequencies and load-deflection curves. Moreover, a two-step perturbation methodology in conjunction with fourth-order Runge-Kutta method is employed to solve the forced-vibration problem. Several key factors, such as CNT distribution, variations in the elastic foundation, and thermal stress, are considered in the exhaustive analysis. Theoretical results for some particular cases are given to examine the geometric non-linearity behavior of hybrid beam with NPR as well as positive Poisson's ratio (PPR).