A non-polynomial axiomatic framework to investigate the structural responses of CNT-reinforced beams: An analytical solution

Abstract

The current research work investigates the static, buckling, and free vibration behavior of carbon nanotube-reinforced composite (CNTRC) beam using the inverse hyperbolic shear deformation theory. This theory is based upon the shear strain shape function yielding a nonlinear distribution of transverse shear stresses and inherently satisfies the traction-free boundary conditions at the upper and lower surfaces of the beam structures omitting the requirement of the shear correction factor. The governing differential equations are developed using Hamilton's principle, and the closed-form solutions are obtained using Navier's approach. The rule of mixture is adopted to estimate the material characteristics of CNTRC beams. The four different ways of CNT’s reinforcement distribution are used such as uniform distribution, O-beam, X-beam, and V-beam for the analysis. The analytical results in terms of deflection, stresses, critical buckling load as well as natural frequencies of the CNT-reinforced composite beam are obtained for various span thickness ratios, CNT volume fractions, and CNT reinforcement distributions. The result shows that the present theory predicts the responses of the CNTRC beam quite accurately as compared to the existing theories. Some new results are also included for the benchmark solutions of the new research. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024.