Static, Buckling, and Free Vibration Analysis of CNT Reinforced Composite Beams with Elastic Foundation Using IHSDT

Abstract

Purpose: A carbon nanotube-reinforced composite (CNTRC) beam resting on a Pasternak elastic foundation which consists of a Winkler spring and shear layer is investigated to obtain the bending, buckling, and free vibration responses using inverse hyperbolic shear deformation theory (IHSDT). The shear strain shape function is employed in this study to construct a nonlinear distribution of transverse shear stresses. The theory fulfills the traction-free boundary conditions on both the upper and lower surfaces of the beam, hence no shear correction factor is needed. Methods: Hamilton’s principle is employed to derive the equation of motion and Navier’s solution technique is used to determining the closed-from solution for the CNTRC beam on the Pasternak foundation. To determine the material properties of CNTRC beams, the rule of mixture is used. In this study, various types of CNT reinforcement distribution are used such as uniform distribution (UD-Beam), X-Beam, O-Beam, and V-Beam. Results: The deformation, stresses, critical buckling load, and natural frequencies of the simply supported CNTRC beam resting on the Pasternak elastic foundation are investigated using an analytical approach, that takes into account various length-to-thickness ratios, CNT volume fraction, CNT distribution, Winkler spring constant factor, and shear layer constant factor. Conclusion: The present theory predicts the structural responses quite accurately compared to the available theories in the literature. Some new results are also included for the benchmark solutions for the new research. © Springer Nature Singapore Pte Ltd. 2024.