Static, buckling, and free vibration responses of functionally graded carbon nanotube-reinforced composite beams with elastic foundation in non-polynomial framework

Abstract

In this work, the static, buckling, and free vibration analysis of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) beam resting on a Pasternak elastic foundation are studied. The secant function-based shear deformation theory (SFSDT) is used for this analysis. This theory fulfills the traction-free boundary conditions at the top and bottom surfaces of the beam, hence there is no need for a shear correction factor. Hamilton’s principle is used to determine the governing differential equations and boundary conditions whereas Navier’s solution technique is used for determining the closed-form solution. The analytical approach is used to examine the deflection, stresses, critical buckling load, and natural frequencies of the FG-CNTRC beam resting on the Pasternak elastic foundation including a shear layer and Winkler springs. To determine the material characteristics of FG-CNTRC beams, the Rule of the mixture is used. Uniform distribution (UD-beam), FG-X beam, FG-O beam, and FG-V beam are the different forms of CNT reinforcement distribution that are used in this study. Considering different span thickness ratios, the volume fraction and distribution of CNT, the Winkler spring, and the shear layer constant factors, all the structural responses are predicted. It is also observed that the present theory predicts the structural responses of the FG-CNTRC beam accurately when compared to other existing theories. A few new results are also included as the benchmark solutions for the new research.