Bending, buckling and vibration analysis of FG-CNT beams via new polynomial–trigonometric integral shear deformation theory

In the current manuscript, bending, buckling and vibration analysis of functionally graded carbon nanotube reinforced composite beams on the Winkler–Pasternak foundation are presented and discus. The advantages of the present theory over other higher-order theories are the inclusion of a displacement field containing undetermined integral terms. This theory incorporates both shear deformation. In addition, the present theory does not require shear correction factors as in the case of Timoshenko beam theory. A higher-order displacement field variables is proposed to calculate the stability response of functionally graded carbon nanotube-reinforced composite (FG-CNT) beams Hamilton principle and Navier's method to obtain the stability of FG-CNT beams by explaining an eigenvalue problem. Four different carbon nanotubes (CNTs) distributions including uniform and three types of functionally graded distributions of CNTs through the thickness are considered. The rule of mixture is used to describe the effective material properties of the nanocomposite beams. The accuracy of this theory is demonstrated according to some numerical examples and comparisons with the corresponding data in the literature.