Resumen de Application of Hencky bar-chain model to buckling analysis of elastically restrained Timoshenko axially functionally graded carbon nanotube reinforced composite beams

M. Rezaiee-Pajand, Maryam Mokhtarian, SeyedMojtaba Hozhabrossadati

• Carbon nanotube (CNT) reinforced composites are receiving global attention of the researchers due to their outstanding features. In this context, very limited studies have been carried out addressing the behavior of axially functionally graded carbon nanotube reinforced composites (AFGCNTRC). Within the framework of Timoshenko beam theory, this article aims to develop the Hencky bar-chain model for buckling investigation of AFG-CNTRC beams. Aligned arrays of single walled carbon nanotubes are assumed to be dispersed in the longitudinal direction of the beam with respect to four different patterns. The beam is also considered to be elastically restrained at both ends. The finite difference method (FDM) is applied for validation of the results and calibration of the end rotational and translational springs. The stiffness of internal springs is also derived using the FDM moment and shear equivalence. The effectiveness of the proposed scheme is established through studying several benchmark problems found in the literature. Numerical results are also provided to illustrate the effects of slenderness, CNT distribution patterns, CNT volume fraction and support rigidity on stability responses of AFG-CNTRC beams