Bending of axially functionally graded carbon nanotubes reinforced composite nanobeams

Ahmed Drai , Ahmed Amine Daikh , Mohamed Oujedi Belarbi , Mohammed Sid Ahmed Houari , Benoumer Aour , Amin Hamdi , Mohamed A. Eltaher

Abstract

This work presents a modified analytical model for the bending behavior of axially functionally graded (AFG) carbon nanotubes reinforced composite (CNTRC) nanobeams. New higher order shear deformation beam theory is exploited to satisfy parabolic variation of shear through thickness direction and zero shears at the bottom and top surfaces.A Modified continuum nonlocal strain gradient theoryis employed to include the microstructure and the geometrical nano-size length scales. The extended rule of the mixture and the molecular dynamics simulations are exploited to evaluate the equivalent mechanical properties of FG-CNTRC beams. Carbon nanotubes reinforcements are distributed axially through the beam length direction with a new power graded function with two parameters. The equilibrium equations are derived with associated nonclassical boundary conditions, and Navier's procedure are used to solve the obtained differential equation and get the response of nanobeam under uniform, linear, or sinusoidal mechanical loadings. Numerical results are carried out to investigate the impact of inhomogeneity parameters, geometrical parameters, loadings type, nonlocal and length scale parameters on deflections and stresses of the AFG CNTRC nanobeams. The proposed model can be used in the design and analysis of MEMS and NEMS systems fabricated from carbon nanotubes reinforced composite nanobeam.

Key Words

analytical solution; axially CNts distribution; new higher order shear deformation; nonlocal strain gradient theory; static bending and stress analyses

Address

Ahmed Drai — Department of Mechanical Engineering, Mustapha STAMBOULI University of Mascara, 29000, Algeria/ LABAB Laboratory of ENPO, Oran, 31000, Algeria
Ahmed Amine Daikh — Department of Technology, University Centre of Naama, Naama 45000, Algeria/ Laboratoire d'Etude des Structures et de Mécanique des Matériaux, Département de Génie Civil, Faculté des Sciences et de la Technologie, Université Mustapha Stambouli B.P. 305, R.P. 29000 Mascara, Algérie
Mohamed Oujedi Belarbi — Laboratoire de Recherche en Génie Civil, LRGC, Université de Biskra, B.P. 145, R.P. 07000, Biskra, Algeria
Mohammed Sid Ahmed Houari — Laboratoire d'Etude des Structures et de Mécanique des Matériaux, Département de Génie Civil, Faculté des Sciences et de la Technologie, Université Mustapha Stambouli B.P. 305, R.P. 29000 Mascara, Algérie
Benoumer Aour — LABAB Laboratory of ENPO, Oran, 31000, Algeria
Amin Hamdi — Department of Civil Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah, Saudi Arabia
Mohamed A. Eltaher — Faculty of Engineering, Mechanical Design and Production Department, Zagazig University, P.O. Box 44519, Zagazig, Egypt/ Faculty of Engineering, Mechanical Engineering Department, King Abdulaziz University, P.O. Box 80204, Jeddah, Saudi Arabia

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