A nonlocal strain gradient model for buckling analysis of advanced FG CNT-reinforced composite nanobeams

Djillali Mokhefi , Aicha Bessaim , Mohammed Sid Ahmed Houari , Zakaria Deffane , Hakima Houari-Belkadi , Belhocine Ali , Ahmed Amine Daikh , Habib Hebali , Hadj Youzera , Tarek Merzouki

Abstract

The main objective of this paper is to investigate the buckling behavior of symmetric and non-symmetric carbon nanotube-reinforced composite (CNTRC) nanobeams with nonlocal strain gradient effects. For this purpose, a novel trigonometric shear deformation beam theory is employed, and the Galerkin method is used for analysis. The carbon nanotube-reinforced composite beam consists of a polymeric matrix reinforced with aligned and distributed single-walled carbon nanotubes (SWCNTs) having various reinforcement patterns. The material properties of the carbon nanotube-reinforced composite beams are estimated using the rule of mixture. The governing equations of the problem are derived based on the principle of total potential energy. The proposed theory accurately represents the parabolic distribution of transverse shear stress across the beam thickness and satisfies the zero traction boundary conditions on the top and bottom surfaces without requiring shear correction factors. The mathematical models presented in this work are validated numerically by comparing them with existing literature to assess their accuracy and reliability. The buckling analyses of the carbon nanotube-reinforced composite nanobeams are conducted, considering various factors such as beam types, nonlocal length-scale parameter, strain gradient microstructure-scale parameter, geometry, carbon nanotube volume fraction, and boundary conditions. Additionally, new results are reported in this study, which can serve as a benchmark for future research.

Key Words

CNTRC beams; elastic buckling; Galerkin method; higher order nonlocal strain gradient theory; shear deformation beam theory

Address

Djillali Mokhefi, Aicha Bessaim, Mohammed Sid Ahmed Houari — 1Laboratoire 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., Mascara 29000, Algeria
Zakaria Deffane — Aerospace Engineering Division, Universitat Politécnica de Catalunya, 08034, Barcelona, Spain
Hakima Houari-Belkadi — Dental Technology and Biomaterials Research Laboratory, Department of Dentistry-Oran's, Faculty of Medicine, University of Oran, 31000, Algeria
Belhocine Ali — 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., Mascara 29000, Algeria
Ahmed Amine Daikh — 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., Mascara 29000, Algeria; Artificial Intelligence Laboratory for Mechanical and Civil Structures, and Soil, University Centre of Naama, P.O. Box 66, Naama 45000, Algeria
Habib Hebali, Hadj Youzera — 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., Mascara 29000, Algeria
Tarek Merzouki — LISV, University of Versailles Saint-Quentin, 10-12 avenue de l'Europe, 78140 Vélizy, France

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