Static analysis of multilayer nonlocal strain gradient nanobeam reinforced by carbon nanotubes
Ahmed Amine Daikh,Ahmed Drai,Mohamed Sid Ahmed Houari,Mohamed A. Eltaher
Abstract
This article presents a comprehensive static analysis of simply supported cross-ply carbon nanotubes reinforced composite (CNTRC) laminated nanobeams under various loading profiles. The nonlocal strain gradient constitutive relation is exploited to present the size-dependence of nano-scale. New higher shear deformation beam theory with hyperbolic function is proposed to satisfy the zero-shear effect at boundaries and parabolic variation through the thickness. Carbon nanotubes (CNTs), as the reinforced elements, are distributed through the beam thickness with different distribution functions, which are, uniform distribution (UD-CNTRC), V- distribution (FG-V CNTRC), O- distribution (FG-O CNTRC) and X- distribution (FG-X CNTRC). The equilibrium equations are derived, and Fourier series function are used to solve the obtained differential equation and get the response of nanobeam under uniform, linear or sinusoidal mechanical loadings. Numerical results are obtained to present influences of CNTs reinforcement patterns, composite laminate structure, nonlocal parameter, length scale parameter, geometric parameters on center deflection ad stresses of CNTRC laminated nanobeams. The proposed model is effective in analysis and design of composite structure ranging from macro-scale to nano-scale.
Key Words
static and stress analysis; Nonlocal strain gradient theory; hyperbolic shear deformation theory; carbon nanotubes reinforced nanobeams; fourier series
Address
Ahmed Amine Daikh — Department of Civil Engineering, Laboratoire d\'Etude des Structures et de Meecanique des Mateeriaux, Mascara, Algeria; Mechanics of Structures and Solids Laboratory, Faculty of Technology, University of Sidi Bel Abbes, Sidi Bel Abbes, Algeria
Ahmed Drai — Department of Mechanical Engineering, Mustapha STAMBOULI, University of Mascara, 29000, Algeria; LABAB Laboratory of ENPO, Oran, 31000, Algeria
Mohamed Sid Ahmed Houari — Department of Civil Engineering, Laboratoire d\'Etude des Structures et de Meecanique des Mateeriaux, Mascara, Algeria
Mohamed A. Eltaher — Faculty of Engineering, Department of Mechanical Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah, Saudi Arabia; Faculty of Engineering, Department of Mechanical Design and Production, Zagazig University, P.O. Box 44519, Zagazig, Egypt
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