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Advances in Nano Research
  Volume 11, Number 6, December 2021 , pages 621-640
DOI: https://doi.org/10.12989/anr.2021.11.6.621
 


Novel four-unknowns quasi 3D theory for bending, buckling and free vibration of functionally graded carbon nanotubes reinforced composite laminated nanoplates
Adnan I. Khadir, Ahmed Amine Daikh, Mohamed A. Eltaher

 
Abstract
    Effect of thickness stretching on mechanical behavior of functionally graded (FG) carbon nanotubes reinforced composite (CNTRC) laminated nanoplates resting on elastic foundation is analyzed in this paper using a novel quasi 3D higher-order shear deformation theory. The key feature of this theoretical formulation is that, in addition to considering the thickness stretching effect, the number of unknowns of the displacement field is reduced to four, and which is more than five in the other models. Single-walled carbon nanotubes (SWCNTs) are the reinforced elements and are distributed with four power-law functions which are, uniform distribution, V-distribution, O-distribution and X-distribution. To cover various boundary conditions, an analytical solution is developed based on Galerkin method to solve the governing equilibrium equations by considering the nonlocal strain gradient theory. A modified two-dimensional variable Winkler elastic foundation is proposed in this study for the first time. A parametric study is executed to determine the influence of the reinforcement patterns, power-law index, nonlocal parameter, length scale parameter, thickness and aspect ratios, elastic foundation, thermal environments, and various boundary conditions on stresses, displacements, buckling loads and frequencies of the CNTRC laminated nanoplate.
 
Key Words
    bending; buckling; free vibration; galerkin method; nonlocal strain gradient theory; quasi 3D shear deformation theory; variable Winkler elastic foundation
 
Address
Adnan I. Khadir: Faculty of Engineering, Mechanical Engineering Department, King Abdulaziz University, P.O. Box 80204, Jeddah, Saudi Arabia/ Faculty of Engineering, Mechanical Engineering Department, Jordan University of Science and Technology, P.O. Box 3030, 2011 Irbid, Jordan

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. 29000 Mascara, Algérie

Mohamed A. Eltaher: Faculty of Engineering, Mechanical Engineering Department, King Abdulaziz University, P.O. Box 80204, Jeddah, Saudi Arabia/ Faculty of Engineering, Mechanical Design and Production Department, Zagazig University, P.O. Box 44519, Zagazig, Egypt
 

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