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Steel and Composite Structures
  Volume 44, Number 5, September10 2022 , pages 707-720

Multiscale bending and free vibration analyses of functionally graded graphene platelet/ fiber composite beams
A. Garg, T. Mukhopadhyay, H.D. Chalak, M.O. Belarbi, L. Li and R. Sahoo

    In the present work, bending and free vibration analyses of multilayered functionally graded (FG) graphene platelet (GPL) and fiber-reinforced hybrid composite beams are carried out using the parabolic function based shear deformation theory. Parabolic variation of transverse shear stress across the thickness of beam and transverse shear stress-free conditions at top and bottom surfaces of the beam are considered, and the proposed formulation incorporates a transverse displacement field. The present theory works only with four unknowns and is computationally efficient. Hamilton's principle has been employed for deriving the governing equations. Analytical solutions are obtained for both the bending and free vibration problems in the present work considering different variations of GPLs and fibers distribution, namely, FG-X, FG-U, FG-A, , and FG-O for beams having simply-supported boundary condition. First, the matrix is assumed to be strengthened using GPLs, and then the fibers are embedded. Multiscale modeling for material properties of functionally graded graphene platelet/fiber hybrid composites (FGGPL/FHRC) is performed using Halpin-Tsai micromechanical model. The study reveals that the distributions of GPLs and fibers have significant impacts on the stresses, deflections, and natural frequencies of the beam. The number of layers and shape factors widely affect the behavior of FG-GPL-FHRC beams. The multilayered FG-GPL-FHRC beams turn out to be a good approximation to the FG beams without exhibiting the stress-channeling effects.
Key Words
    hybrid composite; bending; free vibration; graphene platelet/fiber composite; functionally graded material
A. Garg:1)Department of Aerospace Engineering, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh, India - 208016
2)Department of Civil and Environmental Engineering, The NorthCap University, Gurugram, Haryana, India – 122017

T. Mukhopadhyay: Department of Aerospace Engineering, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh, India - 208016

H.D. Chalak:Department of Civil Engineering, National Institute of Technology Kurukshetra, Kurukshetra, Haryana, India – 136119

M.O. Belarbi:Laboratoire de Recherche en Génie Civil, LRGC. Université de Biskra B.P. 145, R.P. 07000, Biskra, Algeria

L. Li:State Key Laboratory of Digital Manufacturing Equipment and Technology, School of Mechanical Science and Engineering, Huazhong
University of Science and Technology, Wuhan 430074, China

R. Sahoo: Department of Civil Engineering, Indian Institute of Technology (BHU) Varanasi, Varanasi, Uttar Pradesh, India - 221005

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