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The Nonlinear Bending of Sector Nanoplate via Higher-Order Shear Deformation Theory and Nonlocal Strain Gradient Theory

Author

Listed:
  • Mostafa Sadeghian

    (Faculty of Mechanical Engineering and Design, Kaunas University of Technology, Studentu 56, 51424 Kaunas, Lithuania)

  • Asif Jamil

    (Faculty of Mechanical Engineering and Design, Kaunas University of Technology, Studentu 56, 51424 Kaunas, Lithuania)

  • Arvydas Palevicius

    (Faculty of Mechanical Engineering and Design, Kaunas University of Technology, Studentu 56, 51424 Kaunas, Lithuania)

  • Giedrius Janusas

    (Faculty of Mechanical Engineering and Design, Kaunas University of Technology, Studentu 56, 51424 Kaunas, Lithuania)

  • Vytenis Naginevicius

    (Study Programmes Department, Kaunas University of Applied Engineering Sciences, 50155 Kaunas, Lithuania)

Abstract

In this context, the nonlinear bending investigation of a sector nanoplate on the elastic foundation is carried out with the aid of the nonlocal strain gradient theory. The governing relations of the graphene plate are derived based on the higher-order shear deformation theory (HSDT) and considering von Karman nonlinear strains. Contrary to the first shear deformation theory (FSDT), HSDT offers an acceptable distribution for shear stress along the thickness and removes the defects of FSDT by presenting acceptable precision without a shear correction parameter. Since the governing equations are two-dimensional and partial differential, the extended Kantorovich method (EKM) and differential quadrature (DQM) have been used to solve the equations. Furthermore, the numeric outcomes were compared with a reference, which shows good harmony between them. Eventually, the effects of small-scale parameters, load, boundary conditions, geometric dimensions, and elastic foundations are studied on maximum nondimensional deflection. It can be concluded that small-scale parameters influence the deflection of the sector nanoplate significantly.

Suggested Citation

  • Mostafa Sadeghian & Asif Jamil & Arvydas Palevicius & Giedrius Janusas & Vytenis Naginevicius, 2024. "The Nonlinear Bending of Sector Nanoplate via Higher-Order Shear Deformation Theory and Nonlocal Strain Gradient Theory," Mathematics, MDPI, vol. 12(8), pages 1-16, April.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:8:p:1134-:d:1372923
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    Cited by:

    1. Mostafa Sadeghian & Arvydas Palevicius & Paulius Griskevicius & Giedrius Janusas, 2024. "Nonlinear Analysis of the Multi-Layered Nanoplates," Mathematics, MDPI, vol. 12(22), pages 1-19, November.

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