A Quasi-3D Higher-Order Theory for Bending of FG Nanoplates Embedded in an Elastic Medium in a Thermal Environment

Ashraf M. Zenkour, Mashhour A. Alazwari and Ahmed F. Radwan
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Ashraf M. Zenkour: Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
Mashhour A. Alazwari: Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Ahmed F. Radwan: Department of Mathematics and Statistics, High Institute of Management and Information Technology, Nile for Science and Technology Kafrelsheikh, Kafrelsheikh 33514, Egypt

Mathematics, 2022, vol. 10, issue 2, 1-19

Abstract: This paper presents the effects of temperature and the nonlocal coefficient on the bending response of functionally graded (FG) nanoplates embedded in an elastic foundation in a thermal environment. The effects of transverse normal strain, as well as transverse shear strains, are considered where the variation of the material properties of the FG nanoplate are considered only in thickness direction. Unlike other shear and deformations theories in which the number of unknown functions is five and more, the present work uses shear and deformations theory with only four unknown functions. The four-unknown normal and shear deformations model, associated with Eringen nonlocal elasticity theory, is used to derive the equations of equilibrium utilizing the principle of virtual displacements. The effects due to nonlocal coefficient, side-to-thickness ratio, aspect ratio, normal and shear deformations, thermal load and elastic foundation parameters, as well as the gradation in FG nanoplate bending, are investigated. In addition, for validation, the results obtained from the present work are compared to ones available in the literature.

Keywords: nonlocal theory; FG nanoplates; thermal load; four-unknown normal and shear deformations theory; elastic foundations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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