Structural Engineering and Mechanics

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Nonlocal strain gradient theory for bending analysis of 2D functionally graded nanobeams

  • Aicha Bessaim (Laboratoire d'Etude des Structures et de Mecanique des Materiaux, Departement de Genie Civil, Faculte des Sciences et de la Technologie, Universite Mustapha Stambouli) ;
  • Mohammed Sid Ahmed Houari (Laboratoire d'Etude des Structures et de Mecanique des Materiaux, Departement de Genie Civil, Faculte des Sciences et de la Technologie, Universite Mustapha Stambouli) ;
  • Smain Bezzina (Mechanical. Engineering Department, King Abdulaziz University) ;
  • Ali Merdji (Department of Mechanical Engineering, Faculty of Science and Technology, University of Mascara) ;
  • Ahmed Amine Daikh (Laboratoire d'Etude des Structures et de Mecanique des Materiaux, Departement de Genie Civil, Faculte des Sciences et de la Technologie, Universite Mustapha Stambouli) ;
  • Mohamed-Ouejdi Belarbi (Laboratoire de Recherche en Genie Civil, LRGC, Universite de Biskra) ;
  • Abdelouahed Tounsi (YFL (Yonsei Frontier Lab), Yonsei University)
  • Received : 2022.12.21
  • Accepted : 2023.04.03
  • Published : 2023.06.25
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Abstract

This article presents an analytical approach to explore the bending behaviour of of two-dimensional (2D) functionally graded (FG) nanobeams based on a two-variable higher-order shear deformation theory and nonlocal strain gradient theory. The kinematic relations are proposed according to novel trigonometric functions. The material gradation and material properties are varied along the longitudinal and the transversal directions. The equilibrium equations are obtained by using the virtual work principle and solved by applying Navier's technique. A comparative evaluation of results against predictions from literature demonstrates the accuracy of the proposed analytical model. Moreover, a detailed parametric analysis checks for the sensitivity of the bending and stresses response of (2D) FG nanobeams to nonlocal length scale, strain gradient microstructure scale, material distribution and geometry.

Keywords

Acknowledgement

This research work was funded by Institutional Fund Projects under grand no. (IFPIP: 845-305-1443). The authors gratefully acknowledge technical and financial support provided by the Ministry of Education and King Abdulaziz University, DSR, Jeddah, Saudi Arabia.

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