Steel and Composite Structures

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On bending of cutout nanobeams based on nonlocal strain gradient elasticity theory

  • Alazwari, Mashhour A. (Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University) ;
  • Eltaher, Mohamed A. (Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University) ;
  • Abdelrahman, Alaa A. (Mechanical Design & Production Department, Faculty of Engineering, Zagazig University)
  • Received : 2020.01.23
  • Accepted : 2022.04.18
  • Published : 2022.06.25
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Abstract

This article aims to investigate the size dependent bending behavior of perforated nanobeams incorporating the nonlocal and the microstructure effects based on the nonlocal strain gradient elasticity theory (NSGET). Shear deformation effect due to cutout process is studied by using Timoshenko beams theory. Closed formulas for the equivalent geometrical characteristics of regularly squared cutout shape are derived. The governing equations of motion considering the nonlocal and microstructure effects are derived in comprehensive procedure and nonclassical boundary conditions are presented. Analytical solution for the governing equations of motion is derived. The derived non-classical analytical solutions are verified by comparing the obtained results with the available results in the literature and good agreement is observed. Numerical results are obtained and discussed. Parametric studies are conducted to explore effects of perforation characteristics, the nonclassical material parameters, beam slenderness ratio as well as the boundary and loading conditions on the non-classical transverse bending behavior of cutout nanobeams. Results obtained are supportive for the design, analysis and manufacturing of such nanosized structural system.

Keywords

Acknowledgement

This work was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, under grant No. (D-747-135-1443). The authors, therefore, acknowledge with thanks DSR technical and financial support.

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