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Steel and Composite Structures
  Volume 35, Number 4, May25 2020, pages 555-566
DOI: http://dx.doi.org/10.12989/scs.2020.35.4.555
 


Stability of perforated nanobeams incorporating surface energy effects
Khalid H. Almitani, Alaa A. Abdelrahman and Mohamed A. Eltaher

 
Abstract
    This paper aims to present an analytical methodology to investigate influences of nanoscale and surface energy on buckling stability behavior of perforated nanobeam structural element, for the first time. The surface energy effect is exploited to consider the free energy on the surface of nanobeam by using Gurtin-Murdoch surface elasticity theory. Thin and thick beams are considered by using both classical beam of Euler and first order shear deformation of Timoshenko theories, respectively. Equivalent geometrical constant of regularly squared perforated beam are presented in simplified form. Problem formulation of nanostructure beam including surface energies is derived in detail. Explicit analytical solution for nanoscale beams are developed for both beam theories to evaluate the surface stress effects and size-dependent nanoscale on the critical buckling loads. The closed form solution is confirmed and proven by comparing the obtained results with previous works. Parametric studies are achieved to demonstrate impacts of beam filling ratio, the number of hole rows, surface material characteristics, beam slenderness ratio, boundary conditions as well as loading conditions on the non-classical buckling of perforated nanobeams in incidence of surface effects. It is found that, the surface residual stress has more significant effect on the critical buckling loads with the corresponding effect of the surface elasticity. The proposed model can be used as benchmarks in designing, analysis and manufacturing of perforated nanobeams.
 
Key Words
    surface energy effects; perforated nanobeams; thin and thick beams; non-classical; buckling; analytical solution
 
Address
Khalid H. Almitani: Department of Mechanical Engineering, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah, Saudi Arabia
Alaa A. Abdelrahman: Department of Mechanical Design & Production, Faculty of Engineering, Zagazig University, P.O. Box 44519, Zagazig, Egypt
Mohamed A. Eltaher: Department of Mechanical Engineering, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah, Saudi Arabia;
Department of Mechanical Design & Production, Faculty of Engineering, Zagazig University, P.O. Box 44519, Zagazig, Egypt
 

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