Modified porosity model in analysis of functionally graded porous nanobeams

  • M. A. Eltaher
  • N. Fouda
  • Tawfik El-midany
  • A. M. Sadoun
Technical Paper


This work studies the mechanical bending and vibration of functionally graded nanobeams using finite elements according to Euler beam theory. We implement a modified porosity model that represents porosity and Young’s modulus in an implicit form, where the density is assumed as a function of the porosity parameter, while Young’s modulus is assumed as a ratio of the mass density with porosity to that without porosity. The effect of nano-scale is described by the nonlocal continuum theory by adding the length scale into the constitutive equations as a material parameter comprising information about nanoscopic forces and its interactions. The material gradation of constituents is described by a power function through the thickness of nanobeam. The beam is simply supported and is assumed to be thin, and hence, the kinematic assumptions of Euler–Bernoulli beam theory are held. The mathematical model is solved numerically using the finite-element method. Numerical results show that the increase of porosity, material graduation, and nano-scale parameters tend to decrease the bending resistance as well as the fundamental frequencies of the nanobeam.


Functionally graded material Modified porosity model Nanobeams Finite-element method 


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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2018

Authors and Affiliations

  • M. A. Eltaher
    • 1
    • 2
  • N. Fouda
    • 3
  • Tawfik El-midany
    • 3
  • A. M. Sadoun
    • 2
  1. 1.Department of Mechanical Engineering, Faculty of EngineeringKing Abdulaziz UniversityJeddahSaudi Arabia
  2. 2.Mechanical Design and Production Department, Faculty of EngineeringZagazig UniversityZagazigEgypt
  3. 3.Production Engineering and Mechanical Design Department, Faculty of EngineeringMansoura UniversityMansouraEgypt

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