Advances in nano research

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The nano scale buckling properties of isolated protein microtubules based on modified strain gradient theory and a new single variable trigonometric beam theory

  • Alwabli, Afaf S. (Department of Biological Sciences, Rabigh College of Science and Arts, King Abdulaziz University) ;
  • Kaci, Abdelhakim (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Bellifa, Hichem (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Bousahla, Abdelmoumen Anis (Laboratoire de Modelisation et Simulation Multi-echelle, Departement de Physique, Faculte des Sciences Exactes, Departement de Physique, Universite de Sidi Bel Abbes) ;
  • Tounsi, Abdelouahed (Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals) ;
  • Alzahrani, Dhafer A. (Department of Biological Sciences, Rabigh College of Science and Arts, King Abdulaziz University) ;
  • Abulfaraj, Aala A. (Department of Biological Sciences, Rabigh College of Science and Arts, King Abdulaziz University) ;
  • Bourada, Fouad (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Benrahou, Kouider Halim (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Tounsi, Abdeldjebbar (Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals) ;
  • Mahmoud, S.R. (King Abdulaziz University, Faculty of Applied Studies, GRC Department) ;
  • Hussain, Muzamal (Department of Mathematics, Govt. College University Faisalabad)
  • Received : 2019.11.05
  • Accepted : 2020.10.11
  • Published : 2021.01.25
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Abstract

Microtubules (MTs) are the main part of the cytoskeleton in living eukaryotic cells. In this article, a mechanical model of MT buckling, considering the modified strain gradient theory, is analytically examined. The MT is assumed as a cylindrical beam and a new single variable trigonometric beam theory is developed in conjunction with a modified strain gradient model. The main benefit of the present formulation is shown in its new kinematic where we found only one unknown as the Euler-Bernoulli beam model, which is even less than the Timoshenko beam model. The governing equations are deduced by considering virtual work principle. The effectiveness of the present method is checked by comparing the obtained results with those reported by other higher shear deformation beam theory involving a higher number of unknowns. It is shown that microstructure-dependent response is more important when material length scale parameters are closer to the outer diameter of MTs. Also, it can be confirmed that influences of shear deformation become more considerable for smaller shear modulus and aspect ratios.

Keywords

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