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

Afaf S. Alwabli, Abdelhakim Kaci, Hichem Bellifa, Abdelmoumen Anis Bousahla, Abdelouahed Tounsi, Dhafer A. Alzahrani, Aala A. Abulfaraj, Fouad Bourada, Kouider Halim Benrahou, Abdeldjebbar Tounsi, S.R. Mahmoud and Muzamal Hussain

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.

Key Words

protein microtubules; modified strain gradient theory; single variable beam theory; buckling

Address

(1) Afaf S. Alwabli, Dhafer A. Alzahrani, Aala A. Abulfaraj: Department of Biological Sciences, Rabigh College of Science and Arts, King Abdulaziz University, Rabigh 21911, Saudi Arabia (2) Abdelhakim Kaci, Hichem Bellifa, Fouad Bourada, Kouider Halim Benrahou: Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria (3) Abdelhakim Kaci: Université Dr Tahar Moulay, Faculté de Technologie, Département de Génie Civil et Hydraulique, BP 138 Cité En-Nasr 20000 Saida, Algeria (4) Abdelmoumen Anis Bousahla: Laboratoire de Modélisation et Simulation Multi-échelle, Département de Physique, Faculté des Sciences Exactes, Département de Physique, Université de Sidi Bel Abbés, Algeria (5) Abdelmoumen Anis Bousahla, Abdelouahed Tounsi, Fouad Bourada, Kouider Halim Benrahou, Abdeldjebbar Tounsi: Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia (6) Abdelouahed Tounsi: YFL (Yonsei Frontier Lab), Yonsei University, Seoul, Korea (7) Fouad Bourada: Département des Sciences et de la Technologie, centre universitaire de Tissemsilt, BP 38004 Ben Hamouda, Algeria (8) S.R. Mahmoud: King Abdulaziz University, Faculty of Applied Studies, GRC Department, Jeddah, Saudi Arabia (9) Muzamal Hussain: Department of Mathematics, Govt. College University Faisalabad, 38000, Faisalabad, Pakistan

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