The nano scale bending and dynamic properties of isolated protein microtubules based on modified strain gradient theory

Djazia Leila Benmansour , Abdelhakim Kaci , Abdelmoumen Anis Bousahla , Houari Heireche , Abdelouahed Tounsi , Afaf S. Alwabli , Alawiah M. Alhebshi , Khalid Al-ghmady , S.R. Mahmoud

Abstract

In this investigation, dynamic and bending behaviors of isolated protein microtubules are analyzed. Microtubules (MTs) can be considered as bio-composite structures that are elements of the cytoskeleton in eukaryotic cells and posses considerable roles in cellular activities. They have higher mechanical characteristics such as superior flexibility and stiffness. In the modeling purpose of microtubules according to a hollow beam element, a novel single variable sinusoidal beam model is proposed with the conjunction of modified strain gradient theory. The advantage of this model is found in its new displacement field involving only one unknown as the Euler-Bernoulli beam theory, which is even less than the Timoshenko beam theory. The equations of motion are constructed by considering Hamilton's principle. The obtained results are validated by comparing them with those given based on higher shear deformation beam theory containing a higher number of variables. A parametric investigation is established to examine the impacts of shear deformation, length scale coefficient, aspect ratio and shear modulus ratio on dynamic and bending behaviors of microtubules. It is remarked that when length scale coefficients are almost identical of the outer diameter of MTs, microstructure-dependent behavior becomes more important.

Key Words

protein microtubules; modified strain gradient theory; single variable beam theory; bending; vibration

Address

(1) Djazia Leila Benmansour, Abdelmoumen Anis Bousahla, Houari Heireche — Laboratoire de Modélisation et Simulation Multi-échelle, Département de Physique, Faculté des Sciences Exactes, Département de Physique, Université de Sidi Bel Abbés, Algeria
(2) Abdelhakim Kaci — Université Dr Tahar Moulay, Faculté de Technologie, Département de Génie Civil et Hydraulique, BP 138 Cité En-Nasr 20000 Saida, Algérie
(3) Abdelhakim Kaci, Abdelouahed Tounsi — Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria
(4) Abdelmoumen Anis Bousahla — Centre Universitaire de Relizane, Algérie
(5) Abdelouahed Tounsi — Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia
(6) Afaf S. Alwabli, Alawiah M. Alhebshi, Khalid Al-ghmady — Department of Biology, Faculty of Sciences, King Abdulaziz University, Jeddah, Saudi Arabia
(7) S.R. Mahmoud — GRC Department, Jeddah Community College, King Abdulaziz University, Jeddah, Saudi Arabia.

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