Confinement effectiveness of Timoshenko and Euler Bernoulli theories on buckling of microfilaments

Muhammad Taj , Mohamed A. Khadimallah , Muzamal Hussain , Shaid Mahmood , Muhammad Safeer , Abdullah F. Al Naim , Manzoor Ahmad

Abstract

Study of cytoskeleton components have been the topic of interest during the last few decades. The key components of cytoskeleton are microtubules, microfilaments and intermediate filaments. These components provide shapes and give strength to the cell and also perform many other functions. While performing various functions, these components vibrate, buckle and bend with the effects of each other. The critical buckling force is investigated for length of filament using Timoshenko beam theory and Euler Bernoulli beam theory with various boundary conditions. Moreover, for these both theories the critical buckling force with surface effects is analyzed to length of filament by using various boundary conditions. The buckling behavior of microfilaments without and with the effects of the surface. We found that with surface effects, the critical buckling force increases due to mechanical coupling with the surrounding surface. Our results well demonstrate the physical situation of the components.

Key Words

microfilaments (actin-filaments); buckling; residual stress; young's Laplace equation

Address

Muhammad Taj — Department of Mathematics, University of Azad Jammu and Kashmir, Muzaffarabad, 1300, Azad Kashmir, Pakistan
Mohamed A. Khadimallah — Prince Sattam Bin Abdulaziz University, College of Engineering, Civil Engineering Department, BP 655, Al-Kharj, 16273, Saudi Arabia; Laboratory of Systems and Applied Mechanics, Polytechnic School of Tunisia, University of Carthage, Tunis, Tunisia
Muzamal Hussain — Department of Mathematics, Govt. College University Faisalabad, 38000, Faisalabad, Pakistan
Shaid Mahmood — Department of Mathematics, University of Azad Jammu and Kashmir, Muzaffarabad, 1300, Azad Kashmir, Pakistan
Muhammad Safeer — Department of Mathematics, University of Azad Jammu and Kashmir, Muzaffarabad, 1300, Azad Kashmir, Pakistan; Department of Mathematics University of Poonch Rawalwkot 12350 Azad Kashmir, Pakistan
Abdullah F. Al Naim — Department of Physics, College of Science, King Faisal University, P.O. Box 400,Al-Ahsa 31982, Saudi Arabia
Manzoor Ahmad — Department of Mathematics, University of Azad Jammu and Kashmir, Muzaffarabad, 1300, Azad Kashmir, Pakistan

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