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A simple mathematical model of microtubules surrounded by an elastic matrix by nonlocal finite element method

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  • Civalek, Ömer
  • Demir, Cigdem

Abstract

A simple nonlocal beam model is proposed to study buckling response of protein microtubules. The size-effect for buckling model of microtubules is considered by using the nonlocal continuum theory. Finite element procedure is used for solution of nonlocal differential equation of microtubules for elastic stability. The influence of the small length scale on the buckling value is examined for different geometric parameters. The effect of elastic matrix surrounded of microtubules is also examined and some benchmark results are presented.

Suggested Citation

  • Civalek, Ömer & Demir, Cigdem, 2016. "A simple mathematical model of microtubules surrounded by an elastic matrix by nonlocal finite element method," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 335-352.
    • Handle: RePEc:eee:apmaco:v:289:y:2016:i:c:p:335-352
    DOI: 10.1016/j.amc.2016.05.034
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    References listed on IDEAS

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    1. G. R. Liu & Y. Cheng & Dong Mi & Z. R. Li, 2005. "A Study On Self-Insertion Of Peptides Into Single-Walled Carbon Nanotubes Based On Molecular Dynamics Simulation," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 16(08), pages 1239-1250.
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    Cited by:

    1. Jahangiri, M. & Asghari, M., 2023. "The strain gradient-based torsional vibration analysis of micro-rotors with nonlinear flexural-torsional coupling," Applied Mathematics and Computation, Elsevier, vol. 440(C).
    2. Solorza-Calderón, Selene, 2021. "Torsional waves of infinite fully saturated poroelastic cylinders within the framework of Biot viscosity-extended theory," Applied Mathematics and Computation, Elsevier, vol. 391(C).
    3. Imani Aria, A. & Biglari, H., 2018. "Computational vibration and buckling analysis of microtubule bundles based on nonlocal strain gradient theory," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 313-332.
    4. Ali Farajpour & Wendy V. Ingman, 2023. "In-Plane Wave Propagation Analysis of Human Breast Lesions Using a Higher-Order Nonlocal Model and Deep Learning," Mathematics, MDPI, vol. 11(23), pages 1-24, November.

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