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Advances in Cell Mechanics pp 257–316Cite as

Application of Nonlocal Shell Models to Microtubule Buckling in Living Cells

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Abstract

A version of nonlocal elasticity theory is employed to develop a nonlocal shear deformable shell model. The governing equations are based on higher order shear deformation shell theory with a von Kármán-type of kinematic nonlinearity and include small scale effects. These equations are then used to solve buckling problems of microtubules (MTs) embedded in an elastic matrix of cytoplasm subjected to bending. The surrounding elastic medium is modeled as a Pasternak foundation. The thermal effects are also included and the material properties are assumed to be temperature-dependent. The small scale parameter e0a is estimated by matching the buckling curvature of MTs observed from measurements with the numerical results obtained from the nonlocal shear deformable shell model. The numerical results show that buckling loads are decreased with the increasing small scale parameter e0a. The results reveal that the lateral constraint has a significant effect on the buckling moments of a microtubule when the foundation stiffness is sufficiently large.

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Author information

Authors and Affiliations

  1. Department of Engineering Mechanics, Shanghai Jiao Tong University, Shanghai, 200030, People’s Republic of China

    Hui-Shen Shen

  2. State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai, 200030, People’s Republic of China

    Hui-Shen Shen

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  1. Hui-Shen Shen
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Correspondence to Hui-Shen Shen .

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Editors and Affiliations

  1. Department of Civil and Environmental Engineering, The University of California at Berkeley, USA

    Shaofan Li

  2. Centre for Mechanics, Smart Structures and Microsystems, Cape Peninsula University of Technology, Cape Town, South Africa

    Bohua Sun

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© 2011 Higher Education Press, Beijing and Springer-Verlag Berlin Heidelberg

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Shen, HS. (2011). Application of Nonlocal Shell Models to Microtubule Buckling in Living Cells. In: Li, S., Sun, B. (eds) Advances in Cell Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17590-9_9

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  • DOI: https://doi.org/10.1007/978-3-642-17590-9_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-17589-3

  • Online ISBN: 978-3-642-17590-9

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