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    Geometrically Nonlinear Static Analysis of an Embedded Multiwalled Carbon Nanotube and the van der Waals Interaction

    Source: Journal of Nanomechanics and Micromechanics:;2017:;Volume ( 007 ):;issue: 004
    Author:
    Chih-Ping Wu
    ,
    Zong-Li Hong
    ,
    Yung-Ming Wang
    DOI: 10.1061/(ASCE)NM.2153-5477.0000134
    Abstract: On the basis of Reissner’s mixed variational theorem (RMVT), rather than the principle of virtual displacement (PVD), the authors presented a nonlocal Timoshenko beam theory (TBT) for the geometrically nonlinear static analysis of multiwalled carbon nanotubes (MWCNT) embedded in an elastic medium. The embedded MWCNT was subjected to mechanical loads on its outer-most surface, with combinations of free, simply supported, and clamped edge conditions. The van der Waals interaction between any pair of walls constituting the MWCNT was considered, and the interaction between the MWCNT and its surrounding medium was simulated using the Pasternak-type foundation model. In the formulation, the governing equations of a typical wall and the associated boundary conditions were derived, in which von Kármán geometrical nonlinearity was considered. Eringen’s nonlocal elasticity theory was used to account for the small-length scale effect. The deformations induced in the embedded MWCNT were obtained using the differential quadrature method and a direct iteration approach. In the numerical examples, solutions of the RMVT-based nonlocal TBT converged rapidly, and the convergent solutions of its linear counterpart closely agreed with the analytical and numerical solutions of the PVD-based nonlocal beam theories available in the literature.
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      Geometrically Nonlinear Static Analysis of an Embedded Multiwalled Carbon Nanotube and the van der Waals Interaction

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    http://yetl.yabesh.ir/yetl1/handle/yetl/4244087
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    contributor authorChih-Ping Wu
    contributor authorZong-Li Hong
    contributor authorYung-Ming Wang
    date accessioned2017-12-30T12:58:32Z
    date available2017-12-30T12:58:32Z
    date issued2017
    identifier other%28ASCE%29NM.2153-5477.0000134.pdf
    identifier urihttp://138.201.223.254:8080/yetl1/handle/yetl/4244087
    description abstractOn the basis of Reissner’s mixed variational theorem (RMVT), rather than the principle of virtual displacement (PVD), the authors presented a nonlocal Timoshenko beam theory (TBT) for the geometrically nonlinear static analysis of multiwalled carbon nanotubes (MWCNT) embedded in an elastic medium. The embedded MWCNT was subjected to mechanical loads on its outer-most surface, with combinations of free, simply supported, and clamped edge conditions. The van der Waals interaction between any pair of walls constituting the MWCNT was considered, and the interaction between the MWCNT and its surrounding medium was simulated using the Pasternak-type foundation model. In the formulation, the governing equations of a typical wall and the associated boundary conditions were derived, in which von Kármán geometrical nonlinearity was considered. Eringen’s nonlocal elasticity theory was used to account for the small-length scale effect. The deformations induced in the embedded MWCNT were obtained using the differential quadrature method and a direct iteration approach. In the numerical examples, solutions of the RMVT-based nonlocal TBT converged rapidly, and the convergent solutions of its linear counterpart closely agreed with the analytical and numerical solutions of the PVD-based nonlocal beam theories available in the literature.
    titleGeometrically Nonlinear Static Analysis of an Embedded Multiwalled Carbon Nanotube and the van der Waals Interaction
    typeJournal Paper
    journal volume7
    journal issue4
    journal titleJournal of Nanomechanics and Micromechanics
    identifier doi10.1061/(ASCE)NM.2153-5477.0000134
    page04017012
    treeJournal of Nanomechanics and Micromechanics:;2017:;Volume ( 007 ):;issue: 004
    contenttypeFulltext
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