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    A stable and efficient meshfree Galerkin method with consistent integration schemes for strain gradient thin beams and plates

    Access Status
    Fulltext not available
    Authors
    Wang, B.B.
    Lu, Chunsheng
    Fan, C.Y.
    Zhao, M.H.
    Date
    2020
    Type
    Journal Article
    
    Metadata
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    Citation
    Wang, B.B. and Lu, C. and Fan, C.Y. and Zhao, M.H. 2020. A stable and efficient meshfree Galerkin method with consistent integration schemes for strain gradient thin beams and plates. Thin-Walled Structures. 153: Article No. 106791.
    Source Title
    Thin-Walled Structures
    DOI
    10.1016/j.tws.2020.106791
    ISSN
    0263-8231
    Faculty
    Faculty of Science and Engineering
    School
    School of Civil and Mechanical Engineering
    URI
    http://hdl.handle.net/20.500.11937/80195
    Collection
    • Curtin Research Publications
    Abstract

    © 2020 Elsevier Ltd

    The strain gradient (SG) theory, incorporating with thin beam and plate models, can effectively describe size effects of micro- and nano-structures. However, since these models are determined by a sixth-order partial differential equation that requires the C2 continuity of deflection in a Galerkin weak form, it is difficult to make stable and efficient numerical analysis. In this paper, a meshfree Galerkin method is presented for SG thin beams and plates. To satisfy the continuity and convergence requirement, moving least square or reproducing kernel shape functions are employed with cubic approximation bases. To pass the patch test, integration constraints are derived and consistent integration schemes are proposed with nodal smoothed derivatives instead of standard ones on evaluating points. Numerical results show that consistent integration is superior to the standard Gauss integration in convergence, accuracy and efficiency.

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