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    Consistent integration schemes for meshfree analysis of strain gradient elasticity

    Access Status
    Fulltext not available
    Authors
    Wang, B.B.
    Lu, Chunsheng
    Fan, C.Y.
    Zhao, M.H.
    Date
    2019
    Type
    Journal Article
    
    Metadata
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    Citation
    Wang, B.B. and Lu, C. and Fan, C.Y. and Zhao, M.H. 2019. Consistent integration schemes for meshfree analysis of strain gradient elasticity. Computer Methods in Applied Mechanics and Engineering. 357: UNSP 112601.
    Source Title
    Computer Methods in Applied Mechanics and Engineering
    DOI
    10.1016/j.cma.2019.112601
    ISSN
    0045-7825
    Faculty
    Faculty of Science and Engineering
    School
    School of Civil and Mechanical Engineering
    URI
    http://hdl.handle.net/20.500.11937/78291
    Collection
    • Curtin Research Publications
    Abstract

    Integration schemes with nodal smoothed derivatives, which meet integration constraint conditions, are robust and efficient for use in meshfree Galerkin methods, however, most of them are focussed on the classical elasticity determined by a second-order partial differential equation. In this paper, arbitrary-order integration constraint conditions are derived for strain gradient elasticity in a fourth-order partial differential equation. These integration constraint conditions provide the discrete forms of nodal shape functions and their first- and second-order derivatives. Furthermore, to meet the integration constraint conditions, consistent integration schemes are designed with nodal smoothed (but not standard) derivatives at evaluating points. It is shown that such nodal smoothed derivatives are able to satisfy the differentiation of approximation consistency. Finally, several case studies are given and the results demonstrate that, based on convergence, accuracy and efficiency, the numerical performance of consistent integration in meshfree analysis of strain gradient elasticity is superior to the standard Gaussian one.

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