An extended edge-based smoothed discrete shear gap method for free vibration analysis of cracked Reissner–Mindlin plate

Gang Yang, Dean Hu, Xu Han, Guowei Ma

    Research output: Contribution to journalArticle

    2 Citations (Scopus)

    Abstract

    An extended edge-based smoothed discrete shear gap method (XES-DSG3) is proposed for free vibration analysis of cracked Reissner–Mindlin plate by implementing the edge-based strain smoothing operation into the discrete shear gap-based extended finiteelement method (XFEM-DSG3). In present method, the strain smoothing operation is implemented into the bending strain gradient matrices, in which the enriched functions are included. Then, the derivatives of element shape functions and derivatives of crack-tip singular enriched functions are not required in the computation. The calculation of element matrices is performed over the smoothing domains which are associated with edges of elements. The transverse shear locking of Reissner–Mindlin plate can be avoided by using the integration of discrete shear gap (DSG) method. Several numerical examples are investigated to illustrate the accuracy of XES-DSG3 for the free vibration analysis of cracked Reissner–Mindlin plate. Moreover, numerical results show that the present method is insensitive to mesh distortion and it is more stable than the pervious XFEM-DSG3.

    Original languageEnglish
    Pages (from-to)477-504
    Number of pages28
    JournalApplied Mathematical Modelling
    Volume51
    DOIs
    Publication statusPublished - 1 Nov 2017

    Fingerprint

    Vibration Analysis
    Free Vibration
    Vibration analysis
    Smoothing
    Derivatives
    Bending (deformation)
    Shape Derivative
    Shear Locking
    Crack tips
    Strain Gradient
    Crack Tip
    Shape Function
    Transverse
    Finite Element Method
    Mesh
    Derivative
    Numerical Examples
    Numerical Results

    Cite this

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    title = "An extended edge-based smoothed discrete shear gap method for free vibration analysis of cracked Reissner–Mindlin plate",
    abstract = "An extended edge-based smoothed discrete shear gap method (XES-DSG3) is proposed for free vibration analysis of cracked Reissner–Mindlin plate by implementing the edge-based strain smoothing operation into the discrete shear gap-based extended finiteelement method (XFEM-DSG3). In present method, the strain smoothing operation is implemented into the bending strain gradient matrices, in which the enriched functions are included. Then, the derivatives of element shape functions and derivatives of crack-tip singular enriched functions are not required in the computation. The calculation of element matrices is performed over the smoothing domains which are associated with edges of elements. The transverse shear locking of Reissner–Mindlin plate can be avoided by using the integration of discrete shear gap (DSG) method. Several numerical examples are investigated to illustrate the accuracy of XES-DSG3 for the free vibration analysis of cracked Reissner–Mindlin plate. Moreover, numerical results show that the present method is insensitive to mesh distortion and it is more stable than the pervious XFEM-DSG3.",
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    An extended edge-based smoothed discrete shear gap method for free vibration analysis of cracked Reissner–Mindlin plate. / Yang, Gang; Hu, Dean; Han, Xu; Ma, Guowei.

    In: Applied Mathematical Modelling, Vol. 51, 01.11.2017, p. 477-504.

    Research output: Contribution to journalArticle

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    AU - Yang, Gang

    AU - Hu, Dean

    AU - Han, Xu

    AU - Ma, Guowei

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    N2 - An extended edge-based smoothed discrete shear gap method (XES-DSG3) is proposed for free vibration analysis of cracked Reissner–Mindlin plate by implementing the edge-based strain smoothing operation into the discrete shear gap-based extended finiteelement method (XFEM-DSG3). In present method, the strain smoothing operation is implemented into the bending strain gradient matrices, in which the enriched functions are included. Then, the derivatives of element shape functions and derivatives of crack-tip singular enriched functions are not required in the computation. The calculation of element matrices is performed over the smoothing domains which are associated with edges of elements. The transverse shear locking of Reissner–Mindlin plate can be avoided by using the integration of discrete shear gap (DSG) method. Several numerical examples are investigated to illustrate the accuracy of XES-DSG3 for the free vibration analysis of cracked Reissner–Mindlin plate. Moreover, numerical results show that the present method is insensitive to mesh distortion and it is more stable than the pervious XFEM-DSG3.

    AB - An extended edge-based smoothed discrete shear gap method (XES-DSG3) is proposed for free vibration analysis of cracked Reissner–Mindlin plate by implementing the edge-based strain smoothing operation into the discrete shear gap-based extended finiteelement method (XFEM-DSG3). In present method, the strain smoothing operation is implemented into the bending strain gradient matrices, in which the enriched functions are included. Then, the derivatives of element shape functions and derivatives of crack-tip singular enriched functions are not required in the computation. The calculation of element matrices is performed over the smoothing domains which are associated with edges of elements. The transverse shear locking of Reissner–Mindlin plate can be avoided by using the integration of discrete shear gap (DSG) method. Several numerical examples are investigated to illustrate the accuracy of XES-DSG3 for the free vibration analysis of cracked Reissner–Mindlin plate. Moreover, numerical results show that the present method is insensitive to mesh distortion and it is more stable than the pervious XFEM-DSG3.

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    KW - Extended finite element method

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