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A stabilized discrete shear gap extended finite element for the analysis of cracked Reissner–Mindlin plate vibration problems involving distorted meshes

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Abstract

In this work, a new approach in the framework of the local partition of unity finite element method (XFEM) to significantly improve the accuracy of natural frequency in free vibration analysis of cracked Reissner–Mindlin plates is presented. Different from previous approaches, the present formulation is expected to be more accurate and effective in modeling cracked plates by integrating the stabilized discrete shear gap (DSG) into the XFEM setting. Intensive numerical results at low frequency demonstrated that the novel DSG-based XFEM approach possesses the following desirable properties: (1) the awkwardness of transverse shear-locking phenomenon can be overcome easily; (2) the DSG-based XFEM can be applicable to both moderately thick and thin plates straightforwardly; (3) the representation of cracks is independent of finite element mesh; (4) mesh distortion is insensitive and controllable; (5) the accuracy of natural frequency obtained by the present method is high and (6) the present method uses three-node triangular elements that can be much easily generated automatically for problems even with complicated geometry. These properties of the DSG-based XFEM are confirmed through several numerical examples of cracked plates with different boundary conditions.

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Acknowledgments

The support by the Graint-in-Aid for Scientific Research (No. 26-04055) - Japan Society for the Promotion of Science (JSPS, ID No. P14055), and the National Natural Science Foundation of China (Grant No. 51179063) is gratefully acknowledged.

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Authors and Affiliations

  1. Department of Engineering Mechanics, Hohai University, Nanjing, 210098, China

    Tiantang Yu

  2. Department of Mechanical and Environmental Informatics, Tokyo Institute of Technology, 2-12-1-W8-22, Ookayama, Meguro-ku, Tokyo, 152-8552, Japan

    Tinh Quoc Bui & Sohichi Hirose

  3. College of Civil Engineering, Hunan University, Changsha, 410012, China

    Peng Liu

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  1. Tiantang Yu
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  2. Tinh Quoc Bui
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Correspondence to Tinh Quoc Bui.

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Yu, T., Bui, T.Q., Liu, P. et al. A stabilized discrete shear gap extended finite element for the analysis of cracked Reissner–Mindlin plate vibration problems involving distorted meshes. Int J Mech Mater Des 12, 85–107 (2016). https://doi.org/10.1007/s10999-014-9282-x

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  • DOI: https://doi.org/10.1007/s10999-014-9282-x

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