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The partition of unity finite element method for elastic wave propagation in Reissner–Mindlin plates

Authors

  • N. Hu,

    Corresponding author
    1. Department of Engineering Mechanics, Chongqing University, Chongqing 400044, People's Republic of China
    2. Department of Aerospace Engineering, Tohoku University, Aramaki-Aza-Aoba 6-6 01, Aoba-ku, Sendai 980-8579, Japan
    • Department of Aerospace Engineering, Tohoku University, Aramaki-Aza-Aoba 6-6-01, Aoba-ku, Sendai 980-8579, Japan
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    • Associate Professor.

  • H. H. Wang,

    1. School of Mechanical and Power Engineering, East China University of Science and Technology, Shanghai 200237, People's Republic of China
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  • B. Yan,

    1. Department of Engineering Mechanics, Chongqing University, Chongqing 400044, People's Republic of China
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  • H. Fukunaga,

    Corresponding author
    1. Department of Aerospace Engineering, Tohoku University, Aramaki-Aza-Aoba 6-6 01, Aoba-ku, Sendai 980-8579, Japan
    • Department of Aerospace Engineering, Tohoku University, Aramaki-Aza-Aoba 6-6-01, Aoba-ku, Sendai 980-8579, Japan
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  • D. Roy Mahapatra,

    1. Department of Aerospace Engineering, Indian Institute of Science, Bangalore 560012, India
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  • S. Gopalakrishnan

    1. Department of Aerospace Engineering, Indian Institute of Science, Bangalore 560012, India
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Abstract

This paper reports a numerical method for modelling the elastic wave propagation in plates. The method is based on the partition of unity approach, in which the approximate spectral properties of the infinite dimensional system are embedded within the space of a conventional finite element method through a consistent technique of waveform enrichment. The technique is general, such that it can be applied to the Lagrangian family of finite elements with specific waveform enrichment schemes, depending on the dominant modes of wave propagation in the physical system. A four-noded element for the Reissner–Mindlin plate is derived in this paper, which is free of shear locking. Such a locking-free property is achieved by removing the transverse displacement degrees of freedom from the element nodal variables and by recovering the same through a line integral and a weak constraint in the frequency domain. As a result, the frequency-dependent stiffness matrix and the mass matrix are obtained, which capture the higher frequency response with even coarse meshes, accurately. The steps involved in the numerical implementation of such element are discussed in details. Numerical studies on the performance of the proposed element are reported by considering a number of cases, which show very good accuracy and low computational cost. Copyright © 2006 John Wiley & Sons, Ltd.

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