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Vibration analysis of cracked plates using the extended finite element method

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Abstract

In the present paper, the extended finite element method (X-FEM) is adopted to analyze vibrations of cracked plates. Mindlin’s plate theory taking into account the effects of shear deformation and rotatory inertia is included in the development of the model. First, conventional FEM without any discontinuity is carried out, then the enrichment proposed by Moës et al. (Int J Numer Methods Eng 46, 131–150, 1999) of nodal elements containing cracks is added to the FEM formulation. Numerical implementation of enriched elements by discontinuous functions is performed, and thus dynamic equations (stiffness and mass matrices) are established. A FORTRAN computer code based on the X-FEM formulation is hence developed. Rectangular and square plates containing through-edge and central cracks with different boundary conditions are considered. The subspace iteration method is used to solve the eigenvalue problem. Natural frequencies as well as the corresponding eigenfunctions are consequently calculated as a function of the crack length. The obtained results show that the X-FEM is an efficient method in the dynamic analysis of plates containing discontinuities.

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Medea, Medea, Algeria

    M. Bachene

  2. Department of Mechanical Engineering, University of Blida, Blida, Algeria

    R. Tiberkak

  3. Laboratory of Mechanical Engineering and Development, National Polytechnic School of Algiers, 10 Avenue Hassan Badi, El-Harrach, 16112, Algiers, Algeria

    S. Rechak

Authors
  1. M. Bachene
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  2. R. Tiberkak
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  3. S. Rechak
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Correspondence to S. Rechak.

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Bachene, M., Tiberkak, R. & Rechak, S. Vibration analysis of cracked plates using the extended finite element method. Arch Appl Mech 79, 249–262 (2009). https://doi.org/10.1007/s00419-008-0224-7

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  • DOI: https://doi.org/10.1007/s00419-008-0224-7

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