An Extended Cell-Based Smoothed Three-Node Mindlin Plate Element (XCS-MIN3) for Free Vibration Analysis of Cracked FGM Plates

T. Nguyen-Thoi, Timon Rabczuk, V. Ho-Huu, L. Le-Anh, H. Dang-Trung, T. Vo-Duy

Research output: Contribution to journalArticle

15 Citations (Scopus)


A cell-based smoothed three-node Mindlin plate element (CS-MIN3) was recently proposed and proven to be robust for static and free vibration analyses of Mindlin plates. The method improves significantly the accuracy of the solution due to softening effect of the cell-based strain smoothing technique. In addition, it is very flexible to apply for arbitrary complicated geometric domains due to using only three-node triangular elements which can be easily generated automatically. However so far, the CS-MIN3 has been only developed for isotropic material and for analyzing intact structures without possessing internal cracks. The paper hence tries to extend the CS-MIN3 by integrating itself with functionally graded material (FGM) and enriched functions of the extended finite element method (XFEM) to give a so-called extended cell-based smoothed three-node Mindlin plate (XCS-MIN3) for free vibration analysis of cracked FGM plates. Three numerical examples with different conditions are solved and compared with previous published results to illustrate the accuracy and reliability of the XCS-MIN3 for free vibration analysis of cracked FGM plates.

Original languageEnglish
JournalInternational Journal of Computational Methods
Publication statusAccepted/In press - 2016
Externally publishedYes



  • cell-based smoothed three-node Mindlin method (CS-MIN3)
  • Cracked functionally graded material plate
  • extended finite element method (XFEM)
  • free vibration analysis
  • smoothed finite element methods (SFEM)

ASJC Scopus subject areas

  • Computer Science (miscellaneous)
  • Computational Mathematics

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