Computational Mechanics

, Volume 51, Issue 1, pp 65–81 | Cite as

A cell-based smoothed three-node Mindlin plate element (CS-MIN3) for static and free vibration analyses of plates

  • T. Nguyen-Thoi
  • P. Phung-Van
  • H. Luong-Van
  • H. Nguyen-Van
  • H. Nguyen-Xuan
Original Paper

Abstract

The cell-based strain smoothing technique is combined with the well-known three-node Mindlin plate element (MIN3) to give a so-called the cell-based smoothed MIN3 (CS-MIN3) for static and free vibration analyses of plates. In the process of formulating the system stiffness matrix of the CS-MIN3, each triangular element will be divided into three sub-triangles, and in each sub-triangle, the stabilized MIN3 is used to compute the strains and to avoid the transverse shear locking. Then the strain smoothing technique on whole the triangular element is used to smooth the strains on these three sub-triangles. The numerical examples demonstrated that the CS-MIN3 is free of shear locking, passes the patch test and shows four superior properties such as: (1) be a strong competitor to many existing three-node triangular plate elements in the static analysis, (2) can give high accurate solutions for problems with skew geometries in the static analysis, (3) can give high accurate solutions in free vibration analysis, (4) can provide accurately the values of high frequencies of plates by using only coarse meshes.

Keywords

Reissner–Mindlin plate Shear locking Finite element method (FEM) Cell-based smoothed three-node Mindlin plate element (CS-MIN3) Three-node Mindlin plate element (MIN3) Strain smoothing technique 

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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • T. Nguyen-Thoi
    • 1
    • 2
  • P. Phung-Van
    • 2
  • H. Luong-Van
    • 3
  • H. Nguyen-Van
    • 4
  • H. Nguyen-Xuan
    • 1
    • 2
  1. 1.Department of Mechanics, Faculty of Mathematics & Computer ScienceUniversity of Science, Vietnam National University HCMHochiminh CityVietnam
  2. 2.Division of Computational  MechanicsTon Duc Thang UniversityHochiminh CityVietnam
  3. 3.Faculty of Civil EngineeringHochiminh City University of Technology (HCMUT)Hochiminh CityVietnam
  4. 4.Faculty of Civil EngineeringHochiminh City University of ArchitectureHochiminh CityVietnam

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