Acta Mechanica Solida Sinica

, Volume 26, Issue 2, pp 140–150 | Cite as

An Improved Modal Analysis for Three-Dimensional Problems using Face-Based Smoothed Finite Element Method

  • Zhicheng He
  • Guangyao Li
  • Zhihua Zhong
  • Aiguo Cheng
  • Guiyong Zhang
  • Eric Li
Article

Abstract

In this work, we further extended the face-based smoothed finite element method (FS-FEM) for modal analysis of three-dimensional solids using four-node tetrahedron elements. The FS-FEM is formulated based on the smoothed Galerkin weak form which employs smoothed strains obtained using the gradient smoothing operation on face-based smoothing domains. This strain smoothing operation can provide softening effect to the system stiffness and make the FS-FEM provide more accurate eigenfrequency prediction than the FEM does. Numerical studies have verified this attractive property of FS-FEM as well as its ability and effectiveness on providing reliable eigenfrequency and eigenmode prediction in practical engineering application.

Key words

numerical method meshfree method modal analysis face-based smoothed finite element method (FS-FEM) 

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References

  1. [1]
    Zienkiewicz, O.C and Taylor, R.L., The Finite Element Method (5th edn). Butterworth Heinemann: Oxford, 2000.MATHGoogle Scholar
  2. [2]
    Liu, G.R and Quek, S.S., Finite Element Method: a Practical Course. Butter-worth-heinemann: Burlington, MA, 2003.MATHGoogle Scholar
  3. [3]
    Liu, G.R., Meshfree Methods: Moving Beyond the Finite Element Method (2nd Ed). CRC Press: Boca Raton, U.S.A., 2009.CrossRefGoogle Scholar
  4. [4]
    Dokumaci, E., On superaccurate finite elements and their duals for eigenvalue computation. Journal of Sound and Vibration, 2006, 298(1–2): 432–438.MathSciNetCrossRefGoogle Scholar
  5. [5]
    Zhang, Z.Q. and Liu, G.R., Upper and lower bounds for natural frequencies: a property of the smoothed finite element methods. International Journal for Numerical Method in Engineering, 2010, 84(2): 149–178.MathSciNetMATHGoogle Scholar
  6. [6]
    Mackie, R.I., Improving finite element predictions of modes of vibration. International Journal for Numerical Method in Engineering, 1992, 33: 333–44.CrossRefGoogle Scholar
  7. [7]
    Wiberg, N.E., Bausys, R. and Hager, P., Improved eigenfrequencies and eigenmodes in free vibration. Computers and Structures, 1999, 73: 79–89.CrossRefGoogle Scholar
  8. [8]
    Avrashi, J. and Cook, R.D., New error estimation for C0 eigen-problems in finite element analysis. Engineering Computations, 1993, 10(3): 243–256.CrossRefGoogle Scholar
  9. [9]
    Friberg, O., Moller, P., Makovicka, D. and Wiberg, N.E., An adaptive procedure for eigenvalue problems using hier-archical finite element method. International Journal for Numerical Method in Engineering, 1987, 24: 319–335.CrossRefGoogle Scholar
  10. [10]
    Liu, G.R., A weakened weak (W2) form for a unified formulation of compatible and incompatible methods, Part I: Theory and Part II: Applications to solid mechanics problems. International Journal for Numerical Method in Engineering, 2010, 81: 1093–1156.Google Scholar
  11. [11]
    Liu, G.R., A Generalized gradient smoothing technique and the Smoothed bilinear form for Galerkin formulation of wide class of computational methods. International Journal for Numerical Method in Engineering, 2008, 5: 199–236.MathSciNetMATHGoogle Scholar
  12. [12]
    Liu, G.R., Zhang, G.Y., Dai, K.Y., Wang, Y.Y., Zhong, Z.H., Li, G.Y. and Han, X., A linearly conforming point interpolation method (LC-PIM) for 2D solid mechanics problems. International Journal of Computational Methods, 2005, 2(4): 645–665.CrossRefGoogle Scholar
  13. [13]
    Zhang, G.Y., Liu, G.R., Wang, Y.Y., Huang, H.T., Zhong, Z.H., Li, G.Y. and Han, X., A linearly conforming point interpolation method (LC-PIM) for three-dimensional elasticity problems. International Journal for Numerical Method in Engineering, 2007, 72(113): 1524–1543.MathSciNetCrossRefGoogle Scholar
  14. [14]
    Liu, G.R., Nguyen, T.T., Nguyen, H.X. and Lam, K.Y., A node-based smoothed finite element method (NS-FEM) for upper bound solutions to solid mechanics problems. Computers and Structures, 2009, 87: 14–26.CrossRefGoogle Scholar
  15. [15]
    Liu, G.R. and Zhang, G.Y., Upper bound solution to elasticity problems: a unique property of the linearly conforming point interpolation method (LC-PIM). International Journal for Numerical Method in Engineering, 2008, 74: 1128–1161.MathSciNetCrossRefGoogle Scholar
  16. [16]
    Liu, G.R., Nguyen, T.T. and Lam, K.Y., An edge-based smoothed finite element method (ES-FEM) for static and dynamic problems of solid mechanics. Journal of Sound and Vibration, 2009, 320: 1100–1130.CrossRefGoogle Scholar
  17. [17]
    He, Z.C., Liu, G.R., Zhong, Z.H., Wu, S.C., Zhang, G.Y. and Cheng, A.G., An edge-based smoothed finite element method (ES-FEM) for analyzing three-dimensional acoustic problems. Computer Methods in Applied Mechanics and Engineering, 2009, 199: 20–33.MathSciNetCrossRefGoogle Scholar
  18. [18]
    He, Z.C., Cheng, A.G., Zhang, G.Y., Zhong, Z.H. and Liu, G.R., Dispersion error reduction for acoustic problems using the edge-based smoothed finite element method (ES-FEM). International Journal for Numerical Method in Engineering, 2011, 86(11): 1322–1338.MathSciNetCrossRefGoogle Scholar
  19. [19]
    Nguyen, T.T., Liu, G.R., Lam, K.Y. and Zhang, G.Y., A face-based smoothed finite element method (FS-FEM) for 3D linear and geometrically nonlinear solid mechanics problems using 4-node tetrahedral elements. International Journal for Numerical Method in Engineering, 2009, 78: 324–353.CrossRefGoogle Scholar
  20. [20]
    Nguyen, T.T., Liu, G.R., Vu-Do, H.C. and Nguyen, H.X., A face-based smoothed finite element method (FS-FEM) for visco-elastoplastic analyses of 3-D solids using tetrahedral mesh. Computer Methods in Applied Mechanics and Engineering, 2009, 198: 3479–3498.CrossRefGoogle Scholar
  21. [21]
    He, Z.C., Liu, G.R., Zhong, Z.H., Cui, X.Y., Zhang, G.Y. and Cheng, A.G., A coupled edge-/face-based smoothed finite element method for structural-acoustic problems. Applied Acoustics, 2010, 71(10): 955–964.CrossRefGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2013

Authors and Affiliations

  • Zhicheng He
    • 1
  • Guangyao Li
    • 1
  • Zhihua Zhong
    • 1
  • Aiguo Cheng
    • 1
  • Guiyong Zhang
    • 2
  • Eric Li
    • 3
  1. 1.State Key Laboratory of Advanced Design and Manufacturing for Vehicle BodyHunan UniversityChangshaChina
  2. 2.Intelligent Systems for Medicine Laboratory, School of Mechanical and Chemical EngineeringThe University of Western AustraliaCrawleyAustralia
  3. 3.Department of Mechanical EngineeringNational University of SingaporeSingaporeSingapore

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