Kriging-Based Timoshenko Beam Element for Static and Free Vibration Analyses

Wong F.T., Syamsoeyadi H.




Abstract


An enhancement of the finite element method using Kriging interpolation (K-FEM) has been recently proposed and applied to solve one- and two- dimensional linear elasticity problems. The key advantage of this innovative method is that the polynomial refinement can be performed without adding nodes or changing the element connectivity. This paper presents the development of the K-FEM for static and free vibration analyses of Timoshenko beams. The transverse displacement and the rotation of the beam are independently approximated using Kriging interpolation. For each element, the interpolation function is constructed from a set of nodes within a prescribed domain of influence comprising the element and its several layers of neighbouring elements. In an attempt to eliminate the shear locking, the selective-reduced integration technique is utilized. The developed beam element is tested to several static and free vibration problems. The results demonstrate the excellent performance of the developed element.


Keywords


Finite element, kriging, Timoshenko beam, shear locking, selective-reduced integration

References


  1. Gu, L., Moving Kriging Interpolation and Element-Free Galerkin Method, International Journal for Numerical Methods in Engineering, John Wiley and Sons, 56 (1), 2003, pp. 1-11.
  2. Plengkhom, K. and Kanok-Nukulchai, W., An Enhancement of Finite Element Method with Moving Kriging Shape Functions, International Journal of Computational Methods, World Scientific, 2 (4), 2005, pp. 451-475. [CrossRef]
  3. Wong, F.T. and Kanok-Nukulchai, W., Kriging-based Finite Element Method for Analyses of Reissner-Mindlin Plates, Proceedings of the Tenth East-Asia Pacific Conference on Structural Engineering and Construction, Emerging Trends: Keynote Lectures and Symposia, 3-5 August 2006, Bangkok, Thailand, Asian Institute of Technology, pp. 509-514.
  4. Wong, F.T. and Kanok-Nukulchai, W., On Alleviation of Shear Locking in the Kriging-based Finite Element Method, Proceedings of International Civil Engineering Conference “Towards Sustainable Engineering Practice”, 25-26 August 2006, Surabaya, Indonesia, Petra Christian University, pp. 39-47.
  5. Wong, F.T. and Kanok-Nukulchai, W., On the Convergence of the Kriging-based Finite Element Method, International Journal of Computational Methods, World Scientific, 6 (1), 2009, pp. 93-118. [CrossRef]
  6. Kanok-Nukulchai, W. and Wong, F.T., A Finite Element Method using Node-based Interpolation, Proceedings of the Third Asia-Pacific Congress on Computational Mechanics and the Eleventh International Conference on Enhancement and Promotion of Computational Methods in Engineering and Sciences, 3-6 December 2007, Kyoto, Japan, APACM and EPMESC, Paper No. PL3-3.
  7. Kanok-Nukulchai, W. and Wong, F.T., A Break-Through Enhancement of FEM using Node-based Kriging Interpolation, IACM Expressions, International Association for Computational Mechanics, 23, June 2008, pp. 24-29.
  8. Wong, F.T. and Kanok-Nukulchai, W., Kriging-based Finite Element Method: Element-by-Element Kriging Interpolation, Civil Engineering Dimension, Petra Christian University, 11(1), 2009, pp. 15-22.
  9. Wong, F.T. and Kanok-Nukulchai, W., A Kriging-based Finite Element Method for Analyses of Shell Structures, Proceedings of the Eighth World Congress on Computational Mechanics and the Fifth European Congress on Computational
  10. Methods in Applied Sciences and Engineering, 30 June-4 July 2008, Venice, Italy, IACM and ECCOMAS, Paper No. a1247.
  11. Wong, F.T., Kriging-based Finite Element Method for Analyses of Plates and Shells, Asian Institute of Technology Dissertation No. St 09 01, Asian Institute of Technology, Bangkok, Thailand, 2009.
  12. Sommanawat, W. and Kanok-Nukulchai, W., Multiscale Simulation Based on Kriging-Based Finite Element Method, Interaction and Multiscale Mechanics, Techno Press, 2 (4), 2009, pp. 387-408.
  13. Friedman, Z. and Kosmatka, J.B., An Improved Two-node Timoshenko Beam Finite Element, Computers & Structures, 47(3), 1993, pp. 473-481. [CrossRef]
  14. Olea, R.A., Geostatistics for Engineers and Earth Scientists, Kluwer Academic Publishers, Boston, USA, 1999. [CrossRef]
  15. Wackernagel, H., Multivariate Geostatistics, 2nd edition, Springer, Berlin, Germany, 1998. [CrossRef]
  16. Hughes, T.J.R., Taylor, R.L. and Kanok-Nukulchai, W., A Simple and Efficient Finite Element for Plate Bending, International Journal for Numerical Methods in Engineering, John Wiley and Sons, 11, 1977, pp. 1529-1543. [CrossRef]
  17. Reddy, J. N., An Introduction to the Finite Element Method., 3th edition, McGraw-Hill, Singapore, 2006.
  18. Syamsoeyadi, H., Development of Kriging-based Timoshenko Beam Element for Static and Free Vibration Analyses (in Indonesian language), Petra Christian University Undergraduate Thesis No. 11011660/SIP/2009, Petra Christian University, Surabaya, Indonesia, 2009.
  19. Wicaksana, C., Dynamic Analysis using Kriging-based Finite Element Methods, Asian Institute of Technology Thesis No. St 06 15, Asian Institute of Technology, Bangkok, Thailand, 2006.
  20. Prathap, G., The Finite Element Method in Structural Mechanics, Kluwer Academic Publisher, Dordrecht, Netherlands, 1993.
  21. Lee, J. and Schultz, W.W., Eigenvalue Analysis of Timoshenko Beams and Axisymmetric Mindlin Plates by the Pseudospectral Method, Journal of Sound and Vibration, 269 (3-5), 2004, pp. 609-621. [CrossRef]


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