Locking-free Kriging-based Timoshenko Beam Elements using an Improved Implementation of the Discrete Shear Gap Technique


  • Wong Foek Tjong Department of Civil EngineeringPetra Christian University
  • Stevanus W. Santoso Structural Engineer Federal Engineering Consultant Inc., Taipei
  • Mellyssa Sutrisno Department of Civil Engineering Petra Christian University




Kriging-based finite element method, Timoshenko beam, shear locking, discrete shear gap


Kriging-based finite element method (K-FEM) is an enhancement of the conventional finite element method using a Kriging interpolation as the trial solution in place of a polynomial function. In the application of the K-FEM to the Timoshenko beam model, the discrete shear gap (DSG) technique has been employed to overcome the shear locking difficulty. However, the applied DSG was only effective for the Kriging-based beam element with a cubic basis and three element-layer domain of influencing nodes. Therefore, this research examines a modified implementation of the DSG by changing the substitute DSG field from the Kriging-based interpolation to linear interpolation of the shear gaps at the element nodes. The results show that the improved elements of any polynomial degree are free from shear locking. Furthermore, the results of beam deflection, cross-section rotation, and bending moment are very accurate, while the shear force field is piecewise constant.

Author Biography

Wong Foek Tjong, Department of Civil EngineeringPetra Christian University

Assistant Professor Department of Civil Engineering


Plengkhom, K. and Kanok-Nukulchai, W., An Enhancement of Finite Element Method with Moving Kriging Shape Functions, International Journal of Computational Methods, 02(04), 2005, pp. 451–475.

Wong, F.T. and Kanok-Nukulchai, W., Kriging-based Finite Element Method : Element-By-Element Kriging Interpolation, Civil Engineering Dimension, 11(1), 2009, pp. 15–22.

Kanok-Nukulchai, W, Wong, F.T., and Sommanawat, W., Generalization of FEM using Node-Based Shape Functions, Civil Engineering Dimension, 17(3), 2015, pp. 152–157.

Wong, F.T. and Kanok-Nukulchai, W., On the Convergence of the Kriging-based Finite Element Method, International Journal of Computational Methods, 06(01), 2009, pp. 93–118.

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”, Surabaya, Indonesia, August 25-26, 2006, pp. 39–47.

Wong, F. T., Kriging-based Finite Element Method for Analyses of Plates and Shells, Doctoral Dissertation, Asian Institute of Technology, Pathumthani, 2009.

Wong, F.T. and Syamsoeyadi, H., Kriging-based Timoshenko Beam Element for Static and Free Vibration Analyses, Civil Engineering Dimen¬sion, 13(1), 2011, pp. 42–49.

Wong, F.T., Sulistio, A., and Syamsoeyadi, H., Kriging-Based Timoshenko Beam Elements with the Discrete Shear Gap Technique, International Journal of Computational Methods, 15(7), 2018, pp. 1850064-1–27.

Koschnick, F., Bischoff, M., Camprubí, N., and Bletzinger, K.U., The Discrete Strain Gap Method and Membrane Locking, Computer Methods in Applied Mechanics and Engineering, 194(21-24), 2005, pp. 2444–2463.

Bletzinger, K.U., Bischoff, M., and Ramm, E., A Unified Approach for Shear-Locking-Free Triangular and Rectangular Shell Finite Elements, Computers and Structures, 75(3), 2000, pp. 321–334.

Wong, F.T. and Sugianto, S., Study of the Discrete Shear Gap Technique in Timoshenko Beam Elements, Civil Engineering Dimension, 19(1), 2017, pp. 54–62, 2017.

Wong, F.T, Gunawan, J., Agusta, K., Herryanto, and Tanaya, L.S., On the Derivation of Exact Solutions of a Tapered Cantilever Timoshenko Beam, Civil Engineering Dimension, 21(2), 2019, pp. 89–96.

Hughes, T.J.R., The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, Prentice-Hall, New Jersey, 1987.

Garikipati, K., Introduction to Finite Element Methods, Open Michigan, 2013. https://open. umich.edu/find/open-educational-resources/engineering/introduction-finite-element-methods (accessed Jan. 23, 2019).

Onate, E., Structural Analysis with the Finite Element Method-Vol. 2: Beams, Plates and Shells, First edition, Springer, Barcelona, 2013.

Bischoff, M., Koschnick, F., and Bletzinger, K.Y, Stabilized DSG Elements – A New Paradigm in Finite Element Technology, Proceedings of the 4th European LS-DYNA Users Conference, Ulm, Germany, May 22-23, 2003.

Cowper, G.R., The Shear Coefficient in Timo-shenko’s Beam Theory, Journal of Applied Mechanics, 33(2), 1966, pp. 335–340.

Friedman, Z. and Kosmatka, J.B., An Improved Two-node Timoshenko Beam Finite Element, Computers and Structuers, 47(3), 1993, pp. 473–481.




How to Cite

Tjong, W. F., Santoso, S. W. ., & Sutrisno, M. . (2022). Locking-free Kriging-based Timoshenko Beam Elements using an Improved Implementation of the Discrete Shear Gap Technique. Civil Engineering Dimension, 24(1), 11-18. https://doi.org/10.9744/ced.24.1.11-18