FREE VIBRATION ANALYSIS OF PLANE STRESS/STRAIN MODELS USING KRIGING-BASED FINITE ELEMENT METHOD
DOI:
https://doi.org/10.9744/duts.12.2.122-142Keywords:
finite element, free vibration, kriging, convergence, plane stress, plane strain, mode shape, eigen value, eigen vectorAbstract
Kriging-based finite element method (K-FEM) is an enhancement of standard FEM that employs Kriging interpolation over nodal points both within and outside the element domain. This method significantly increase the accuracy of conventional FEM. This paper presents the development and applications of the K-FEM to free vibration analysis of plane bodies with negligible damping. Six benchmark problems are examined: a cantilever beam, a simply supported beam, an arch, a shear wall, a slope, and a tapered cantilever plate with a hole. The computed natural frequencies and mode shapes demonstrate close agreement with reference solutions. Convergence toward the reference values is achieved as the mesh is refined and the degree of the polynomial basis increases, while additional DOI layers exert only a minor influence. These findings confirm that K‑FEM is a viable alternative to the conventional FEM for free vibration analysis of plane stress and plane strain models.
References
Cook, RD, Malkus, DS, Plesha, ME, & Witt, RJ (2002). Concept and Applications of Finite Element Analysis. Hoboken: John Wiley & Sons, Inc.
Coombs, WM, Charlton, TJ, Cortis, M., & Augarde, CE (2018). Overcoming volumetric locking in material point methods. Computer Methods in Applied Mechanics and Engineering, 333, 1-21.
Dai, KY, Liu, GR, Lim, KM, & Gu, YT (2003). Comparison between the radial point interpolation and the Kriging interpolation used in mesh-free methods. Computational Mechanics, 32 (1), 60-70.
Gu, L. (2003). Moving Kriging interpolation and element-free Galerkin method. International Journal for Numerical Methods In Engineering, 56 (1), 1-11.
Kim, NH (2014). Introduction to Nonlinear Finite Element Analysis. Springer Science & Business Media.
Lee, NS, & Bathe, KJ (1993). Effects of element distortions on the performance of isoparametric elements. International Journal for Numerical Methods in Engineering, 36 (20), 3553-3576.
Logan, DL (2016). A First Course in the Finite Element Method. Cengage Learning.
Ludong, TA, Kentaro, C., & Wong, FT (2018). Triangle elements based on Kriging with continuous stress at nodal points (in Indonesian language). Journal of Civil Engineering Dimension Pratama, 7 (1), 310-318.
Nguyen-Thanh, N., Rabczuk, T., Nguyen-Xuan, H., & Bordas, SP (2010). An alternative alpha finite element method (AαFEM) for free and forced structural vibration using triangular meshes. Journal of computational and applied mathematics, 233 (9), 2112-2135.
Olea, RA (2012). Geostatistics for Engineers and Earth Scientists. Springer Science & Business Media.
Plengkhom, K., & Kanok-Nukulchai, W. (2005). An enhancement of finite element method with moving Kriging shape functions. International Journal of Computational Methods, 2 (04), 451-475.
Provatidis, C. (2006). Free vibration analysis of two-dimensional structures using Coons-patch macroelements. Finite elements in analysis and design, 42 (6), 518-531.
Wong, F. T., Widjaja, K & Soetanto, R. M. (2016). Studi keakuratan dan kekonvergenan metode elemen hingga berbasis kriging dan konvensional. Prosiding Seminar dan Pameran HAKI, Jakarta, 23-24 Agustus 2016, Paper No. 25.
Wong, F. T., & Kanok-Nukulchai, W. (2006). Kriging-based finite element method for analyses of Reissner-Mindlin plates. Proceedings of the Tenth East-Asia Pacific Conference on Structural Engineering and Construction. Keynote Lectures and Symposia, Bangkok, 509-514.
Wong, FT, & Kanok-Nukulchai, W. (2009). On the convergence of the Kriging-based finite element method. International Journal of Computational Methods, 6 (01), 93-118.
Wong, FT, & Syamsoeyadi, H. (2011). Kriging-based Timoshenko beam element for static and vibration-free analyses. Civil Engineering Dimension, 13 (1), 42-49.
Yang, Y., Xu, D., & Zheng, H. (2016). Application of the three-node triangular element with continuous nodal stress for free vibration analysis. Computers & Structures, 169, 69-80.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2025 christiana, Wong Foek Tjong
This work is licensed under a Creative Commons Attribution 4.0 International License.
