AN ENHANCEMENT OF KRIGING BASED FINITE ELEMENT FOR PLATE ANALYSIS BY USING MITC3+ ELEMENT
DOI:
https://doi.org/10.9744/duts.8.2.31-50Keywords:
plate structure, finite element method, kriging interpolation, MITC3 element, shear-lockingAbstract
A development of Kriging-based finite elements method has been carried out by
implementing the MITC3+ plate elements for modeling the plate structure. The MITC3+
element used is a development of the MITC3 element whose performance is considered quite
good and can overcome problems that arise in the application of conventional Kriging-based
finite elements, one of which is the shear-locking. The application of Kriging interpolation on
MITC3+ elements is carried out with the Kriging shape function formulation in the formation of
the bending stiffness matrix only. The elements are then tested with various benchmark
problems such as Patch Test, hard clamped square plate, Rhombic Plate, and its ability to
solve complex-shaped plates. The results showed that the MITC3+ was able to avoid the
shear-locking mechanism and also produce an accurate solution. However, it appears there
is an inconsistent convergence pattern on the Patch Test and Rhombic Plate.
References
Gu, L. (2003). Moving Kriging Interpolation and Element-free Galerkin Method. International
Journal for Numerical Methods in Engineering, 56(1), 1–11.
Jeon, H. M., Lee, Y., Lee, P. S., & Bathe, K. J. (2015). The MITC3+ Shell Element in
Geometric Nonlinear Analysis. Computers and Structures, 146, 91–104.
Katili, A. M., Maknun, I. J., & Katili, I. (2019a). Theoretical Equivalence and Numerical
Performance of T3γ and MITC3 Plate Finite Elements. Structural Engineering and
Mechanics, 69(5), 527–536.Sebastian, Wong: An Enhancement of MITC3+ Plater Element Using Kriging Interpolation
20
Katili, I. (1993). A New Discrete Kirchhoff-Mindlin Element Based on Mindlin-Reissner Plate
Theory and Assumed Shear Strain Fields. International Journal for Numerical Methods
in Engineering, 36(August 1992), 1885–1908.
Katili, I., Jauhari Maknun, I., Batoz, J. L., & Katili, A. M. (2019). A Comparative Formulation
of T3γ, DST, DKMT and MITC3+ Triangular Plate Elements With New Numerical
Results Based on s-norm Tests. European Journal of Mechanics, 78.
Ko, Y., Lee, Y., Lee, P. S., & Bathe, K. J. (2017). Performance of The MITC3+ and MITC4+
Shell Elements in Widely-used Benchmark Problems. Computers and Structures, 193,
187–206. http://dx.doi.org/10.1016/j.compstruc.2017.08.003
Lee, P. S., & Bathe, K. J. (2004). Development of MITC Isotropic Triangular Shell Finite
Elements. Computers and Structures, 82(11–12), 945–962.
Lee, P. S., Noh, H. C., & Bathe, K. J. (2007). Insight Into 3-node Triangular Shell Finite
Elements: The Effects of Element Isotropy and Mesh Patterns. Computers and
Structures, 85(7–8), 404–418.
Lee, Y., Yoon, K., & Lee, P. S. (2012). Improving The MITC3 Shell Finite Element by Using
The Hellinger-Reissner Principle. Computers and Structures, 110–111, 93–106.
Nguyen-Xuan, H., Liu, G. R., Thai-Hoang, C., & Nguyen-Thoi, T. (2010). An Edge-Based
Smoothed Finite Element Method (ES-FEM) With Stabilized Discrete Shear Gap
Technique For Analysis of Reissner-Mindlin Plates. Computer Methods in Applied
Mechanics and Engineering, 199(9–12), 471–489.
http://dx.doi.org/10.1016/j.cma.2009.09.001
Plengkhom, K., & Kanok-Nukulchai, W. (2005). An Enhancement of Finite Element Method
With Moving Kriging Shape Functions. International Journal of Computational Methods,
02(04), 451–475.
Tessler, A., & Hughes, T. J. R. (1985). A Three-node Mindlin Plate Element With Improved
Transverse Shear. Computer Methods in Applied Mechanics and Engineering, 50(1),
71–101.
Tongsuk, P., & Kanok-Nukulchai, W. (2004). Further Investigation of Element-Free Galerkin
Method Using Moving Kriging Interpolation. International Journal of Computational
Methods, 01(02), 345–365.
Verwoerd, M. H., & Kok, A. W. M. (1990). A Shear Locking Free Six-node Mindlin Plate
Bending Element. Computers and Structures, 36(3), 547–551.
Wijaya, D. (2016). Eliminasi Shear Locking Pada Elemen Pelat Reissner-Mindlin Berbasis
Kriging Dengan Metode Discrete Shear Gap (DSG).
Winata, E. T., Salim, C. J., & Wong, F. T. (2016). Studi Elemen Discrete-Kirchhoff Mindlin
Triangle (DKMT) Untuk Analisis Statik Pelat Lentur Dan Pengembangan Untuk Analisis
Dinamik Getaran Bebas.
Wong, F. T., & Kanok-Nukulchai, W. (2009). On The Convergence of The Kriging-based
Finite Element Method. International Journal of Computational Methods, 6(1), 93–118.
Wong, F. T., & Kanok-Nukulchai, W. (2006). On Alleviation of Shear Locking in the KrigingBased Finite Element Method. Proceedings of International Civil Engineering
Conference “Towards Sustainable Engineering Practice,” January, 39–47.
Journal for Numerical Methods in Engineering, 56(1), 1–11.
Jeon, H. M., Lee, Y., Lee, P. S., & Bathe, K. J. (2015). The MITC3+ Shell Element in
Geometric Nonlinear Analysis. Computers and Structures, 146, 91–104.
Katili, A. M., Maknun, I. J., & Katili, I. (2019a). Theoretical Equivalence and Numerical
Performance of T3γ and MITC3 Plate Finite Elements. Structural Engineering and
Mechanics, 69(5), 527–536.Sebastian, Wong: An Enhancement of MITC3+ Plater Element Using Kriging Interpolation
20
Katili, I. (1993). A New Discrete Kirchhoff-Mindlin Element Based on Mindlin-Reissner Plate
Theory and Assumed Shear Strain Fields. International Journal for Numerical Methods
in Engineering, 36(August 1992), 1885–1908.
Katili, I., Jauhari Maknun, I., Batoz, J. L., & Katili, A. M. (2019). A Comparative Formulation
of T3γ, DST, DKMT and MITC3+ Triangular Plate Elements With New Numerical
Results Based on s-norm Tests. European Journal of Mechanics, 78.
Ko, Y., Lee, Y., Lee, P. S., & Bathe, K. J. (2017). Performance of The MITC3+ and MITC4+
Shell Elements in Widely-used Benchmark Problems. Computers and Structures, 193,
187–206. http://dx.doi.org/10.1016/j.compstruc.2017.08.003
Lee, P. S., & Bathe, K. J. (2004). Development of MITC Isotropic Triangular Shell Finite
Elements. Computers and Structures, 82(11–12), 945–962.
Lee, P. S., Noh, H. C., & Bathe, K. J. (2007). Insight Into 3-node Triangular Shell Finite
Elements: The Effects of Element Isotropy and Mesh Patterns. Computers and
Structures, 85(7–8), 404–418.
Lee, Y., Yoon, K., & Lee, P. S. (2012). Improving The MITC3 Shell Finite Element by Using
The Hellinger-Reissner Principle. Computers and Structures, 110–111, 93–106.
Nguyen-Xuan, H., Liu, G. R., Thai-Hoang, C., & Nguyen-Thoi, T. (2010). An Edge-Based
Smoothed Finite Element Method (ES-FEM) With Stabilized Discrete Shear Gap
Technique For Analysis of Reissner-Mindlin Plates. Computer Methods in Applied
Mechanics and Engineering, 199(9–12), 471–489.
http://dx.doi.org/10.1016/j.cma.2009.09.001
Plengkhom, K., & Kanok-Nukulchai, W. (2005). An Enhancement of Finite Element Method
With Moving Kriging Shape Functions. International Journal of Computational Methods,
02(04), 451–475.
Tessler, A., & Hughes, T. J. R. (1985). A Three-node Mindlin Plate Element With Improved
Transverse Shear. Computer Methods in Applied Mechanics and Engineering, 50(1),
71–101.
Tongsuk, P., & Kanok-Nukulchai, W. (2004). Further Investigation of Element-Free Galerkin
Method Using Moving Kriging Interpolation. International Journal of Computational
Methods, 01(02), 345–365.
Verwoerd, M. H., & Kok, A. W. M. (1990). A Shear Locking Free Six-node Mindlin Plate
Bending Element. Computers and Structures, 36(3), 547–551.
Wijaya, D. (2016). Eliminasi Shear Locking Pada Elemen Pelat Reissner-Mindlin Berbasis
Kriging Dengan Metode Discrete Shear Gap (DSG).
Winata, E. T., Salim, C. J., & Wong, F. T. (2016). Studi Elemen Discrete-Kirchhoff Mindlin
Triangle (DKMT) Untuk Analisis Statik Pelat Lentur Dan Pengembangan Untuk Analisis
Dinamik Getaran Bebas.
Wong, F. T., & Kanok-Nukulchai, W. (2009). On The Convergence of The Kriging-based
Finite Element Method. International Journal of Computational Methods, 6(1), 93–118.
Wong, F. T., & Kanok-Nukulchai, W. (2006). On Alleviation of Shear Locking in the KrigingBased Finite Element Method. Proceedings of International Civil Engineering
Conference “Towards Sustainable Engineering Practice,” January, 39–47.
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Published
2021-10-30
How to Cite
Sebastian, S., & Tjong, W. F. (2021). AN ENHANCEMENT OF KRIGING BASED FINITE ELEMENT FOR PLATE ANALYSIS BY USING MITC3+ ELEMENT. Dimensi Utama Teknik Sipil, 8(2), 31–50. https://doi.org/10.9744/duts.8.2.31-50
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