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Minimizing Artificial Stiffness in Linear Tetrahedral Element Using Virtual Mesh Refinement

Published online by Cambridge University Press:  22 November 2016

S. Waluyo
S. Waluyo*
Affiliation:
Department of Industrial EngineeringUniversity of Jenderal SoedirmanPurbalingga, Indonesia
*
*Corresponding author (sugeng.waluyo@unsoed.ac.id)
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Abstract

This work presents a new method to minimize artificial stiffness in linear tetrahedral element using virtual mesh refinement (VRM) method. The basic idea behind this work is to give additional degree of freedom by using internal mesh over the linear tetrahedral element. This local internal mesh and its corresponding equilibrium condition under particular boundary condition are invisible to users or virtual. Using specialized displacement test vectors, strain energy is obtained and used to calculate reduction factor for artificial stiffness. Numerical experiments are performed at the end to briefly qualitatively show performance of our proposed method.

Keywords

Linear tetrahedral elementVMRStrain energyDisplacement test vector
Type
Research Article
Information
Journal of Mechanics , Volume 34 , Issue 3 , June 2018 , pp. 291 - 297
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2018 

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References

1. Zienkiewicz, O. C. and Taylor, R. L., The Finite Element Method, Volume 1: The Basis. Butterworth-Heinemann, Oxford (2000).Google Scholar
2. Saucedo-Mora, L. and Marrow, T. J., “Method for the explicit insertion of microstructure in Cellular Automata Finite Element (CAFE) models based on an irregular tetrahedral Finite Element mesh: Application in a multi-scale Finite Element Microstructure MEshfree framework (FEMME),” Finite Elements in Analysis and Design, 105, pp. 56–62 (2015).CrossRefGoogle Scholar
3. Taylor, R. L., “A mixed-enhanced formulation for tetrahedral finite elements,” International Journal for Numerical Methods in Engineering, 47, pp. 205–227 (2000).3.0.CO;2-J>CrossRefGoogle Scholar
4. Thoutireddy, P., Molinari, J. F., Repetto, E. A. and Ortiz, M., “Tetrahedral composite finite elements,” International Journal for Numerical Methods in Engineering, 53, pp. 1337–1351 (2002).CrossRefGoogle Scholar
5. Onishi, Y. and Ayama, K., “A locking-free smoothed finite element formulation (modified selective FS/NSFEM-T4) with tetrahedral mesh rezoning for large deformation problems,” The 11th World Congress on Computational Mechanics (WCCM XI), Barcelona, Spain (2014).Google Scholar
6. Ostien, J. T., Foulk, J. W., Mota, A. and Veilleux, M. G., “A 10Node Composite Tetrahedral Finite Element for Solid Mechanics,” International Journal for Numerical Methods in Engineering, 10.1002/nme.5218 (2016).CrossRefGoogle Scholar
7. Waluyo, S., “Accuracy improvement for linear tetrahedral finite element by means of virtual mesh refinement,” Journal of Mechanical Engineering, University Technology Mara, 12, pp. 19–30 (2015).Google Scholar
8. Geuzaine, C. and Remacle, J. F., “Gmsh: a three dimensional finite element generator with built-in pre- and post-processing facilities,” International Journal for Numerical Methods in Engineering, 79, pp. 1309–1331 (2009).Google Scholar
9. Parthasarathy, V. N., Graichen, C. M. and Hathaway, A. F., “A comparison of tetrahedron quality measures,” Finite Elements in Analysis and Design, 15, pp. 255–261 (1994).Google Scholar
10. Wang, E., Nelson, T. and Rauch, R., “Back to elements-tetrahedra vs. hexahedra,” Proceedings of the 2004 International ANSYS Conference (2004).Google Scholar