A Four-Node Tetrahedral Finite Element Based on Space Fiber Rotation Concept

Open access


The paper presents a four-node tetrahedral solid finite element SFR4 with rotational degrees of freedom (DOFs) based on the Space Fiber Rotation (SFR) concept for modeling three-dimensional solid structures. This SFR concept is based on the idea that a 3D virtual fiber, after a spatial rotation, introduces an enhancement of the strain field tensor approximation. Full numerical integration is used to evaluate the element stiffness matrix. To demonstrate the efficiency and accuracy of the developed four-node tetrahedron solid element and to compare its performance with the classical four-node tetrahedral element, extensive numerical studies are presented.

If the inline PDF is not rendering correctly, you can download the PDF file here.

  • [1] Pawlak T. P. Yunus S. M. and Cook R. D. “Solid elements with rotational degrees of freedom: Part II–tetrahedron elements” International Journal for Numerical Methods in Engineering 31 593–610 1991. doi.org/10.1002/nme.1620310311.

  • [2] Sze K. and Pan Y. “Hybrid stress tetrahedral elements with Allman’s rotational DOFs” International journal for numerical methods in engineering 48 1055–1070 2000. doi.org/10.1002/(SICI)1097-0207(20000710)48:7<1055::AID-NME916>3.0.CO;2-P

  • [3] Matsubara H. Iraha S. Tomiyama J. Yamashiro T. and Yagawa G. “Free mesh method using tetrahedral element including the vertex rotations” in: Proceedings-Japan Society of Civil Engineers DOTOKU GAKKAI pp. 97–108 2004.

  • [4] Tian R. and Yagawa G. “Generalized nodes and high-performance elements” International Journal for Numerical Methods in Engineering 64 2039–2071 2005. doi.org/10.1002/nme.1436.

  • [5] Tian R. Matsubara H. and Yagawa G. “Advanced 4-node tetrahedrons” International Journal for Numerical Methods in Engineering 68 1209–1231 2006. doi.org/10.1002/nme.1744

  • [6] Tian R. Matsubara H. Yagawa G. Iraha S. and Tomiyama J. “Accuracy improvements on free mesh method: A high performance quadratic triangular/tetrahedral element with only corners” in: Proc. of the Sixth World Congress on Computational Mechanics (WCCM VI) 2004.

  • [7] Hua X. and To C. “Simple and efficient tetrahedral finite elements with rotational degrees of freedom for solid modeling” Journal of Computing and Information Science in Engineering 7 382–393 2007. doi:10.1115/1.2798120.

  • [8] Ayad R. “Contribution à la Modélisation numérique pour l’analyse des solides et des structures et pour la mise en forme des fluides non newtoniens. Application à des matériaux d’emballage [Contribution to the numerical modeling of solids and structures and the non-Newtonian fluids forming process. Application to packaging materials]” Habilitation to conduct researches University of Reims Reims France (in French) 2002.

  • [9] Meftah K. “Modélisation numérique des solides par éléments finis volumiques basés sur le concept SFR [Numerical modeling of 3D structure by solid finite elements based upon the SFR concept] (Space Fiber Rotation)” PhD thesis University of Biskra Algeria (in French) 2013.

  • [10] Meftah K. Ayad R. and Hecini M. “A new 3D 6-node solid finite element based upon the “Space Fibre Rotation” concept” European Journal of Computational Mechanics 22 1-29 2012. doi.org/10.1080/17797179.2012.721502.

  • [11] Ayad R. Zouari W. Meftah K. Zineb T. B. and Benjeddou A. “Enrichment of linear hexahedral finite elements using rotations of a virtual space fiber” International Journal for Numerical Methods in Engineering 95 46-70 2013. doi.org/10.1002/nme.4500.

  • [12] Meftah K. Zouari W. Sedira L. and Ayad R. “Geometric non-linear hexahedral elements with rotational DOFs” Computational Mechanics 57 37-53 2016. doi.org/10.1007/s00466-015-1220-8.

  • [13] Meftah K. Sedira L. Zouari W. Ayad R. and Hecini M. “A multilayered 3D hexahedral finite element with rotational DOFs” European Journal of Computational Mechanics 24 107-28 2015. doi.org/10.1080/17797179.2015.1089462.

  • [14] Zouari W. Assarar M. Meftah K. and Ayad R. “Free vibration analysis of homogeneous piezoelectric structures using specific hexahedral elements with rotational DOFs” Acta Mechanica 226 1737-56 2015. doi.org/10.1007/s00707-014-1274-2.

  • [15] Dhondt G. D. C. “The finite element method for three-dimensional thermomechanical applications” John Wiley & Sons Inc 2004.

  • [16] Timoshenko S. P. and Goodier J. N. “Theory of Elasticity” 3rd edition McGraw-Hill New York 1970.

  • [17] MacNeal R. H. and Harder R. L. “A proposed standard set of problems to test finite element accuracy” Finite Elements in Analysis and Design 1 3–20 1985. doi.org/10.1016/0168-874X(85)90003-4.

Journal information
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 13 13 3
PDF Downloads 9 9 3