Subdivision templates for converting a non-conformal hex-dominant mesh to a conformal hex-dominant mesh without pyramid elements | Engineering with Computers Skip to main content
Springer Nature Link
Log in

Subdivision templates for converting a non-conformal hex-dominant mesh to a conformal hex-dominant mesh without pyramid elements

  • Original Article
  • Published:
Engineering with Computers Aims and scope Submit manuscript

Abstract

This paper presents a computational method for converting a non-conformal hex-dominant mesh to a conformal hex-dominant mesh without help of pyramid elements. During the conversion, the proposed method subdivides a non-conformal element by applying a subdivision template and conformal elements by a conventional subdivision scheme. Although many finite element solvers accept mixed elements, some of them require a mesh to be conformal without a pyramid element. None of the published automated methods could create a conformal hex-dominant mesh without help of pyramid elements, and therefore the applicability of the hex-dominant mesh has been significantly limited. The proposed method takes a non-conformal hex-dominant mesh as an input and converts it to a conformal hex-dominant mesh that consists only of hex, tet, and prism elements. No pyramid element will be introduced. The conversion thus considerably increases the applicability of the hex-dominant mesh in many finite element solvers.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
¥17,985 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Japan)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27
Fig. 28
Fig. 29

Similar content being viewed by others

References

  1. George PL (1999) Tet meshing: construction, optimization and adaptation. In: Proceedings of 8th international meshing roundtable, pp 133–141

  2. Yamakawa S, Shimada K (2003) Anisotropic tetrahedral meshing via bubble packing and advancing front. Inter J Numer Methods Eng 57:1923–1942

    Article  MathSciNet  MATH  Google Scholar 

  3. Shewchuk J (2002) Constrained delaunay tetrahedralizations and provably good boundary recovery. In: Proceedings of 11th international meshing roundtable, pp 193–204

  4. Blacker TD, Meyers RJ (1993) Seams and wedges in plastering: a 3-D hexahedral mesh generation algorithm. Eng Comput 2:83–93

    Article  Google Scholar 

  5. Schneiders R (1996) A grid-based algorithm for the generation of hexahedral element meshes. Eng Comput 12:168–177

    Article  Google Scholar 

  6. Tautges TJ, Blacker T, Mitchell SA (1996) The whisker weaving algorithm: a connectivity-based method for constructing all-hexahedral finite element meshes. Inter J Numer Methods Eng 39:3327–3349

    Article  MathSciNet  MATH  Google Scholar 

  7. Ledoux F, Weill J-C (2007) An extension of the reliable whisker weaving algorithm. In: Proceedings of 16th international meshing roundtable, pp 215–232

  8. Staten ML, Owen SJ, Blacker TD (2005) Unconstrained paving and plastering: a new idea for all hexahedral mesh generation, In: Proceedings of 14th international meshing roundtable, pp 399–416

  9. Taghavi R (2000) Automatic block decomposition using fuzzy logic analysis. In: Proceedings of 9th international meeting roundtable, pp 187–192

  10. Kwak D-Y, Im Y-T (2002) Remeshing for metal forming simulations-Part II: three-dimensional hexahedral mesh generation. Inter J Numer Methods Eng 53:2501–2528

    Article  MATH  Google Scholar 

  11. Hariya M, Nishigaki I, Kataoka I, Hiro Y (2006) Automatic hexahedral mesh generation with feature line extraction. In: Proceedings of 15th international meshing roundtable, pp 453–467

  12. Maréhal L (2001) A new approach to octree-based hexahedral meshing. In: Proceedings of 10th international meshing roundtable, pp 209–221

  13. Yamakawa S, Shimada K (2002) HEXHOOP: modular templates for converting a hex-dominant mesh to an all-hex Mesh. Eng Comput. 18:211–228

    Article  Google Scholar 

  14. Mitchell SA (1998) The all-hex geode-template for conforming a diced tetrahedral mesh to any diced hexahedral mesh. In: Proceedings of 7th international meshing roundtable, pp 29–305

  15. White DR, Tautges TJ (2000) Automatic scheme selection for toolkit hex meshing. Intern J Numer Methods Eng 49:127–144

    Article  MATH  Google Scholar 

  16. Lai M, Benzley S, White D (2000) Automated hexahedral mesh generation by generalized multiple source to multiple target sweeping. Inter J Numeri Methods Eng 49:261–275

    Article  MATH  Google Scholar 

  17. Shepherd J, Mitchell SA, Knupp P, White D (2000) Methods for multisweep automation. In: Proceedings of 9th international meshing roundtable, pp 77–87

  18. Quadros WR, Shimada K (2002) Hex-layer: layered all-hex mesh generation on thin section solids via chordal surface transformation. In: Proceedings of 11th international meshing roundtable, pp 169–180

  19. Meshkat S, Talmor D (2000) Generating a mixed mesh of hexahedra, pentahedra and tetrahedra from an underlying tetrahedral mesh. Inter J Numer Methods Eng 49:17–30

    Article  MATH  Google Scholar 

  20. Meyers RJ, Tautges TJ, Tuchinsky PM (1998) The “Hex-tet” hex-dominant meshing algorithm as implemented in CUBIT. In: Proceedings of 7th international meshing roundtable, pp 151–58

  21. Owen SJ, Saigal S (2000) H-Morph: an indirect approach to advancing front hex meshing. Inter J Numer Methods in Eng 49:289–312

    Article  MathSciNet  MATH  Google Scholar 

  22. Yamakawa S, Shimada K (2003) Fully-automated hex-dominant mesh generation with directionality control via packing rectangular solid cells. Int J Numer Methods Eng 57:2099–2129

    Article  MathSciNet  MATH  Google Scholar 

  23. Becker EB, Carey GF, Oden JT (1981) Finite elements: an introduction, vol. 1. Prentice Hall, NJ

  24. Knupp PM (2000) Achieving finite element mesh quality via optimization of the Jacobian matrix norm and associated Quantities. Part II —A framework for volume mesh optimization and the condition number of the jacobian matrix. Int J Numer Methods Eng 48:1165–1185

    Google Scholar 

  25. Freitag LA, Plassmann PE (2001) Local optimization-based untangling algorithms for quadrilateral meshes. In: Proceedings of 10th international meshing roundtable, pp 397–406

  26. Zhou T, Shimada K (2000) An angle-based approach to two-dimensional mesh smoothing. In: Proceedings of 9th international meshing roundtable, pp 373–384

  27. Calvo NA, Idelsohn SR (2001) All-hexahedral mesh smoothing with a node-based measure of quality. Int J Numer Methods Eng 50:1957–1967

    Article  MATH  Google Scholar 

  28. Klingner BM, Shewchuck JR (2007) Aggressive tetrahedral mesh improvement. In: Proceedings of 16th international meshing roundtable, pp 3–23

  29. Joe B (1995) Construction of three-dimensional improved-quality triangulations using local transformations. SIAM J Sci Comput 16:1292–1307

    Article  MathSciNet  MATH  Google Scholar 

  30. Molinari JF, Ortiz M (2002) Three-dimensional adaptive meshing by subdivision and edge-collapse in finite-deformation dynamic-plasticity problems with application to adiabatic shear banding. Int J Numer Methods Eng 53:1101–1126

    Article  Google Scholar 

  31. Yamakawa S, Shimada K (2008) Converting a tetrahedral mesh to a prism-tetrahedral hybrid mesh for FEM accuracy and efficiency. In: Proceedings of ACM symposium on solid and physical modeling, pp 287–294

  32. Abaqus, Dassault Systemes. http://www.simulia.com

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, USA

    Soji Yamakawa, Iacopo Gentilini & Kenji Shimada

Authors
  1. Soji Yamakawa
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Iacopo Gentilini
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Kenji Shimada
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Soji Yamakawa.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yamakawa, S., Gentilini, I. & Shimada, K. Subdivision templates for converting a non-conformal hex-dominant mesh to a conformal hex-dominant mesh without pyramid elements. Engineering with Computers 27, 51–65 (2011). https://doi.org/10.1007/s00366-010-0178-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00366-010-0178-6

Keywords