Skip to main content
Springer Nature Link
Log in

An automated approach to quadrilateral mesh generation with complex geometric feature constraints

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

Abstract

An automated approach to quadrilateral mesh generation with complex internal geometric feature constraints is presented in this paper. It can deal with all kinds of feature constraints such as internal holes, constraint lines, constraint points, density lines and density points, etc., and satisfy special requirements of mesh generation for numerical analysis. The quadrilateral mesh is generated based on the looping algorithm. As the core of the algorithm, the new splitting criteria are put forward to improve the quality and efficiency of mesh generation. The method of dealing with feature constraints is proposed by considering constraint lines and points, density lines and density points as internal holes with zero area. The method for generating boundary elements is also introduced to improve the element quality around the boundary and feature constraints. For the situation in which feature constraints subdivide the domain into sub-domains, an automatic determination method of sub-domain boundaries is presented. An improved looping algorithm is presented for 3D surface meshing with feature constraints. The determination of proper splitting plane and the handling of feature constraints are put forward. The program of quadrilateral mesh generation has been developed based on the method presented in this paper and successfully applied to mesh generation in several engineering fields.

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
$34.99 /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 excludes VAT (USA)
Tax calculation will be finalised during checkout.

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. Ho-Le K (1988) Finite element mesh generation methods: a review and classification. Comput Aided Des 20:27–38

    Article  MATH  Google Scholar 

  2. Schneiders R (2000) Algorithms for quadrilateral and hexahedral mesh generation. In: Proceedings of the VKI lecture series on computational fluid dynamic, 20–24 March 2000

  3. Yeung SF, Hsu MB (1973) A mesh generation method based on set theory. Comput Struct 3:1063–1077

    Article  MathSciNet  Google Scholar 

  4. Durocher L, Gasper A (1979) A versatile two-dimensional mesh generator with automatic bandwidth reduction. Comput Struct 10:561–575

    Article  MATH  Google Scholar 

  5. Schneiders R (1996) A grid-based algorithm for the generation of hexahedral element meshes. Eng Comput 12:68–77

    Article  Google Scholar 

  6. Petersen SB, Gouveia BPPA, Rodrigues JMC, Martins PAF (1988) A metal-forming approach to automatic generation of graded initial quadrilateral finite element meshes. Eng Comput 15(5):577–587

    Article  Google Scholar 

  7. Petersen SB, Rodrigues JMC, Martins PAF (2000) Automatic generation of quadrilateral meshes for the finite element analysis of metal forming processes. Finite Elem Anal Des 35:157–168

    Article  MATH  Google Scholar 

  8. Liang XH, Ebeida MS, Zhang YJ (2009) Guaranteed-quality all-quadrilateral mesh generation with feature preservation. In: Proceedings of 18th international meshing roundtable, Salt Lake City, UT, October 2009, pp 45–63

  9. Zhang YJ, Bajaj C (2006) Adaptive and quality quadrilateral/hexahedral meshing from volumetric data. Comput Methods Appl Mech Eng 195(9–12):942–960

    Article  MATH  MathSciNet  Google Scholar 

  10. Blacker TD, Stephenson MB (1991) Paving: a new approach to automated quadrilateral mesh generation. Int J Numer Method Eng 32:811–847

    Article  MATH  Google Scholar 

  11. White DR, Kinney P (1997) Redesign of the paving algorithm: robustness enhancements through element by element meshing. In: Proceedings of 6th international meshing roundtable, Albuquerque, NM, October 1997, pp 323–335

  12. Yoshimura S, Wada Y, Yagawa G (1999) Automatic mesh generation of quadrilateral elements using intelligent local approach. Comput Methods Appl Mech Eng 179:125–138

    Article  MATH  Google Scholar 

  13. Roger JC, Steven EB (1996) Generalized 3-d paving: an automated quadrilateral surface mesh generation algorithm. Int J Numer Meth Eng 39:1475–1489

    Article  MATH  Google Scholar 

  14. Owen SJ, Staten ML, Canann SA (1999) Q-Morph: an indirect approach to advancing front quad meshing. Int J Numer Method Eng 44(9):1317–1340

    Article  MATH  Google Scholar 

  15. Sluiter MLC, Hansen DC (1982) A general purpose automatic mesh generator for shell and solid finite elements. Comput Eng 3:29–34

    Google Scholar 

  16. Talbert JA, Parkinson AR (1990) Development of an automatic, two-dimension finite element mesh generator using quadrilateral elements and Bezier curve boundary definition. Int J Numer Method Eng 29:1551–1567

    Article  Google Scholar 

  17. Wu WT, Oh SI et al (1990) Automated mesh generation for forming simulation. In: ASME international computers in engineering conference proceedings, vol 1. ASME, Boston, Massachusetts, August 1990, pp 507–515

  18. Sarrate J, Huerta A (2000) Efficient unstructured quadrilateral mesh generation. Int J Numer Method Eng 49:1327–1350

    Article  MATH  Google Scholar 

  19. Joun MS, Lee MC (1997) Quadrilateral finite-element generation and mesh quality control for metal forming simulation. Int J Numer Method Eng 40:4059–4075

    Article  MATH  Google Scholar 

  20. Ma XW, Zhao GQ, Sun L (2011) AUTOMESH-2D/3D: robust automatic mesh generator for metal forming simulation. Mater Res Innov 15(s1):S482–S486

    Article  Google Scholar 

  21. Tsvelikh A, Axenenko O (1998) Automatic generation of quadrilateral finite element meshes. Comput Mater Sci 9:367–378

    Article  Google Scholar 

  22. Bastian M, Li B (2003) An efficient automatic mesh generator for quadrilateral elements implemented using C++. Finite Elem Anal Des 39:905–930

    Article  Google Scholar 

  23. Lee KY, Kim II, Cho DY, Kim TW (2003) An algorithm for automatic 2D quadrilateral mesh generation with line constraints. Comput Aided Des 35:1055–1068

    Article  Google Scholar 

  24. Park C, Noh JS, Jang IS, Kang JM (2007) A new automated scheme of quadrilateral mesh generation for randomly distributed line constraints. Comput Aided Des 39:258–267

    Article  Google Scholar 

  25. Sun L, Zhao GQ, Ma XW (2012) Adaptive generation and local refinement methods of three-dimensional hexahedral element mesh. Finite Elem Anal Des 50:184–200

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgments

This project is supported by Shandong Young Scientists Award Foundation (Grant No. BS2011ZZ008) and State Key Laboratory of Materials Processing and Die & Mould Technology, Huazhong University of Science and Technology.

Author information

Authors and Affiliations

  1. Key Laboratory for Liquid-Solid Structural Evolution and Processing of Materials (Ministry of Education), Shandong University, Jinan, 250061, China

    Xinwu Ma & Guoqun Zhao

  2. Engineering Research Center for Mould and Die, Shandong University, Jinan, 250061, China

    Xinwu Ma & Guoqun Zhao

Authors
  1. Xinwu Ma
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Guoqun Zhao
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Xinwu Ma.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ma, X., Zhao, G. An automated approach to quadrilateral mesh generation with complex geometric feature constraints. Engineering with Computers 31, 325–345 (2015). https://doi.org/10.1007/s00366-014-0353-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00366-014-0353-2

Keywords