Engineering with Computers

, Volume 30, Issue 1, pp 41–56 | Cite as

TUM.GeoFrame: automated high-order hexahedral mesh generation for shell-like structures

  • C. SorgerEmail author
  • F. Frischmann
  • S. Kollmannsberger
  • E. Rank
Original Article


This paper presents a fully automated high-order hexahedral mesh generation algorithm for shell-like structures based on enhanced sweeping methods. Traditional sweeping techniques create all-hexahedral element meshes for solid structures by projecting an initial single surface mesh along a specified trajectory to a specified target surface. The work reported here enhances the traditional method for thin solids by creating conforming high-order all-hexahedral finite element meshes on an enhanced surface model with surfaces intersecting in parallel, perpendicular and skew-angled directions. The new algorithm is based on cheap projection rules separating the original surface model into a set of disjoint single surfaces and a so-called interface skeleton. The core of this process is reshaping the boundary representations of the initial surfaces, generating new sweeping templates along the intersection curves and joining the single swept hex meshes in an independently generated interface mesh.


Mesh generation Hexahedron High order Thin walled Shell like TUM.GeoFrame 



This research work has been partly supported by the Excellence Initiative of the German Federal and State Governments via the TUM International Graduate School of Science and Engineering. This support is gratefully acknowledged. Additionally, we would like to acknowledge the support of M. Breitenbach, who has generated the geometry of the power plant model seen in Fig. 24.


  1. 1.
    Gordon WJ, Hall ChA (1973) Transfinite element methods: blending function interpolation over arbitrary curved element domains. Numerische Mathematik 21:109–129CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Kiràlyfalvi G, Szabò BA (1997) Quasi-regional mapping for the p-version of the finite element method. Finite Elements Anal Des 27(1):85–97CrossRefzbMATHGoogle Scholar
  3. 3.
    Rank E, Düster A, Nübel V, Preusch K, Bruhns OT (2003) high-order finite elements for shells. Comput Methods Appl Mech Eng 194(21−24):2494–2512Google Scholar
  4. 4.
    Hughes TJR, Cottrell JA, Bazilevs Y (2005) Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Comput Methods Appl Mech Eng 194(39−41):4135–4195CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Cottrell JA, Hughes TJR, Reali A (2005) Studies of refinement and continuity in isogeometric structural analysis. Comput Methods Appl Mech Eng 196(41−44):4160–4183Google Scholar
  6. 6.
    Cottrell JA, Hughes TJR, Bazilevs Y (2009) Towards Integration of CAD and FEA. Wiley, ChichesterGoogle Scholar
  7. 7.
    Bazilevs Y, Calo VM, Cottrell JA, Evans JA, Hughes TJR, Lipton S, Scott MA, Sederberg TW (2010) Isogeometric analysis using T-splines. Comput Methods Appl Mech Eng 199: 229–263 Google Scholar
  8. 8.
    Kima HJ, Seoa YD, You SK (2009) Isogeometric analysis for trimmed CAD surfaces. Comput Methods Appl Mech Eng 198:2982–2995CrossRefGoogle Scholar
  9. 9.
    Kima HJ, Seoa YD, You SK (2010) Isogeometric analysis with trimming technique for problems of arbitrary complex topology. Comput Methods Appl Mech Eng 198:2796–2812CrossRefGoogle Scholar
  10. 10.
    CUBIT: Geometry and Mesh Generation Toolkit. Sandia National Laboratories.
  11. 11.
    Gmsh: a three-dimensional finite element mesh generator with built-in pre- and post-processing facilities Christophe Geuzaine and Jean-François Remacle,
  12. 12.
    Netgen: An automatic 3d tetrahedral mesh generator. Joachim Schöberl.
  13. 13.
    TetGen: A Quality Tetrahedral Mesh Generator and a 3D Delaunay Triangulator. Weierstrass Institute for Applied Analysis and Stochastics (WIAS).
  14. 14.
    Owen SJ (1998) A survey of unstructured mesh generation technology. In: Proceedings of the 7th International Meshing Roundtable, Sandia National Labratories, pp 239−267Google Scholar
  15. 15.
    Lu Y, Gadh R, Tautges TJ (2001) Feature based hex meshing methodology: feature recognition and volume decomposition. Computer-Aided Des 33:221–232CrossRefGoogle Scholar
  16. 16.
    Lu Y, Gadh R, Tautges TJ (1999) Volume decomposition and feature recognition for hexahedral mesh generation. In: Proceedings of the 8th International Meshing Roundtable, South Lake Tahoe, CA, pp 269−280Google Scholar
  17. 17.
    Shih BY, Sakurai H (1997) Shape recognition and shape-specific meshing for generating all hexahedral meshes. In: Proceedings of the 6th International Meshing Roundtable, Park City, UT, pp 197−209Google Scholar
  18. 18.
    Blacker TD (1996) The Cooper Tool. In: Proceedings of the 5th International Meshing Roundtable, Pittsburgh, PA, pp 13−29Google Scholar
  19. 19.
    Knupp PM (1998) Next-generation sweep tool: a method for generation all-hex meshes on two-and-one-half dimensional geometries. In: Proceedings of the 7th International Meshing Roundtable, Dearborn, MI, pp 505−513Google Scholar
  20. 20.
    Staten ML, Canann SA, Owen SJ (1999) BMSweep: locating interior nodes during sweeping. Eng Comput 15:212–218CrossRefzbMATHGoogle Scholar
  21. 21.
    Mingwu L, Benzley S, White DR (2000) Automated hexahedral mesh generation by generalized multiple source to multiple target sweeping. Int J Numer Methods Eng 49:261–275CrossRefzbMATHGoogle Scholar
  22. 22.
    Dohrmann CR, Key SW, Heinstein MW (2000) Methods for connecting dissimilar three-dimensional finite element meshes. Int J Numer Methods Eng 47:1057–1080CrossRefzbMATHGoogle Scholar
  23. 23.
    Puso MA, Laursen TA (2003) Mesh Tying on Curved Interfaces in 3D. Eng Comput 20(3):305–319CrossRefzbMATHGoogle Scholar
  24. 24.
    Wohlmuth BI (2001) Discretization methods and iterative solvers based on domain decomposition. Springer, HeidelbergCrossRefzbMATHGoogle Scholar
  25. 25.
    Park KC, Felippa CA, Rebel G (2002) A simple algorithm for localized construction of non-matching structural interfaces. Int J Numer Methods Eng 53:2117–2142CrossRefzbMATHMathSciNetGoogle Scholar
  26. 26.
    Puso MA (2004) A 3D mortar method for solid mechanics. Int J Numer Methods Eng 59:315–336CrossRefzbMATHGoogle Scholar
  27. 27.
    Staten ML, Shepherd JF, Shimada K (2008) Mesh matching−creating conforming interfaces between hexahedral meshes. In: Proceedings of the 17th International Meshing Roundtable, vol 7, pp 467−484Google Scholar
  28. 28.
    Staten ML, Shepherd JF, Ledoux F, Shimada K (2010) Hexahedral Mesh Matching: Converting non-conforming hexahedral-to-hexahedral interfaces into conforming interfaces. Int J Numer Methods Eng 82:1475–1509zbMATHGoogle Scholar
  29. 29.
    Sherbrooke EC, Patrikalakis NM, Brisson E (1996) An algorithm for the medial axis transform of 3D polyhedral solids. Vis Comput Graph 2(1):44–61CrossRefGoogle Scholar
  30. 30.
    Armstrong CG, McKeag RM, Ou H, Price MA (2000) Geometric processing for analysis. In: Proceedings of the Geometric modeling and processing 2000. Theory and Applications, Belfast, IR, pp 45−56Google Scholar
  31. 31.
    Kwon KY, Lee BC, Chae SW (2006) Medial surface generation using chordal axis transformation in shell structures. Comput Struct 84(26−27):1673–1683CrossRefGoogle Scholar
  32. 32.
    Armstrong CG, Robinson TT, Ou H (2008) Recent advances in CAD/CAE technologies for thin-walled structures design and analysis. Proceedings of the 5th International Conference on Thin-Walled Structures, Brisbane, AustraliaGoogle Scholar
  33. 33.
    Owen SJ, Staten ML, Canann SA, Saigal S (1999) Q-Morph: An indirect approach to advancing front quad meshing. Int J Numer Methods Eng 44:1317–1340CrossRefzbMATHGoogle Scholar
  34. 34.
    Cass RJ, Benzley SE, Meyers RJ, Blacker TD (1996) Generalized 3-D paving: an automated quadrilateral surface mesh generation algorithm. Int J Numer Methods Eng 39:1475–1489CrossRefzbMATHGoogle Scholar
  35. 35.
    Geuzaine C, Remacle JF (2009) Gmsh: a three-dimensional finite element mesh generator with built-in pre- and post-processing facilities. Int J Numer Methods Eng 79:1309–1331CrossRefzbMATHMathSciNetGoogle Scholar
  36. 36.
    Remacle JF, Henrotte F, Baudouin TC, Geuzaine C, Béchet E, Mouton T, Marchandise E (2012) A frontal delaunay quad mesh generator using the l\(\infty\) norm. In: Proceedings of the 20th International Meshing Roundtable, pp 455−472Google Scholar
  37. 37.
    Düster A, Bröker H, Heidkamp H, Heißerer U, Kollmannsberger S, Wassouf Z, Krause R, Muthler A, Niggl A, Nübel V, Rücker M, Scholz D (2010) AdhoC4−User’s Guide. Lehrstuhl für Computation in Engineering, TU München, Numerische Strukturanalyse mit Anwendungen in der Schiffstechnik, TU Hamburg-HarburgGoogle Scholar
  38. 38.
    Nokia (2011) Qt Development Frameworks.
  39. 39.
    OPEN CASCADE SAS (2011) Open CASCADE Technology.
  40. 40.
    Kitware Inc. (2011) Visualization Toolkit (VTK).
  41. 41.
    Society for Industrial and Applied Mathematics (2010) LAPACK Linear Algebra PACKage.
  42. 42.
    Bank RE (1990) PLTMG: A Software Package for Solving Elliptic Partial Differential Equations. SIAM Frontiers in Applied MathematicsGoogle Scholar
  43. 43.
    Schweingruber-Straten M (1999) Generierung von Oberflächennetzen nach der Gebietsteilungstechnik. PhD thesis, Fach Numerische Methoden und Informationsverarbeitung, Universität DortmundGoogle Scholar
  44. 44.
    Sorger C, Kollmannsberger S, Frischmann F, Scholz D, Halfmann A (2009) Interfacing Do_Mesh—User’s Guide. Lehrstuhl für Computation in Engineering, Technische Universität MünchenGoogle Scholar
  45. 45.
    Schoeberl J (1997) NETGEN—an advancing front 2D/3D-mesh generator based on abstract rules. Comput Vis Sci 1(1):41–52CrossRefzbMATHGoogle Scholar
  46. 46.
    IGES/PDES Organization. 2006. Initial graphics exchange specification—IGES 5.3. US Product Data Association (US PRO)Google Scholar
  47. 47.
    SCRA. 2006. STEP application handbook—ISO 10303—version 3. U.S. Product Data Association (US PRO)Google Scholar
  48. 48.
    Babuška I, Chen Q (1995) Approximate optimal points for polynomial interpolation of real functions in an interval and in a triangle. Comput Methods Appl Mech Eng 128:405–417CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2012

Authors and Affiliations

  • C. Sorger
    • 1
    Email author
  • F. Frischmann
    • 1
  • S. Kollmannsberger
    • 1
  • E. Rank
    • 1
  1. 1.Chair for Computation in Engineering, Faculty of Civil Engineering and GeodesyTechnische Universität MünchenMunichGermany

Personalised recommendations