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A computational framework for automating generation of sizing function in assembly meshing via disconnected skeletons

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Abstract

This paper proposes a framework for generating mesh sizing functions for assembly models. Size control is crucial in obtaining a high-quality mesh with a reduced number of elements. The reduction in the number of elements will decrease computation time and memory use during mesh generation and analysis. The framework consists of a background octree lattice for storing the sizing function, a set of source entities for providing sizing information based on geometric information, and an interpolation module for calculating the sizing on the background octree lattice using the source entities. Source entities are generated by performing a detailed systematic study to identify all the geometric factors of an assembly. Disconnected skeletons are extracted and used as tools to measure 3D proximity and 2D proximity, which are two of the geometric factors. The framework facilitates the generation of a variety of meshes with a low computational cost, to meet industry needs. The framework has been tested on many industrial parts, and sizing control on a few typical assemblies has been presented to demonstrate the effectiveness of the proposed framework.

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References

  1. Owen SJ (1998) A survey of unstructured mesh generation technology. In: Proceedings of 7th international meshing roundtable

  2. Lohner R, Parikh P (1988) Generation of three-dimensional unstructured grids by the advancing front method. AIAA-88-0515

  3. Chew LP (1989) Constrained delaunay triangulations. Algorithmica 4:97–108

    Article  MATH  MathSciNet  Google Scholar 

  4. Cunha A, Canann S, Saigal S (1997) Automatic boundary sizing for 2D and 3D meshes. AMD trends in unstructured mesh generation, ASME, vol 220, pp 65–72

  5. Owen SJ, Saigal S (1997) Neighborhood based element sizing control for finite element surface meshing. In: Proceedings of 6th international meshing roundtable, pp 143–154

  6. Pirzadeh S (1993) Structured background grids for generation of unstructured grids by advancing-front method. AIAA, vol 31

  7. Tracker WC (1980) A brief review of techniques for generating irregular computational grids. Int J Numer Methods Eng 15:1335–1341

    Article  Google Scholar 

  8. Shephard MS (1988) Approaches to the automatic generation and control of finite element meshes. Appl Mech Rev 41:169–185

    Article  Google Scholar 

  9. Zhu J, Blacker T, Smith R (2002) Background overlay grid size functions. In: Proceedings of 11th international meshing roundtable, pp 65–74

  10. Zhu J (2003) A new type of size function respecting premeshed entities. In: Proceedings of 12th international meshing roundtable

  11. Borouchaki H, Hecht F (1997) Mesh gradation control. In: Proceedings of 6th international meshing roundtable

  12. Persson P-O (2004) PDE-based gradient limiting for mesh size functions. In: Proceedings of 13th international meshing roundtable, pp 377–388

  13. Blum H (1967) A transformation for extracting new descriptors of shape. Models for the perception of speech and visual form. MIT Press, Cambridge, pp 326–380

  14. Srinivasan V, Nackman LR, Tang JM, Meshkat SN (1992) Automatic mesh generation using the symmetric axis transformation of polygonal domains. Proc IEEE 80(9):1485–1501

    Article  Google Scholar 

  15. Gursoy HN (1989) Shape interrogation by medial axis transform for automated analysis. MIT Ph.D. Thesis

  16. Gursoy HN, Patrikalakis NM (1992) An automatic coarse and fine surface mesh generation scheme based on MAT, part I: algorithms. Eng Comput 8:121–137

    Article  Google Scholar 

  17. Quadros WR, Ramaswami K, Prinz FB, Gurumoorthy B (2001) Automated geometry adaptive quadrilateral mesh generation using MAT. In: Proceedings of ASME DETC

  18. Quadros WR, Ramaswami K, Prinz FB, Gurumoorthy B (2004) LayTracks: a new approach to automated geometry adaptive quadrilateral mesh generation using medial axis transform. Int J Numer Methods Eng 20:249–264

    Google Scholar 

  19. Quadros WR, Owen SJ, Brewer M, Shimada K (2004) Finite element mesh sizing for surfaces using skeleton. In: Proceedings of 13th international meshing roundtable, pp 389–400

  20. Quadros WR, Shimada K, Owen SJ (2004) Skeleton-based computational method for generation of 3D finite element mesh sizing function. Eng Comput 20(3):249–264

    Google Scholar 

  21. George PL (1991) Automatic mesh generation applications to finite element methods. Wiley

  22. Samet H (1995) Spatial data structures. In: Kim W (ed) Modern database systems: the object model, interoperability, and beyond. ACM Press, Addison-Wesley, pp 361–385

  23. White DR, Saigal S, Owen SJ (2004) An Imprint and merge algorithm incorporating geometric tolerances for conformal meshing of misaligned assemblies. Int J Numer Methods Eng 59:1839–1860

    Article  MATH  Google Scholar 

  24. Quadros WR, Shimada K, Owen SJ (2004) 3D discrete skeleton generation by wave propagation on PR-Octree for finite element mesh sizing. In: Proceedings of ACM symposium on solid modeling and applications, Genova, Italy

  25. Owen SJ, Saigal S (2000) Surface mesh sizing control. Int J Numer Methods Eng 47:497–511

    Article  MATH  MathSciNet  Google Scholar 

  26. Eberly D (2003) Intersection of convex objects: the method of separating axes. Geometric tools, LLC. http://www.geometrictools.com/Documentation/MethodOfSeparatingAxes.pdf. Accessed 05 Jan 2010

  27. Akenine-Möller T (2005) Fast 3D triangle-box overlap testing. In: ACM SIGGRAPH 2005 Courses, Los Angeles, California

  28. 3D Content Central (2005). http://3dcontentcentral.com. Accessed 26 June 2005

  29. Knupp PM (2001) Algebraic mesh quality metrics. SIAM J Sci Comput 23:193–218

    Article  MATH  MathSciNet  Google Scholar 

  30. 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

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Author notes

  1. William Roshan Quadros

    Present address: Sandia National Laboratories, P.O. Box 5800, MS 1321, Albuquerque, NM, 87185-1321, USA

Authors and Affiliations

  1. Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA, 15213, USA

    William Roshan Quadros, Ved Vyas & Kenji Shimada

  2. Sandia National Laboratories, Albuquerque, NM, 87185, USA

    Mike Brewer & Steven James Owen

Authors
  1. William Roshan Quadros
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  2. Ved Vyas
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  3. Mike Brewer
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  4. Steven James Owen
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  5. Kenji Shimada
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Corresponding author

Correspondence to William Roshan Quadros.

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Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy under Contract DE-AC04-94AL85000.

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Quadros, W.R., Vyas, V., Brewer, M. et al. A computational framework for automating generation of sizing function in assembly meshing via disconnected skeletons. Engineering with Computers 26, 231–247 (2010). https://doi.org/10.1007/s00366-009-0164-z

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  • DOI: https://doi.org/10.1007/s00366-009-0164-z

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