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Engineering with Computers

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01.09.2004 | Original article

Skeleton-based computational method for the generation of a 3D finite element mesh sizing function

verfasst von: William Roshan Quadros, Kenji Shimada, Steven James Owen

Erschienen in: Engineering with Computers | Ausgabe 3/2004

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Abstract

This paper focuses on the generation of a three-dimensional (3D) mesh sizing function for geometry-adaptive finite element (FE) meshing. The mesh size at a point in the domain of a solid depends on the geometric complexity of the solid. This paper proposes a set of tools that are sufficient to measure the geometric complexity of a solid. Discrete skeletons of the input solid and its surfaces are generated, which are used as tools to measure the proximity between geometric entities and feature size. The discrete skeleton and other tools, which are used to measure the geometric complexity, generate source points that determine the size and local sizing function at certain points in the domain of the solid. An octree lattice is used to store the sizing function as it reduces the meshing time. The size at every lattice-node is calculated by interpolating the size of the source points. The algorithm has been tested on many industrial models, and it can be extended to consider other non-geometric factors that influence the mesh size, such as physics, boundary conditions, etc.

Vorheriger Artikel Fully automatic and fast mesh size specification for unstructured mesh generation

Nächster Artikel Polygonal surface mesh optimization

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Cook WA, Oakes WR (1982) Mapping methods for generating three-dimensional meshes. Computers in mechanical engineering, CIME research supplement, pp 67–72

Shimada K, Mori N, Kondo T, Itoh T, Kase K, Makinouchi A (1999) Automated mesh generation for sheet metal forming simulation. Int J Vehicle Design 21:278–291

Owen SJ (1998) A survey of unstructured mesh generation technology. In: Proceedings of the 7th international meshing roundtable, Dearborn, Michigan, October 1998

Lohner R, Parikh P (1988) Generation of three-dimensional unstructured grids by the advancing front method. Int J Numer Meth Fluids 8:1135–1149

Chew LP (1989) Constrained Delaunay triangulations. Algorithmica 4:97–108MathSciNetMATH

Chew LP (1989) Guaranteed-quality triangular meshes. Technical report TR-89-983, Cornell University, Ithaca, New York

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

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

Pirzadeh S (1993) Structured background grids for generation of unstructured grids by advancing-front method. AIAA 31(2):257–265

10.

Yerry MA, Shepard MS (1983) A modified-quadtree approach to finite element mesh generation. IEEE Comput Graph Appl 3:39–46

11.

Yerry MA, Shepard MS (1984) Automatic three-dimensional mesh generation by the modified octree technique. Int J Numer Methods Eng 20:1965–1990MATH

12.

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

13.

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

14.

Baehmann PL, Wittchen SL, Shephard MS, Grice KR, Yerry MA (1987) Robust geometrically based automatic two-dimensional mesh generation. Int J Numer Methods Eng 24:1043–1078MATH

15.

Peruchio R, Saxena M, Kela A (1989) Automatic mesh generation from solid models based on recursive spatial decomposition. Int J Numer Methods Eng 28:2469–2502

16.

Shepard MS, Georges MK (1991) Automatic three-dimensional mesh generation by the finite octree technique. Int J Numer Methods Eng 32:709–749

17.

Frey PJ, Marechal L (1998) Fast adaptive quadtree mesh generation. In: Proceedings of the 7th international meshing roundtable, Dearborn, Michigan, 26–28 October 1998

18.

Schneiders R, Schindler R, Weiler F (1996) Octree-based hexahedral mesh generation. Int J Comput Geometry Appl 10:383–393CrossRef

19.

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

20.

Zhu J (2003) A new type of size function respecting premeshed entities. In: Proceedings of the 12th international meshing roundtable, Santa Fe, New Mexico, 14–17 September 2003

21.

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

22.

Gursoy HN (1989) Shape interrogation by medial axis transform for automatd analysis. PhD thesis, MIT, Massachusetts

23.

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

24.

Quadros WR, Ramaswami K, Prinz FB, Gurumoorthy B (2001) Automated geometry adaptive quadrilateral mesh generation using MAT. In: Proceedings of the ASME design engineering technical conferences (DETC), Pittsburgh, Pennsylvania, September 2001

25.

Quadros WR, Shimada K, Owen SJ (2003) Skeleton-based computational method for generation of 3D finite element mesh sizing function. In: Proceedings of the 7th US national congress on computational mechanics (USNCCM 2003), 4th symposium on trends in unstructured mesh generation, Albuquerque, New Mexico, 27–31 July 2003

26.

Tchon K-F, Khachan M, Guibault F, Camarero R (2003) Constructing anisotropic geometric metrics using octrees and skeletons. In: Proceedings of the 12th international meshing roundtable, Santa Fe, New Mexico, 14–17 September 2003, pp 293–304

27.

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

28.

Blum H (1973) Biological shape and visual science (part I). J Theor Biol 38:205–287

29.

Blacker TD, Stephenson MB (1991) PAVING: a new approach to automatic quadrilateral mesh generation. Int J Numer Methods Eng 32:811–847MATH

30.

Sherbrooke EC, Patrikalakis NM, Wolter F (1996) Note on differential and topological properties of medial axis transforms. Graph Models Image Processing 58:547–592

31.

Lam L, Lee SW, Chen CY (1992) Thinning methodologies: a comprehensive survey. IEEE Trans PAMI 14:869–885CrossRef

32.

Zhang YY, Wang PSP (1993) Analytical camparison of thinning algorithms. Int J Pattern Recog Artif Intell 7:1227–1246

33.

Manzanera A, Bernard TM, Preteux F, Longuet B (1999) Medial faces from a concise 3D thinning algorithm. In: Proceedings of the IEEE international conference on computer vision (ICCV’99), Kerkyra, Greece, September 1999, pp 337–343

34.

Danielsson PE (1980) Euclidean distance mapping. Comput Graph Image Processing 14:227–248

35.

Ragnemalm I (1993) The Euclidean distance transformation in arbitrary dimensions. Pattern Recogn Lett 14:883–888CrossRefMATH

36.

Siddiqi K, Bouix S (1999) The Hamilton–Jacobi skeleton. In: Proceedings of the IEEE international conference on computer vision (ICCV’99), Kerkyra, Greece, September 1999, pp 828–834

37.

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

38.

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 the ACM symposium on solid modeling and applications (SM’04), Genova, Italy, 9–11 June 2004

39.

Bitter I, Kaufman AE, Sato M (2001) Penalized-distance volumetric skeleton algorithm. IEEE Trans Visualization Comput Graph 7:195–206CrossRef

40.

Quadros WR, Ramaswami K, Prinz FB, Gurumoorthy B (2001) Skeleton for representation and reasoning in engineering applications. Eng Comput 17:186–198MATH

41.

Prasad L (1997) Morphological analysis of shapes. Available at http://cnls.lanl.gov/Highlights/1997-07/html/July_97.html. Cited July 1997

42.

Berg MD, Kreveld MV, Overmars M, Schwarzkopf O (1997) Computational geometry: algorithms and applications. Springer, Berlin Heidelberg New York

43.

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

44.

Mclvor A, Valkernburg R (1997) A comparison of local geometry estimation methods. Machine Vis Appl 10:17–26CrossRef

45.

Borouchaki H, Hecht F (1997) Mesh gradation control. In: Proceedings of the 6th international meshing roundtable, Park City, Utah, 13–15 October 1997

Titel: Skeleton-based computational method for the generation of a 3D finite element mesh sizing function
verfasst von: William Roshan Quadros
Kenji Shimada
Steven James Owen
Publikationsdatum: 01.09.2004
Verlag: Springer-Verlag
Erschienen in: Engineering with Computers / Ausgabe 3/2004
Print ISSN: 0177-0667
Elektronische ISSN: 1435-5663
DOI: https://doi.org/10.1007/s00366-004-0292-4

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