한국정밀공학회지 (Journal of the Korean Society for Precision Engineering)

  • 제17권3호
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  • Pages.136-148
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  • 2000
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  • 1225-9071(pISSN)
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  • 2287-8769(eISSN)
한국정밀공학회 (Korean Society for Precision Engineering)
권호 표지

쿼드트리를 이용한 일반적인 3차원 트림곡면에서의 유한요소 자동생성

Automatic Mesh Generation in the General Three-Dimensional Trimmed Surface using Qua

  • 유동진 (대진대학교 컴퓨터응용 기계설계학과) ;
  • 윤정환 (LG 생산기술원 Design Engineering Center)
  • 발행 : 2000.03.01
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⟨ 이전 논문 다음 논문 ⟩

초록

In this work, a general method for the mathematical description of three-dimensional trimmed surface is proposed by introducing the base parametric surface and boundary curves. Since mesh density distribution for the analysis may vary by cases, a grid-based mesh generation algorithm using quadtree is proposed in the present work. For the assurance of connectivity of generated meshes among surfaces, a method for the pre-cleaning of boundary curves has been developed to be used in the automatic generation of the finite elements. In addition, mesh-smoothing algorithm is suggested which can be used in the general trimmed surface. In this algorithm nodes are moved on the original surface by the normal projection in each iterative smoothing procedure.

키워드

참고문헌

  1. T.C.Woo and T.Thomasma, 'An algorithm for generating solid elements in objects with holes,' Compt. & Struct., Vol. 18, pp. 333-342, 1984 https://doi.org/10.1016/0045-7949(84)90132-9
  2. J.C.Cavendish, 'Automatic triangulation of arbitrary planar domains for the finite element method,' Int. J. Numer. Meth. Eng., Vol. 8, pp. 679-696, 1974 https://doi.org/10.1002/nme.1620080402
  3. J.M.Nelson, 'A triangulation algorithm for arbitrary planar domains,' Appl. Math. Modeling, Vol. 2, pp. 151-159, 1978 https://doi.org/10.1016/0307-904X(78)90002-1
  4. A.Bykat, 'Design of recursive shape controlling mesh generator,' Int. J. Numer. Meth. Eng., Vol. 19, pp. 1375-1390, 1983 https://doi.org/10.1002/nme.1620190907
  5. J.A. Talbert and A.R. Parkinson, 'Development of an automatic two-dimensional finite element mesh generator using quadriateral elements and Bezier curve boundary definition,' Int. J. Numer. Meth. Eng., Vol. 29, pp. 1551-1567, 1990 https://doi.org/10.1002/nme.1620290712
  6. N. Kikuchi, 'Adaptive grid-design methods for finite element analysis,' Comput. Methods in Applied Mech. Eng., Vol. 55, pp. 129-160, 1986 https://doi.org/10.1016/0045-7825(86)90089-7
  7. R.J. Meyers and T.D. Blacker, 'Generalized 3-D paving : an automated quadrilateral surface mesh generation algorithm,' Int. J. Numer. Meth. Eng., Vol. 39, pp. 1475-1489, 1996 https://doi.org/10.1002/(SICI)1097-0207(19960515)39:9<1475::AID-NME913>3.0.CO;2-W
  8. 이영규, '소성가공공정의 유한요소해석을 위한 3차원 자동격자구성기법,' 한국과학기술원 기계공학과 박사학위논문, 1998
  9. CATIA User's manual, Dassault Systems, Inc., 1996
  10. B.K. Choi, 'Surface modeling for CAD/CAM,' Elsevier Science Publishers B.V., 1991
  11. I.D. Faux and M.I. Pratt, 'Computational geometry for design and manufacture,' Ellis Horwood Ltd., 1979
  12. D.F. Rogers and J.A. Adams, 'Mathematical elements for computer graphics,' McGrawHill, 1990
  13. 이건우, '컴퓨터그래픽과 CAD,' 영지문화사, 1994
  14. W.H.Press, B.P.Flannery, S.A.Teukolsky and W.T.Vetterling, 'Numerical recipes: The art of scientific computing,' Cambridge University Press, 1986
  15. M.A. Yerry and M.S. Shephard, 'A modified quadtree approach to finite element mesh generation,' IEEE Comput. Graph. & Appl., Feb., pp. 39-46, 1983 https://doi.org/10.1109/MCG.1983.262997
  16. N. Nakajima, S. Tokumasu and Y. Kunitomo, 'Feature-based heuristics for finite elemen meshing using quadtree and octrees,' Computer-Aided Design, Vol. 24, pp. 677-690, 1992 https://doi.org/10.1016/0010-4485(92)90023-4
  17. H. Samet, 'Neighbor finding technique for images represented by quadtrees,' Comput. Graph. & Image Proc., Vol. 18, pp. 37-57, 1982 https://doi.org/10.1016/0146-664X(82)90098-3
  18. 정융호, '사면체 Octree 에 근거한 3차원 유한요소의 자동생성,' 서울대학교 대학원 박사학위 논문, 1993
  19. S.H. Lo and C.K. Lee, 'Generation of gradation meshes by the background grid technique,' Comput. & Struct., Vol. 50, pp. 21-32, 1994 https://doi.org/10.1016/0045-7949(94)90434-0
  20. D.F.Watson, 'Computing the n-dimensional Delaunary tessellation with application to Voronoi polygons,' Comp. J., Vol. 24, pp. 167-172, 1981 https://doi.org/10.1093/comjnl/24.2.167
  21. S.H. Lo, 'Delaunay triangulation of non-convex planar domains,' Int J. Numer. Meth. Eng., Vol. 28, pp. 2695-2707, 1989 https://doi.org/10.1002/nme.1620281113
  22. T.P. Fang and L.A. Piegl, 'Algorithm for Delaunay triangulation and convex-hull computation using a sparse matrix,' Computer-Aided Design, Vol. 24, No. 8, pp. 425-436, 1992 https://doi.org/10.1016/0010-4485(92)90010-8
  23. B.K. Choi, H.Y. Shin, Y.I. Yoon and J.W. Lee, 'Triangulation of scattered data in 3D space,' Computer-Aided Design, Vol. 20, No. 5, pp. 239-248, 1988 https://doi.org/10.1016/0010-4485(88)90069-3
  24. D.J. Yoo, I.S. Song, D.Y. Yang and J.H. Lee, 'Rigidplastic finite element analysis of sheet metal forming processes using continuous contact treatment and membrane elements incorporating bending effect,' Int. J. Mech. Sci., Vol. 36, pp. 513-546, 1994 https://doi.org/10.1016/0020-7403(94)90030-2
  25. Advanced Programming, Dassault Systems, Inc., 1996
  26. IUA Application Interface, Dassault Systems, Inc., 1996