Transactions of the Korean Society of Mechanical Engineers A (대한기계학회논문집A)

The Korean Society of Mechanical Engineers (대한기계학회)
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Development of Algorithm for 2-D Automatic Mesh Generation and Remeshing Technique Using Bubble Packing Method (I) -Linear Analysis-

버블패킹방법을 이용한 2차원 자동격자 생성 및 재구성 알고리듬 개발(I) -선형 해석-

  • Published : 2001.06.01
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Abstract

The fully automatic algorithm from initial finite element mesh generation to remeshing in two dimensional geometry is introduced using bubble packing method (BPM) for finite element analysis. BPM determines the node placement by force-balancing configuration of bubbles and the triangular meshes are made by Delaunay triangulation with advancing front concept. In BPM, we suggest two node-search algorithms and the adaptive/recursive bubble controls to search the optimal nodal position. To use the automatically generated mesh information in FEA, the new enhanced bandwidth minimization scheme with high efficiency in CPU time is developed. In the remeshing stage, the mesh refinement is incorporated by the control of bubble size using two parameters. And Superconvergent Patch Recovery (SPR) technique is used for error estimation. To verify the capability of this algorithm, we consider two elasticity problems, one is the bending problem of short cantilever beam and the tension problem of infinite plate with hole. The numerical results indicate that the algorithm by BPM is able to refine the mesh based on a posteriori error and control the mesh size easily by two parameters.

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References

  1. Peggy L. Baehmann, Scott L. Wittchen, Mark S. Shephard, Kurt R. Grice and Mark A. Verry, 1987, 'Robust, Geometrically Based, Automatic Two- Dimensional Mesh Generation,' Int. J. Numer. Methods Eng., Vol. 24, pp. 1043-1078 https://doi.org/10.1002/nme.1620240603
  2. Lee, C.K. and Hobbs, R.E., 1999, 'Automatic Adaptive Finite Element Mesh Generation over Arbitrary Two- Dimensional Domain Using Advancing Front Technique,' Computers and Structures, Vol. 71, pp. 9-34 https://doi.org/10.1016/S0045-7949(98)00215-6
  3. Kenji Shimada and David C. Gossard, 1998, 'Automatic Triangular Mesh Generation of Trimmed Parametric Surfaces for Finite Element Analysis,' Computer Aided Geometric Design, Vol. 15, pp. 199-222 https://doi.org/10.1016/S0167-8396(97)00037-X
  4. 정현석, 김용환, 1996, 'Delaunay 삼각화기법을 이용한 유한요소망의 자동생성과 격자 재구성에의 응용,' 대한기계학회논문집(A), 제20권, 제2호, pp. 553-563
  5. 채수원, 1994, 'h-분할법에 의한 사각형 유한요소망의 적응적 구성,' 대한기계학회 논문집, 제18권, 제11호, pp. 2932-2943
  6. Paulino, G.H., Menezes, I.F.M., Cavalcante Neto, J.B. and Martha, L.F., 1999, 'A Methodology for Adaptive Finite Element Analysis Towards an Integrated Computational Environment,' Computational Mechanics, Vol. 23, pp. 361-388 https://doi.org/10.1007/s004660050416
  7. Zienkiewicz, O.C. and Zhu, J.Z., 1992, 'The Superconvergent Patch Recovery and a Posteriori Error Estimates. Part I : The Recovery Technique,' Int. J. Numer. Methods Eng., Vol. 33, pp. 1331-1364 https://doi.org/10.1002/nme.1620330702
  8. Boroomand, B. and Zienkiewicz, O.C., 1997, 'Recovery by Equilibrium in Patches,' Int. J. Numer. Methods Eng., Vol. 40, pp. 137-164 https://doi.org/10.1002/(SICI)1097-0207(19970115)40:1<137::AID-NME57>3.0.CO;2-5
  9. Chongjiang Du, 1998, 'A Note on Finding Nearest Neighbours and Constructing Delaunay Triangulation in the Plane,' Communications in Numer. Methods Eng., Vol. 14, pp. 871-877 https://doi.org/10.1002/(SICI)1099-0887(199809)14:9<871::AID-CNM195>3.3.CO;2-Y
  10. Ketan Mulmuley, 1994, Computational Geometry : An Introduction Through Randomized Algorithms, Prentice-Hall, pp. 288-289
  11. Jari Puttonen, 1983, 'Simple and Effective Bandwidth Reduction Algorithm,' Int. J. Numer. Methods Eng., Vol. 19, pp. 1139-1152 https://doi.org/10.1002/nme.1620190804
  12. Zienkiewicz, O.C., Zhu, J.Z. and Gong, N.G., 1989, 'Effective and Practical hop-Version Adaptive Analysis Procedure for the Finite Element Method,' Int. J. Numer. Methods Eng., Vol. 28, pp. 879-891 https://doi.org/10.1002/nme.1620280411