Automatic triangular mesh generation of trimmed parametric surfaces for finite element analysis

Computer Aided Geometric Design

Volumn 15, Issue 3, 1998, Pages 199-222

  Shimada, Kenji ^a   Gossard, David C ^b  

^a IBM JAPAN LTD   (Japan)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Bubble meshing; Delaunay triangulation; Dynamic simulation; Finite element analysis; Physically based model; Sphere packing; Triangulation; Voronoi polygons

Indexed keywords

ALGORITHMS; COMPUTER AIDED DESIGN; COMPUTER SIMULATION; FINITE ELEMENT METHOD; FUNCTIONS;

AUTOMATIC TRIANGULAR MESH GENERATION; DELAUNAY TRIANGULATION; VORONOI POLYGONS;

COMPUTATIONAL GEOMETRY;

EID: 0032022668     PISSN: 01678396     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-8396(97)00037-X     Document Type: Article

References (34)

1. Armstrong, C.G. et al. (1991), Automatic generation of well structured meshes using medial axis and surface subdivision, ASME Advances in Design Automation, 139-146.
2. Blacker, T.D. and Stephenson, M.B. (1991), Paving: a new approach to automated quadrilateral mesh generation, International Journal for Numerical Methods in Engineering 32, 811-847.
3. Cavendish, J.C. (1974), Automatic triangulation of arbitrary planar domains for the finite element method. International Journal for Numerical Methods in Engineering 8, 679-696.
4. Crawford, R.H., Waggenspack, W.N. and Anderson, D.C. (1987), Composite mappings for planar mesh generation, International Journal for Numerical Methods in Engineering 24, 2241-2252.
5. Field, D.A. (1991), A generic Delaunay triangulation algorithm for finite element meshes, Advances in Engineering Software 13, 263-272.
6. Frey, W.H. (1987), Selective refinement: a new strategy for automatic node placement in graded triangular meshes. International Journal for Numerical Methods in Engineering 24, 2183-2200.
7. Frey, W.H. and Field, D.A. (1991), Mesh relaxation: a new technique for improving triangulations. International Journal for Numerical Methods in Engineering 31, 1121-1133.
8. Gursoy, H.N. (1989), Shape interrogation by medial axis transform for automated analysis, Ph.D. thesis, Massuchasetts Institute of Technology, Cambridge, MA, USA.
9. Heighway, E.A. (1983), A mesh generator for automatically subdividing irregular polygons into quadrilaterals, IEEE Trans. Magn. 19, 2535-2538.
10. Hinton, E., Rao, N.V.R. and Ozakca, M. (1991), Mesh generation with adaptive finite element analysis, Advances in Engineering Analysis 13, 238-262.
11. Johnston, B.P., Sullivan, J.M. and Kwasnik, A. (1991), Automatic conversion of triangular finite element meshes to quadrilateral elements, International Journal for Numerical Methods in Engineering 31, 67-84.
12. Lee, N.S. (1993), Adaptive procedures for nonlinear elastic and elasto-plastic finite element analysis, Ph.D. thesis, Massachusetts Institute of Technology.
13. Lohner, R. and Parikh, P. (1988), Generation of three-dimensional unstructured grids by the advancing-front method, AIAA-88-0515.
14. Meshkat, S., Ruppert, J. and Li, H. (1991), Three-dimensional automatic unstructured grid generation based on Delaunay tetrahedrization, in: Proc. of Third International Conference on Numerical Grid Generation.
15. Ogata, K., Modern Control Engineering, Printice-Hall, 1970.
16. Patrikalakis, N.M. and Gursoy, H.N. (1990), Shape interrogation by medial axis transformation. Advances in Design Automation, 77-88.
17. Press, W.H. et al. (1988), Numerical Recipes in C: the Art of Scientific Computing, Cambridge University Press, 1988.
18. Rockwood, A., Heaton, K. and Davis, T. (1989), Real-time rendering of trimmed surfaces, Computer Graphics (SIGGRAPH89) 21, 107-116.
19. Ruppert, J. (1992), Results on triangulation and high quality mesh generation, Ph.D. thesis, University of California at Berkeley.
20. Sapidis, N. and Perucchio, R. (1991), Delaunay triangulation of arbitrarily shaped planar domains, Computer Aided Geometric Design 8, 421-437.
21. Schroeder, W.J. (1988), Geometry-based fully automatic mesh generation and the Delaunay triangulation, International Journal for Numerical Methods in Engineering 26, 2503-2115.
22. Sheng, X. and Hirsch, B.E. (1992), Triangulation of trimmed surfaces in parametric spaces, Computer-Aided Design 24, 437-444.
23. Shephard, M.S. and Georges, M.K. (1991), Automatic three-dimensional mesh generation by the finite octree technique, International Journal for Numerical Methods in Engineering 32, 709-749.
24. Shimada, K. and Gossard, D.C. (1992), Computational methods for physically-based FE mesh generation, in: Olling, G.J. and Kimura, F. (eds.), Proc. of the IFIP TC5/WG5.3 Eight International PROLAMAT Conference, 411-420.
25. Shimada, K. (1993), Physically-based mesh generation: automated triangulation of surfaces and volumes via bubble packing, Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, MA.
26. Shimada, K., Balents, B. and Gossard, D.C. (1993), Automatic mesh reconstruction for feature-based sculpting of deformable surfaces, in: Wilson, P.R., Wozny, M.J. and Pratt, M.J., eds., IFIP Transaction B-8, Geometric Modelling for Product realization, 165-188.
27. Srinivasan, V., Nackman, L.R. and Tang, J.-M. (1990), Automatic mesh generation using the symmetric axis transformation of polygonal domains, IBM Research Report, RC16132.
28. Watson, D.F. (1981), Computing the n-dimensional Delaunay tessellation with applications to Voronoi polytopes, Computer Journal 24, 167-172.
29. Wellford, L.C. and Gorman, M.R. (1988), Finite element transitional mesh generation procedure using sweeping functions. International Journal for Numerical Methods in Engineering 26, 2623-2643.
30. Yerry, M.A. and Shephard, M.S. (1983), A modified-quadtree approach to finite element mesh generation, IEEE Computer Graphics & Applications 3, 39-46.
31. Yuen, M.M.F., Tan, S.T. and Hung, K. Y. (1991), A hierarchical approach to automatic finite element mesh generation, International Journal for Numerical Methods in Engineering 32, 501-525.
32. Zhu, J.Z. et al. (1991), A new approach to the development of automatic quadrilateral mesh generation, International Journal for Numerical Methods in Engineering 32, 849-866.
33. Zienkiewicz, O.C. and Phillips, D.V. (1971), An automatic mesh generation scheme for plane and curved surfaces by isoparametric co-ordinates, International Journal for Numerical Methods in Engineering 3, 519-528.
34. Zienkiewicz, O.C. and Zhu, J.Z. (1987), A simple error estimator and adaptive procedure for practical engineering analysis, International Journal for Numerical Methods in Engineering 24. 337-357.