Dynamic FEM Mesh Generation



Today, simulation of production processes is becoming much more important in manufacturing, where complex machining operations and materials handling are encountered. A particular emphasis has been given to research and development of virtual manufacturing, having various computer-aided software tools for analysis and simulation of machine behaviours, aiming at realising an optimal production environment, first-time-right products, yet with high quality, low cost and short lead-time. It often requires an advanced system capability to analyse and simulate the dynamic behaviours of production cells and lines, as if they are under real operating conditions. This type of simulation considers production rate of the entire system while treating each machine as a black box. In order to evaluate and optimise the mechanical integrity and to ensure the true dynamic and thermal behaviours of machine tools, some types of analyses are required for individual machines in addition to system-level simulation. Due to the complex nature of the geometric features of the components and that of the applied loads, finite element method (FEM) and boundary element method (BEM) have been mostly adopted in the last three decades. FEM is a powerful numerical tool for solving mathematical problems related to practical engineering situations. In the past, it was a common practice to over-simplify such problems to the point where an analytical solution could be obtained. Because of the uncertainties associated with such a procedure, large safety factors were introduced in the design of machine tools.


  1. 1.
    W.K. Liu, S. Jun, S. Li, J. Adee, T. Belytschko, Reproducing Kernel particle methods for structural dynamics. Int. J. Numer. Meth. Eng. 28, 1655–1679 (1995)Google Scholar
  2. 2.
    Y.Y. Lu, T. Belytschko, L. Gu, A new implementation of the element free Galerkin method. Comput. Methods Appl. Mech. Eng. 113, 397–414 (1994)Google Scholar
  3. 3.
    E. Oñate, S. Idelsohn, A mesh-free finite point method for advective-diffusive transport and fluid flow problems. Comput. Mech. 21, 283–292 (1998)MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    T. Liszka, J. Orikisz, Finite difference method at arbitrary irregular grids and its application in applied mechanics. Comput. Struct. 11, 83–95 (1980)MATHCrossRefGoogle Scholar
  5. 5.
    Y.X. Mukherjee, S. Mukherjee, The boundary node method for potential problems. Int. J. Numer. Meth. Eng. 40, 797–815 (1997)MATHCrossRefGoogle Scholar
  6. 6.
    C.A. Duarte, J.T. Oden, An h-p adaptive method using clouds. Comput. Methods Appl. Mech. Eng. 139, 237–262 (1996)MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    T. Zhu, J. Zhang, S.N. Atluri, A meshless local boundary integral equation (LBIE) method for solving nonlinear problems. Comput. Methanics 22, 174–186 (1998)MathSciNetMATHGoogle Scholar
  8. 8.
    N.R. Aluru, G. Li, Finite cloud method:Atruemeshless technique based on a fixed reproducing Kernel approximation. Int. J. Numer. Meth. Eng. 50, 2373–2410 (2001)MATHCrossRefGoogle Scholar
  9. 9.
    J.U. Turner, Accurate solid modeling using polyhedral approximations. IEEE Comput. Graph. Appl., pp. 14–27 (1988)Google Scholar
  10. 10.
    W.H. Chen, J.T. Yeh, Finite element analysis of finite deformation contact problems with friction. Comput. Struct. 29(3), 423–436 (1988)MathSciNetMATHCrossRefGoogle Scholar
  11. 11.
    J.M. Guedes, N. Kikuchi, Preprocessing and postprocessing for materials based on the homogenization method with adaptive finite element methods. Comput. Methods Appl. Mech. Eng. 83, 143–198 (1990)MathSciNetMATHCrossRefGoogle Scholar
  12. 12.
    L. Wang, T. Moriwaki, An approach to dynamic finite element mesh generation for machines with relative motions. Mem. Grad. School Sci. Technol., Kobe Univ. 11-A (1993)Google Scholar
  13. 13.
    A. Denayer, Automatic generation of finite element meshes. Comput. Strcuctures 9, 359–364 (1978)MATHCrossRefGoogle Scholar
  14. 14.
    L.R. Herrmann, Laplacian-isoparametric grid generation scheme. J. Eng. Mech.Div. Proc. Am. Soc. Civil Eng. 102(EM5):10 (1976)Google Scholar
  15. 15.
    Z.J. Cendes, D. Shenton, H. Shahnasser, Magnetic field computation using delaunay triangulation and complementary finite element methods. IEEE Trans. Mag. MAG–19, 6 (1983)Google Scholar
  16. 16.
    T.I. Boubez, W.R.J. Funnell, D.A. Lowther, A.R. Pinchuk, P.P. Silvester, Mesh generation for computational analysis. J. Comput. Aided Eng. 10, 190–201 (1986)CrossRefGoogle Scholar
  17. 17.
    W. Brostow, J.P. Dussault, Construction of voronoi polyhedra. J. Comput. Phys. 29, 81–92 (1978)MathSciNetMATHCrossRefGoogle Scholar
  18. 18.
    P.J. Green, R. Sibson, Computing dirichlet tessellations in the plane. Comput. J. 21(2), 168–173 (1977)MathSciNetCrossRefGoogle Scholar
  19. 19.
    B.Wordenweber, Volume triangulation. in TechnicalReport-CADGroup Document (University of Cambridge), No. 110, (1980)Google Scholar
  20. 20.
    B.Wordenweber, Finite element mesh generation. Comput. Aided Des. 16(5), 285–291 (1984)CrossRefGoogle Scholar
  21. 21.
    B.G. Baumgart, Geometric modeling for computer vision. in Report No. CS-463 Stanford Artificial Intelligence Laboratory, Computer Science Department, Stanford, USA, 1974.Google Scholar
  22. 22.
    J. Suhara, J. Fukuda, Automatic Mesh Generation for Finite Element Analysis. Advances in Computational Methods in Structural Mechanics and Design (UAH Press, Huntsville, Alabama, USA, 1972)Google Scholar
  23. 23.
    A.O. Moscardini, B.A. Lewis, M. Cross, AGTHOM-automatic generation of triangular and higher order meshes. Int. J. Numer. Meth. Eng. 19, 1331–1353 (1983)MATHCrossRefGoogle Scholar
  24. 24.
    R.D. Shaw, R.G. Pitchen, Modifications to the SUHARA-FUKUDA method of network generation. Int. J. Numer. Meth. Eng. 12, 93–99 (1978)MATHCrossRefGoogle Scholar
  25. 25.
    S.H. Lo, A new mesh generation scheme for arbitrary planar domains. Int. J. Numer. Meth. Eng. 21, 1403–1426 (1985)MATHCrossRefGoogle Scholar
  26. 26.
    B.A. Lewis, J.S. Robinson, Triangulation of planar rigions with applications. Comput. J. 21(4), 324–332 (1977)CrossRefGoogle Scholar
  27. 27.
    C.O. Frederick, Y.C. Wong, F.W. Edge, Two-dimensional automatic mesh generation for structural analysis. Int. J. Numer. Meth. Eng. 2, 133–144 (1970)CrossRefGoogle Scholar
  28. 28.
    J.M. Nelson, A triangulation algorithm for arbitrary planar domains. Appl. Math. Modeling 2, 151–159 (1978)MATHCrossRefGoogle Scholar
  29. 29.
    M.B. McGirr, D. Corderoy, P. Easterbrook, A. Hellier, A new approach to automatic mesh generation in the continuum. in Proceedings of 4th International Conference Australia Finite Element Method, Melbourne, Australia, pp. 36–40, (1982)Google Scholar
  30. 30.
    J.C. Cavendish, Automatic triangulation of arbitrary planar domains for the finite element method. Int. J. Numer. Meth. Eng. 8, 679–696 (1974)MATHCrossRefGoogle Scholar
  31. 31.
    E.A. Sadek, A scheme for the automatic generation of triangular finite elements. Int. J. Numer. Meth. Eng. 15, 1813–1822 (1980)MATHCrossRefGoogle Scholar
  32. 32.
    Y. Liu, K. Chen, Atwo-dimensionalmesh generator for variable order triangular and rectangular elements. Comput. Struct. 29(6), 1033–1053 (1988)MATHCrossRefGoogle Scholar
  33. 33.
    N. Van Phai, Automatic mesh generation with tetrahedron elements. Int. J. Numer. Meth. Eng. 18, 273–289 (1982)MATHCrossRefGoogle Scholar
  34. 34.
    J.C. Cavendish, D.A. Field, W.H. Frey, An approach to automatic three-dimensional finite element mesh generation. Int. J. Numer. Meth. Eng. 21, 329–347 (1985)MATHCrossRefGoogle Scholar
  35. 35.
    N.A. Calvo, S.R. Idelsohn, All-hexahedral element meshing: Generation of the dual mesh by recurrent subdivision. Comput. Methods Appl. Mech. Eng. 182, 371–378 (2000)MATHCrossRefGoogle Scholar
  36. 36.
    S.H. Lo, Finite element mesh generation over curved surfaces. Comput. Struct. 29(5), 731–742 (1988)MATHCrossRefGoogle Scholar
  37. 37.
    F. Cheng, J.W. Jaromczyk, J.R. Lin, S.S. Chang, J.Y. Lu, A parallel mesh generation algorithm based on the vertex label assignment scheme. Int. J. Numer. Meth. Eng. 28, 1429–1448 (1989)MathSciNetMATHCrossRefGoogle Scholar
  38. 38.
    B.K. Karamete, M.W. Beall, M.S. Shephard, Triangulation of arbitrary polyhedra to support automatic mesh generator. Int. J. Numer. Meth. Eng. 49, 167–191 (2000)MATHCrossRefGoogle Scholar
  39. 39.
    S. Dey, R.M. O’Bara, M.S. Shephard, Towards curvilinear meshing in 3D: The case of quadratic simplices. Comput. Aided Des. 33, 199–209 (2001)CrossRefGoogle Scholar
  40. 40.
    A. Kela, R. Perucchio, H. B. Voelcker, Toward automatic finite element analysis. Comput. Mech. Eng. 5, 1 (1986)Google Scholar
  41. 41.
    W.C. Thacker, A. Gonzalez, G.E. Putland, Amethod for automating the construction of irregular computational grids for storm surge forecast models. J. Comput. Phys. 37, 371–387 (1980)MATHCrossRefGoogle Scholar
  42. 42.
    N. Kikuchi, Adaptive grid-design methods for finite element analysis. Comput. Methods Appl. Mech. Eng. 55, 129–160 (1986)MathSciNetMATHCrossRefGoogle Scholar
  43. 43.
    E.A. Heighway, C. S. Biddlecombe, Two-dimensional automatic triangular mesh generation for the finite element electromagnetics package PE2D. IEEE Trans. on Mag. MAG-18(2), 594–598 (1982)Google Scholar
  44. 44.
    K.K. Wang, N. Hashimoto, Test and evaluation of TIPS-1 system. in Technical Report MME-04 (Cornell University, Ithaca, NY, USA, 1981)Google Scholar
  45. 45.
    T. Akiyama, K. K. Wang, A TIPS-1 Based CAD Program for Mold Design. in Proceedings of 9th North American Manufacturing Research Conference (1981)Google Scholar
  46. 46.
    M.A. Yerry, M.S. Shephard, A modified quadtree approach to finite element mesh generation. IEEE Comput. Graph. Appl., pp. 39–46, (1983)Google Scholar
  47. 47.
    H. Samet, The quadtree and related hierarchical data structures. ACM Comput. Surv. 16(2), 187–260 (1984)MathSciNetCrossRefGoogle Scholar
  48. 48.
    S.F. Yeung, M.B. Hsu, A mesh generation method based on set theory. Comput. Strcuct. 3, 1063–1077 (1973)MathSciNetCrossRefGoogle Scholar
  49. 49.
    R. Haber, M.S. Shephard, J.F. Abel, R.H. Gallagher, D.P. Greenberg, Ageneral two-dimensional graphical finite element preprocessor utilizing discrete transfinite mappings. Int. J. Numer. Meth. Eng. 17, 1015–1044 (1981)MATHCrossRefGoogle Scholar
  50. 50.
    C.A. Hall, Transfinite Interpolation and Applications to Engineering Problems. Theory of Approximation (Academic, New York, 1976)Google Scholar
  51. 51.
    W.A. Cook, Body oriented (natural) co-ordinates for generating three-dimensionalmeshes. Int. J. Numer. Meth. Eng. 8, 27–43 (1974)MATHCrossRefGoogle Scholar
  52. 52.
    W.J. Gordon, C.A. Hall, Construction of curvilinear co-ordinate systems and applications to mesh generation. Int. J. Numer. Meth. Eng. 7, 461–477 (1973)MathSciNetMATHCrossRefGoogle Scholar
  53. 53.
    O.C. Zienkiewicz, D.V. Phillips, An automatic mesh generation scheme for plane and curved surfaces by ‘isoparametric’ co-ordinates. Int. J. Num. Methods Eng. 3, 519–528 (1971)MathSciNetMATHCrossRefGoogle Scholar
  54. 54.
    H.D. Cohen, A method for the automatic generation of triangular elements on a surface. Int. J. Numer. Meth. Eng. 15, 470–476 (1980)MATHCrossRefGoogle Scholar
  55. 55.
    W.D. Barfield, Numerical method for generating orthogonal curvilinear meshes. J. Comput. Phys. 5, 23–33 (1970)MathSciNetMATHCrossRefGoogle Scholar
  56. 56.
    P.R. Brown, A non-interactive method for the automatic generation of finite element meshes using the Schwarz-Christoffel transformation. Comput. Methods Appl. Mech. Eng. 25, 101–126 (1981)MATHCrossRefGoogle Scholar
  57. 57.
    K.H. Baldwin, H.L. Schreyer, Automatic generation of quadrilateral elements by a conformal mapping. Eng. Comput. 2, 187–194 (1985)CrossRefGoogle Scholar
  58. 58.
    A. Bykat, Design of a recursive, shape controlling mesh generator. Int. J. Numer. Meth. Eng. 19, 1375–1390 (1983)MATHCrossRefGoogle Scholar
  59. 59.
    A. Bykat, Automatic generation of triangular grid: I—Subdivision of a general polygon into convex subregions. II—Triangulation of convex polygons. Int. J. Numer.Meth. Eng. 10, 1329–1342 (1976)MATHCrossRefGoogle Scholar
  60. 60.
    M.L.C. Sluiter, D.C. Hansen, A general purpose automatic mesh generator for shell and solid finite elements. Comput. Eng., Vol. 3, Book No. G00217, ASME, pp. 29–34, (1982)Google Scholar
  61. 61.
    D.A. Lindholm,Automatic triangular mesh generation on surfaces of polyhedra. IEEE Trans. Mag. MAG–19(6), 1539–1542 (1983)Google Scholar
  62. 62.
    T.C. Woo, T. Thomasma, An algorithm for generating solid elements in objects with holes. Comput. Struct. 18(2), 333–342 (1984)MATHCrossRefGoogle Scholar
  63. 63.
    M.A. Yerry, M.S. Shephard, Automatic three-dimensional mesh generation by the modifiedoctree technique. Int. J. Numer. Meth. Eng. 20(11), 1965–1990 (1984)MATHCrossRefGoogle Scholar
  64. 64.
    A. Jain, Modern Methods for Automatic FE MeshGeneration. Modern Methods for Automating Finite Element Mesh Generation (The American Society of Civil Engineers, USA, 1986)Google Scholar
  65. 65.
    K. Ho-Le, Finite element mesh generation methods: A review and classification. Comput. Aided Des. 20(1), 27–38 (1988)MATHCrossRefGoogle Scholar
  66. 66.
    International Meshing Roundtable,, last accessed on September 26, 2012
  67. 67.
    J. Sarrate, A. Huerta, Efficient unstructured quadrilateral mesh generation. Int. J. Numer. Meth. Eng. 49, 1327–1350 (2000)MATHCrossRefGoogle Scholar
  68. 68.
    S.J. Owen, S. Saigal, H-Morph: An indirect approach to advancing front hex meshing. Int. J. Numer. Meth. Eng. 49, 289–312 (2000)MATHCrossRefGoogle Scholar
  69. 69.
    S.J. Owen, Hex-dominantmesh generation using 3D constrained triangulation. Comput. Aided Des. 33, 211–220 (2001)CrossRefGoogle Scholar
  70. 70.
    S.J. Owen, M.L. Staten, S.A. Canann, S. Saigal, Q-Morph: An indirect approach to advancing front quad meshing. Int. J. Numer. Meth. Eng. 44, 1314–1340 (1999)CrossRefGoogle Scholar
  71. 71.
    Y. Lu, R. Gadh, T.J. Tautges, Feature based hex meshing methodology: Feature recognition and volume decomposition. Comput. Aided Des. 33, 221–232 (2001)CrossRefGoogle Scholar
  72. 72.
    X.Y. Li, S.H. Teng, A. Üngör, Simultaneous refinement and coarsening for adaptive meshing. Eng. Comput. 15, 280–291 (1999)MATHCrossRefGoogle Scholar
  73. 73.
    M. Halpbern, Industrial requirements and practices in finite element meshing: A survey of trends. in Proceedings of 6th International Meshing Roundtable, SAND97-2399, Sandia National Laboratories, 1997Google Scholar
  74. 74.
    A. Sheffer, M. Bercovier, Hexahedral meshing of non-linear volumes using voronoi faces and edges. Int. J. Numer. Meth. Eng. 49, 329–351 (2000)MathSciNetMATHCrossRefGoogle Scholar
  75. 75.
    M. Lai, S. Benzley, D. White, Automated hexahedral mesh generation by generalized multiple source to multiple target sweeping. Int. J. Numer. Meth. Eng. 49, 261–375 (2000)MATHCrossRefGoogle Scholar
  76. 76.
    M.L. Staten, S.A. Canann, S.J. Owen, BMSweep: Locating interior nodes during sweeping. Eng. Comput. 15, 212–218 (1999)MATHCrossRefGoogle Scholar
  77. 77.
    P. Knupp, Applications of mesh smoothing: Copy, morph, and sweep on unstructured quadrilateral meshes. Int. J. Numer. Meth. Eng. 45, 37–45 (1999)MathSciNetMATHCrossRefGoogle Scholar
  78. 78.
    T.J.Tautges, The generation of hexahedralmeshes for assembly geometry: Survey and progress. Int. J. Numer. Meth. Eng. 50, 2617–2642 (2001)MATHCrossRefGoogle Scholar
  79. 79.
    G. Dhondt, Unstructured 20-node brick element meshing. Comput. Aided Des. 33, 233–249 (2001)CrossRefGoogle Scholar
  80. 80.
    G. Dhondt, A new automatic hexahedral mesher based on cutting. Int. J. Numer. Meth. Eng. 50, 2109–2126 (2001)MATHCrossRefGoogle Scholar
  81. 81.
    T. Tautges, T. Blacker, S. Mitchell, The whisker weaving algorithm: A connectivity-based method for constructing all-hexahedral finite element meshes. Int. J. Numer. Meth. Eng. 39, 3327–3349 (1996)MathSciNetMATHCrossRefGoogle Scholar
  82. 82.
    N.T. Folwell, S.A. Mitchell, Reliable whisker weaving via curve contraction. Eng. Comput. 15, 292–302 (1999)MATHCrossRefGoogle Scholar
  83. 83.
    I. Yokota, From Topological Geometry to Projective Geometry. Modern Mathematics Press, (1993)Google Scholar
  84. 84.
    An Date, Introduction to Data Base System (Addison-Wesley Publishing Company, Third Edition, 1981)Google Scholar

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© Springer-Verlag London 2014

Authors and Affiliations

  1. 1.Department of Production EngineeringKTH Royal Institute of TechnologyStockholmSweden

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