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Dynamic FEM Mesh Generation

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Dynamic Thermal Analysis of Machines in Running State
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Abstract

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.

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References

  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. 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. E. Oñate, S. Idelsohn, A mesh-free finite point method for advective-diffusive transport and fluid flow problems. Comput. Mech. 21, 283–292 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  4. T. Liszka, J. Orikisz, Finite difference method at arbitrary irregular grids and its application in applied mechanics. Comput. Struct. 11, 83–95 (1980)

    Article  MATH  Google Scholar 

  5. Y.X. Mukherjee, S. Mukherjee, The boundary node method for potential problems. Int. J. Numer. Meth. Eng. 40, 797–815 (1997)

    Article  MATH  Google Scholar 

  6. C.A. Duarte, J.T. Oden, An h-p adaptive method using clouds. Comput. Methods Appl. Mech. Eng. 139, 237–262 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    MathSciNet  MATH  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  9. J.U. Turner, Accurate solid modeling using polyhedral approximations. IEEE Comput. Graph. Appl., pp. 14–27 (1988)

    Google Scholar 

  10. W.H. Chen, J.T. Yeh, Finite element analysis of finite deformation contact problems with friction. Comput. Struct. 29(3), 423–436 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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. A. Denayer, Automatic generation of finite element meshes. Comput. Strcuctures 9, 359–364 (1978)

    Article  MATH  Google Scholar 

  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. 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. 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)

    Article  Google Scholar 

  17. W. Brostow, J.P. Dussault, Construction of voronoi polyhedra. J. Comput. Phys. 29, 81–92 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  18. P.J. Green, R. Sibson, Computing dirichlet tessellations in the plane. Comput. J. 21(2), 168–173 (1977)

    Article  MathSciNet  Google Scholar 

  19. B.Wordenweber, Volume triangulation. in TechnicalReport-CADGroup Document (University of Cambridge), No. 110, (1980)

    Google Scholar 

  20. B.Wordenweber, Finite element mesh generation. Comput. Aided Des. 16(5), 285–291 (1984)

    Article  Google Scholar 

  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. 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. 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)

    Article  MATH  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  25. S.H. Lo, A new mesh generation scheme for arbitrary planar domains. Int. J. Numer. Meth. Eng. 21, 1403–1426 (1985)

    Article  MATH  Google Scholar 

  26. B.A. Lewis, J.S. Robinson, Triangulation of planar rigions with applications. Comput. J. 21(4), 324–332 (1977)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  28. J.M. Nelson, A triangulation algorithm for arbitrary planar domains. Appl. Math. Modeling 2, 151–159 (1978)

    Article  MATH  Google Scholar 

  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. J.C. Cavendish, Automatic triangulation of arbitrary planar domains for the finite element method. Int. J. Numer. Meth. Eng. 8, 679–696 (1974)

    Article  MATH  Google Scholar 

  31. E.A. Sadek, A scheme for the automatic generation of triangular finite elements. Int. J. Numer. Meth. Eng. 15, 1813–1822 (1980)

    Article  MATH  Google Scholar 

  32. Y. Liu, K. Chen, Atwo-dimensionalmesh generator for variable order triangular and rectangular elements. Comput. Struct. 29(6), 1033–1053 (1988)

    Article  MATH  Google Scholar 

  33. N. Van Phai, Automatic mesh generation with tetrahedron elements. Int. J. Numer. Meth. Eng. 18, 273–289 (1982)

    Article  MATH  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  36. S.H. Lo, Finite element mesh generation over curved surfaces. Comput. Struct. 29(5), 731–742 (1988)

    Article  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  40. A. Kela, R. Perucchio, H. B. Voelcker, Toward automatic finite element analysis. Comput. Mech. Eng. 5, 1 (1986)

    Google Scholar 

  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)

    Article  MATH  Google Scholar 

  42. N. Kikuchi, Adaptive grid-design methods for finite element analysis. Comput. Methods Appl. Mech. Eng. 55, 129–160 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  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. 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. 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. 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. H. Samet, The quadtree and related hierarchical data structures. ACM Comput. Surv. 16(2), 187–260 (1984)

    Article  MathSciNet  Google Scholar 

  48. S.F. Yeung, M.B. Hsu, A mesh generation method based on set theory. Comput. Strcuct. 3, 1063–1077 (1973)

    Article  MathSciNet  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  50. C.A. Hall, Transfinite Interpolation and Applications to Engineering Problems. Theory of Approximation (Academic, New York, 1976)

    Google Scholar 

  51. W.A. Cook, Body oriented (natural) co-ordinates for generating three-dimensionalmeshes. Int. J. Numer. Meth. Eng. 8, 27–43 (1974)

    Article  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  55. W.D. Barfield, Numerical method for generating orthogonal curvilinear meshes. J. Comput. Phys. 5, 23–33 (1970)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  57. K.H. Baldwin, H.L. Schreyer, Automatic generation of quadrilateral elements by a conformal mapping. Eng. Comput. 2, 187–194 (1985)

    Article  Google Scholar 

  58. A. Bykat, Design of a recursive, shape controlling mesh generator. Int. J. Numer. Meth. Eng. 19, 1375–1390 (1983)

    Article  MATH  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  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. D.A. Lindholm,Automatic triangular mesh generation on surfaces of polyhedra. IEEE Trans. Mag. MAG–19(6), 1539–1542 (1983)

    Google Scholar 

  62. T.C. Woo, T. Thomasma, An algorithm for generating solid elements in objects with holes. Comput. Struct. 18(2), 333–342 (1984)

    Article  MATH  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  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. K. Ho-Le, Finite element mesh generation methods: A review and classification. Comput. Aided Des. 20(1), 27–38 (1988)

    Article  MATH  Google Scholar 

  66. International Meshing Roundtable, http://www.imr.sandia.gov/, last accessed on September 26, 2012

  67. J. Sarrate, A. Huerta, Efficient unstructured quadrilateral mesh generation. Int. J. Numer. Meth. Eng. 49, 1327–1350 (2000)

    Article  MATH  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  69. S.J. Owen, Hex-dominantmesh generation using 3D constrained triangulation. Comput. Aided Des. 33, 211–220 (2001)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  72. X.Y. Li, S.H. Teng, A. Üngör, Simultaneous refinement and coarsening for adaptive meshing. Eng. Comput. 15, 280–291 (1999)

    Article  MATH  Google Scholar 

  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, 1997

    Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  76. M.L. Staten, S.A. Canann, S.J. Owen, BMSweep: Locating interior nodes during sweeping. Eng. Comput. 15, 212–218 (1999)

    Article  MATH  Google Scholar 

  77. P. Knupp, Applications of mesh smoothing: Copy, morph, and sweep on unstructured quadrilateral meshes. Int. J. Numer. Meth. Eng. 45, 37–45 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  78. T.J.Tautges, The generation of hexahedralmeshes for assembly geometry: Survey and progress. Int. J. Numer. Meth. Eng. 50, 2617–2642 (2001)

    Article  MATH  Google Scholar 

  79. G. Dhondt, Unstructured 20-node brick element meshing. Comput. Aided Des. 33, 233–249 (2001)

    Article  Google Scholar 

  80. G. Dhondt, A new automatic hexahedral mesher based on cutting. Int. J. Numer. Meth. Eng. 50, 2109–2126 (2001)

    Article  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  82. N.T. Folwell, S.A. Mitchell, Reliable whisker weaving via curve contraction. Eng. Comput. 15, 292–302 (1999)

    Article  MATH  Google Scholar 

  83. I. Yokota, From Topological Geometry to Projective Geometry. Modern Mathematics Press, (1993)

    Google Scholar 

  84. An Date, Introduction to Data Base System (Addison-Wesley Publishing Company, Third Edition, 1981)

    Google Scholar 

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Wang, L. (2014). Dynamic FEM Mesh Generation. In: Dynamic Thermal Analysis of Machines in Running State. Springer, London. https://doi.org/10.1007/978-1-4471-5273-6_4

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