Advertisement

Geometrical Description and Discretization of Hydraulic Structures

  • Sheng-Hong ChenEmail author
Chapter
Part of the Springer Tracts in Civil Engineering book series (SPRTRCIENG)

Abstract

Pre-processing towards the geometrical description and discretization is one of the prerequisites for the structural analysis using computational mechanics. Despite of tedious and time-consuming overheads, it must be handled carefully to obtain reasonable accuracy for the performance prediction of hydraulic structure. In this chapter, a robust identification algorithm of irregular block system is implemented with the help of the “directed body” concept and by taking into account of the existence of irregular ground surfaces (curved faults and dam surfaces as well) and grouting/drainage curtains. Use is made of the advancing front technique (AFT), a sophisticated element (triangular, quadrilateral, tetrahedral) discretization algorithm is further implemented for a structure domain identified previously or constructed by the technique with CAD/CAM software. These may be competently employed for the discrete approaches (e.g. BEA) and continuum approaches (e.g. FEM, CEM) elaborated in the hereinafter chapters towards hydraulic structures with complex discontinuity system and configuration.

References

  1. Anderson BD. Automated all quadrilateral mesh adaptation through refinement and coarsening. Master’s thesis, Brigham Young University, Provo; 2009.Google Scholar
  2. Babuška I, Henshaw WD, Oliger JE, Flaherty JE, Hopcroft JE, Tezduyar T. Modeling, mesh generation, and adaptive numerical methods for partial differential equations. New York: Springer; 1995.CrossRefGoogle Scholar
  3. Baker TJ. Three dimensional mesh generation by triangulation of arbitrary point sets. In: Proceedings of the AIAA 8th CFD conference. Swansea: Pineridge Press; 1987. p. 255–71.Google Scholar
  4. Batdorf M, Freitag LA, Ollivier-Gooch C. Computational study of the effect of unstructured mesh quality on solution efficiency. In: Proceedings of the 13th annual computational fluid dynamics meeting. Reston: AIAA; 1997.Google Scholar
  5. Baudouin TC, Remacle JF, Marchandise E, Henrotte F, Geuzaine C. A frontal approach to hex-dominant mesh generation. Adv Model Simul Eng Sci. 2014;1:8.CrossRefGoogle Scholar
  6. Beall MW, Shephard MS. A general topology-based mesh data structure. Int J Numer Methods Eng. 1997;40(9):1573–96.MathSciNetCrossRefGoogle Scholar
  7. Blacker TD, Stephenson MS. Paving: a new approach to automated quadrilateral mesh generation. Int J Numer Methods Eng. 1991;32(4):811–47.CrossRefGoogle Scholar
  8. Blacker TD, Stephenson MB, Mitchiner JL, Phillips LR, Lin YT. Automated quadrilateral mesh generation: a knowledge system approach. ASME paper; 1988. 88–WA/CIE–4.Google Scholar
  9. Bonet J, Peraire J. An alternating digital (ADT) algorithm for 3-D geometric searching and intersecting problems. Int J Numer Methods Eng. 1991;31(1):1–17.CrossRefGoogle Scholar
  10. Bornhill RE, Little FF. Three and four-dimensional surfaces. Rochy Mt J Math. 1984;14(1):77–102.MathSciNetCrossRefGoogle Scholar
  11. Buell WR, Bush BA. Mesh generation—a survey. J Int Eng Trans ASME. 1973;95(1):332–8 (Ser. B).CrossRefGoogle Scholar
  12. Canann SA, Stephenson MB, Blacker TD. Optismoothing: an optimization-driven approach to mesh smoothing. Finite Elem Anal Des. 1993;13(2–3):185–90.MathSciNetCrossRefGoogle Scholar
  13. Cao XH, Chen SF, Chen SH. Generation of tetrahedral meshes in 3-D domains by advancing front method. J Wuhan Univ Hydr Elec Eng (WUHEE). 1998;31(1):16–20 (in Chinese).Google Scholar
  14. Cass RJ, Benzley SE, Meyers RJ, Blacker TD. Generalized 3D paving: an automated quadrilateral surface mesh generation algorithm. Int J Numer Methods Eng. 1996;39(9):1475–89.CrossRefGoogle Scholar
  15. Chen SH. Hydraulic structures. Berlin: Springer; 2015.CrossRefGoogle Scholar
  16. Chen SH, Wang JS, Zhang JL. Adaptive elasto-viscoplastic FEM analysis for hydraulic structures. J Hydraulic Eng. 1996;27(2):68–75 (in Chinese).Google Scholar
  17. Chen SF, Chen SH, Cao XH. Automatic generation of unstructured hexahedron mesh for 3D complicated domain. Rock Soil Mech. 1998;19(4):46–51 (in Chinese).Google Scholar
  18. Chen SH, Chen SF, Cao XH. Three dimensional hexahedron mesh generation for rock engineering. In: Yafin SA, (editor). Proceedings of 3rd international conference on advanced computer methods. Moscow: AA Balkema; 2000. p. 203–06.Google Scholar
  19. Cundall PA. Formulation of three-dimensional distinct element model. Part 1. A scheme to detect and represent contacts in system composed of many polyhedral blocks. Int J Rock Mech Min Sci Geomech Abstr. 1988;25(3):107–16.CrossRefGoogle Scholar
  20. Dari EA, Buscaglia GC. Mesh optimization: how to obtain good unstructured 3-D finite element meshes with not-so-good mesh generators. Struct Optim. 1994;8(2):181–8.CrossRefGoogle Scholar
  21. De Berg M, Cheong O, van Kreveld M, Overmars M. Computational geometry: algorithms and applications. 3rd ed. Berlin: Springer; 2008.Google Scholar
  22. De Cougny HL, Shephard MS. Parallel refinement and coarsening of tetrahedral meshes. Int J Numer Meth Eng. 1999;46(7):1101–25.MathSciNetCrossRefGoogle Scholar
  23. Field DA. Laplacian smoothing and Delaunay triangulations. Commun Appl Numer Methods. 1988;4(6):709–12.CrossRefGoogle Scholar
  24. George PL, Borouchaki H. Delaunay triangulation and meshing: application to finite elements. Paris: Hermes Science Publications; 1998. p. 230–4.zbMATHGoogle Scholar
  25. Gordon WJ. Spline-blended surface interpolation through curve networks. J Math Mech. 1969;18(1):931–52.MathSciNetzbMATHGoogle Scholar
  26. Hansbo P. Generalized laplacian smoothing of unstructured grids. Commun Numer Methods Eng. 1995;11(5):455–64.CrossRefGoogle Scholar
  27. Heliot D. Generating a blocky rock mass. Int J Rock Mech Min Sci Geomech Abstr. 1988;25(3):127–39.CrossRefGoogle Scholar
  28. Hermann LR. Laplacian-isoparametric grid generation scheme. J Eng Mech ASCE. 1976;102(EM5):749–56.Google Scholar
  29. Ho LK. Finite element mesh generation methods: a review and classification. Comp Aided Des. 1988;20(1):27–38.CrossRefGoogle Scholar
  30. Ikegawa Y, Hudson JA. A novel automatic identification system for three-dimensional multi-block systems. Eng Comput. 1992;9(2):169–79.CrossRefGoogle Scholar
  31. Ito Y, Nakahashi K. Improvements in the reliability and quality of unstructured hybrid mesh generation. Int J Numer Methods Fluids. 2004;45(1):79–108.CrossRefGoogle Scholar
  32. Jin H, Tanner RI. Generation of unstructured tetrahedral meshes by advancing front technique. Int J Numer Methods Eng. 1993;36(11):1805–23.CrossRefGoogle Scholar
  33. Jin H, Wiberg NE. Two-dimensional mesh generation, adaptive remeshing and refinement. Int J Numer Methods Eng. 1990;29(7):1501–26.CrossRefGoogle Scholar
  34. Jing L, Stephansson O. Topological identification of block assemblages for jointed rock masses. Int J Rock Mech Min Sci Geomech Abstr. 1994;31(2):163–72.CrossRefGoogle Scholar
  35. Joe B. Construction of three-dimensional improved-quality triangulations using local transformations. J Sci Comput SIAM. 1995;16(6):1292–307.MathSciNetCrossRefGoogle Scholar
  36. Kinney P. Clean up: improving quadrilateral finite elements meshes. In: Proceedings of the 6th international meshing roundtable. Park City: Sandia National Laboratories;1997. p. 449–61.Google Scholar
  37. Lau TS, Lo SH. Finite element mesh generation over analytical curved surfaces. Comput Struct. 1996;59(2):301–9.MathSciNetCrossRefGoogle Scholar
  38. Lin D, Fairhurst C, Starfield AM. Geometrical identification of three dimensional rock block systems using topological techniques. Int J Rock Mech Min Sci Geomech Abstr. 1987;24(6):331–8.CrossRefGoogle Scholar
  39. Lo SH. A new mesh generation scheme for arbitrary planar domains. Int J Numer Methods Eng. 1985;21(8):1403–26.CrossRefGoogle Scholar
  40. Lo SH. Generating quadrilateral elements on plane and over curved surfaces. Comput Struct. 1989;31(3):421–6.CrossRefGoogle Scholar
  41. Lo SH. Optimization of tetrahedral meshes based on element shape measures. Comput Struct. 1997;63(5):951–61.CrossRefGoogle Scholar
  42. Lober RR, Tautges TJ, Vaughan CT. Parallel paving: an algorithm for generating distributed, adaptive, all-quadrilateral meshes on parallel computers (Sandia report). Park City: Sandia National Laboratories; 1997.Google Scholar
  43. Löhner R. Some useful data structures for the generation of unstructured grids. Commun Appl Numer Methods. 1988;4(1):123–35.MathSciNetCrossRefGoogle Scholar
  44. Löhner R. A parallel advancing front grid generation scheme. Int J Numer Methods Eng. 2001;51(6):663–78.CrossRefGoogle Scholar
  45. Löhner R, Parikh P. Generation of three-dimensional unstructured grids by the advancing-front method. Int J Numer Methods Fluids. 1988;8(10):1135–49.CrossRefGoogle Scholar
  46. Lori A, Carl O. Tetrahedral mesh improvement using swapping and smoothing. Int J Numer Methods Eng. 1997;40(21):3979–4002.MathSciNetCrossRefGoogle Scholar
  47. Merhof D, Grosso R, Tremel U, Greiner G. Anisotropic quadrilateral mesh generation: an indirect approach. Adv Eng Softw. 2007;38(11–12):860–7.CrossRefGoogle Scholar
  48. Moller P, Hansbo P. On advancing front mesh generation in three dimensions. Int J Numer Methods Eng. 1995;38(21):3551–69.MathSciNetCrossRefGoogle Scholar
  49. Nguyen-Van-Phai. Automatic mesh generation with tetrahedron elements. Int J Numer Methods Eng. 1982;18(2):237–89.CrossRefGoogle Scholar
  50. Nordsletten D, Smith NP. Triangulation of p-order parametric surfaces. J Sci Comput. 2008;34(3):308–35.MathSciNetCrossRefGoogle Scholar
  51. Owen SJ. A survey of unstructured mesh generation technology. In: Proceedings of the 7th international meshing roundtable. Dearborn: Sandia National Laboratories;1998. p. 239–67.Google Scholar
  52. Owen SJ, Staten ML, Canann SA, Saigal S. Q-Morph: an indirect approach to advancing front quadrangle meshing. Int J Numer Methods Eng. 1999;44(9):1317–40.CrossRefGoogle Scholar
  53. Peraire J, Vahdati M, Morgan K, Zienkiewicz OC. Adaptive remeshing for compressible flow computations. J Comp Phys. 1987;72(2):449–66.CrossRefGoogle Scholar
  54. Peraire J, Peiro J, Morgan K. Adaptive remeshing for three-dimensional compressible flow computations. J Comp Phys. 1992;103(2):269–85.CrossRefGoogle Scholar
  55. Polak E. On the mathematical foundations of nondifferentiable optimization in engineering design. SIAM Rev. 1987;29(1):21–89.MathSciNetCrossRefGoogle Scholar
  56. Prenter PM. Splines and variational methods. New York: Wiley; 1975.zbMATHGoogle Scholar
  57. Ruiz-Gironés E, Roca X, Sarrate J. The receding front method applied to hexahedral mesh generation of exterior domains. Eng Comput. 2012;28(4):391–408.CrossRefGoogle Scholar
  58. Schroeder WJ, Shepard MS. A combined octree/delauney method for fully automatic 3-D mesh generation. Int J Numer Methods Eng. 1990;29(2):37–55.CrossRefGoogle Scholar
  59. Sheffer A, Etzion M, Rappoport A, Bercovier M. Hexahedral mesh generation using the embedded Voronoi graph. In: Proceedings of the 7th international meshing roundtable. Dearborn: Sandia National Laboratories; 1998. p. 347–64.Google Scholar
  60. Shi JY, Cai WL. Visualization in scientific computing: algorithm and system. Beijing: Science Press; 1996 (in Chinese).Google Scholar
  61. Sloan SW, Houlsby GT. An implementation of Watson’s algorithm for computing 2-dimensional Delauney triangulations. Adv Eng Softw. 1984;6(4):192–7.CrossRefGoogle Scholar
  62. Staten ML, Owen SJ, Blacker TD. Unconstrained paving & plastering: a new idea for all hexahedral mesh generation. In: Hanks BW, editor. Proceedings of the 14th international meshing roundtable. Berlin: Springer; 2005. p. 399–416.Google Scholar
  63. Thacker WC. A brief review of techniques for generating irregular computational grids. Int J Numer Methods Eng. 1980;15(7):1335–41.CrossRefGoogle Scholar
  64. Thompson JF, Thomas FC, Mastin CW. Automatic numerical generation of body fitted curvilinear coordinate system for field containing any number of arbitrary two-dimensional bodies. J Com Phys. 1974;15(3):299–319.CrossRefGoogle Scholar
  65. Wang WM, Chen SH. Automatic identification method for three-dimensional rock block systems. J Wuhan Univ Hydr Elec Eng (WUHEE). 1998;31(5):51–5 (in Chinese).Google Scholar
  66. Watson DF. Computing the n-dimensional Delaunay tesselation with application to Voronoi polytopes. Comput J. 1981;24(2):167–72.MathSciNetCrossRefGoogle Scholar
  67. Weatherill NP, Hassan O. Efficient three-dimensional Delaunay triangulation with automatic point creation and imposed boundary constraints. Int J Numer Methods Eng. 1994;37(12):2005–39.CrossRefGoogle Scholar
  68. White DR, Kinney P. Redesign of the paving algorithm—robustness enhancements through element by element meshing. In: Proceedings of the 6th international meshing roundtable. Park City: Sandia National Laboratories; 1997. p. 323–35.Google Scholar
  69. Xia HX, Chen SH. 3-D adaptive FEM in rock slope stability analysis. In: Desai CS et al. editors. Proceedings of the 10th international conference on computer methods and advances in geomechnics. Amsterdam: AA Balkema; 2001. p. 1635–9.Google Scholar
  70. Xu H, Newman TS. An angle-based optimization approach for 2D finite element mesh smoothing. Finite Elem Anal Des. 2006;42(13):1150–64.MathSciNetCrossRefGoogle Scholar
  71. Yamakawa S, Shimada K. Fully-automated hex-dominant mesh generation with directionality control via packing rectangular solid cells. Int J Numer Methods Eng. 2003;57(15):2099–129.MathSciNetCrossRefGoogle Scholar
  72. Yerry MA, Shepard MS. Automatic 3-dimensional mesh generation by the modified octree technique. Int J Numer Methods Eng. 1984;20(11):1965–90.CrossRefGoogle Scholar
  73. Yu ZS, Peng QS, Ma LZ. An algorithm for intersection between parametric surface and implicit surface. J Comput Aided Des Comput Graph. 1999;11(2):97–9.Google Scholar
  74. Zavattieri P, Dari EA, Buscaglia GC. Optimization strategies in unstructured mesh generation. Int J Numer Methods Eng. 1996;39(12):2055–71.CrossRefGoogle Scholar
  75. Zhu JZ, Zienkiewicz OC, Hinton E, Wu J. A new approach to the development of automatic quadrilateral mesh generation. Int J Numer Methods Eng. 1991;32(4):849–66.CrossRefGoogle Scholar
  76. Zienkiewicz OC, Phillips DV. An automatic mesh generation scheme for plane and curved surfaces by isoparametric coordinates. Int J Numer Methods Eng. 1971;3(3):519–28.CrossRefGoogle Scholar
  77. Zienkiewicz OC, Zhu JZ. Adaptive and mesh generation. Int J Numer Methods Eng. 1991;32(4):783–810.CrossRefGoogle Scholar
  78. Zienkiewicz OC, Taylor RL, Zhu JZ. The finite element method—its basis & fundamentals. 6th ed. Oxford: Elsevier Butterworth-Heinemann; 2005. Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.School of Water Resources and Hydropower EngineeringWuhan UniversityWuhanP.R. China

Personalised recommendations