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Computational Geomechanics and Hydraulic Structures pp 189–240Cite as

Geometrical Description and Discretization of Hydraulic Structures

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Part of the book series: Springer Tracts in Civil Engineering ((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.

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References

  • Anderson BD. Automated all quadrilateral mesh adaptation through refinement and coarsening. Master’s thesis, Brigham Young University, Provo; 2009.

    Google Scholar 

  • 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.

    Book  Google Scholar 

  • 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 

  • 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 

  • 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.

    Article  Google Scholar 

  • Beall MW, Shephard MS. A general topology-based mesh data structure. Int J Numer Methods Eng. 1997;40(9):1573–96.

    Article  MathSciNet  Google Scholar 

  • Blacker TD, Stephenson MS. Paving: a new approach to automated quadrilateral mesh generation. Int J Numer Methods Eng. 1991;32(4):811–47.

    Article  Google Scholar 

  • 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 

  • 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.

    Article  Google Scholar 

  • Bornhill RE, Little FF. Three and four-dimensional surfaces. Rochy Mt J Math. 1984;14(1):77–102.

    Article  MathSciNet  Google Scholar 

  • Buell WR, Bush BA. Mesh generation—a survey. J Int Eng Trans ASME. 1973;95(1):332–8 (Ser. B).

    Article  Google Scholar 

  • Canann SA, Stephenson MB, Blacker TD. Optismoothing: an optimization-driven approach to mesh smoothing. Finite Elem Anal Des. 1993;13(2–3):185–90.

    Article  MathSciNet  Google Scholar 

  • 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 

  • 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.

    Article  Google Scholar 

  • Chen SH. Hydraulic structures. Berlin: Springer; 2015.

    Book  Google Scholar 

  • 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 

  • 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 

  • 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 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • De Berg M, Cheong O, van Kreveld M, Overmars M. Computational geometry: algorithms and applications. 3rd ed. Berlin: Springer; 2008.

    Google Scholar 

  • De Cougny HL, Shephard MS. Parallel refinement and coarsening of tetrahedral meshes. Int J Numer Meth Eng. 1999;46(7):1101–25.

    Article  MathSciNet  Google Scholar 

  • Field DA. Laplacian smoothing and Delaunay triangulations. Commun Appl Numer Methods. 1988;4(6):709–12.

    Article  Google Scholar 

  • George PL, Borouchaki H. Delaunay triangulation and meshing: application to finite elements. Paris: Hermes Science Publications; 1998. p. 230–4.

    MATH  Google Scholar 

  • Gordon WJ. Spline-blended surface interpolation through curve networks. J Math Mech. 1969;18(1):931–52.

    MathSciNet  MATH  Google Scholar 

  • Hansbo P. Generalized laplacian smoothing of unstructured grids. Commun Numer Methods Eng. 1995;11(5):455–64.

    Article  Google Scholar 

  • Heliot D. Generating a blocky rock mass. Int J Rock Mech Min Sci Geomech Abstr. 1988;25(3):127–39.

    Article  Google Scholar 

  • Hermann LR. Laplacian-isoparametric grid generation scheme. J Eng Mech ASCE. 1976;102(EM5):749–56.

    Google Scholar 

  • Ho LK. Finite element mesh generation methods: a review and classification. Comp Aided Des. 1988;20(1):27–38.

    Article  Google Scholar 

  • Ikegawa Y, Hudson JA. A novel automatic identification system for three-dimensional multi-block systems. Eng Comput. 1992;9(2):169–79.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Jin H, Tanner RI. Generation of unstructured tetrahedral meshes by advancing front technique. Int J Numer Methods Eng. 1993;36(11):1805–23.

    Article  Google Scholar 

  • Jin H, Wiberg NE. Two-dimensional mesh generation, adaptive remeshing and refinement. Int J Numer Methods Eng. 1990;29(7):1501–26.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Joe B. Construction of three-dimensional improved-quality triangulations using local transformations. J Sci Comput SIAM. 1995;16(6):1292–307.

    Article  MathSciNet  Google Scholar 

  • 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 

  • Lau TS, Lo SH. Finite element mesh generation over analytical curved surfaces. Comput Struct. 1996;59(2):301–9.

    Article  MathSciNet  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Lo SH. A new mesh generation scheme for arbitrary planar domains. Int J Numer Methods Eng. 1985;21(8):1403–26.

    Article  Google Scholar 

  • Lo SH. Generating quadrilateral elements on plane and over curved surfaces. Comput Struct. 1989;31(3):421–6.

    Article  Google Scholar 

  • Lo SH. Optimization of tetrahedral meshes based on element shape measures. Comput Struct. 1997;63(5):951–61.

    Article  Google Scholar 

  • 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 

  • Löhner R. Some useful data structures for the generation of unstructured grids. Commun Appl Numer Methods. 1988;4(1):123–35.

    Article  MathSciNet  Google Scholar 

  • Löhner R. A parallel advancing front grid generation scheme. Int J Numer Methods Eng. 2001;51(6):663–78.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Lori A, Carl O. Tetrahedral mesh improvement using swapping and smoothing. Int J Numer Methods Eng. 1997;40(21):3979–4002.

    Article  MathSciNet  Google Scholar 

  • Merhof D, Grosso R, Tremel U, Greiner G. Anisotropic quadrilateral mesh generation: an indirect approach. Adv Eng Softw. 2007;38(11–12):860–7.

    Article  Google Scholar 

  • Moller P, Hansbo P. On advancing front mesh generation in three dimensions. Int J Numer Methods Eng. 1995;38(21):3551–69.

    Article  MathSciNet  Google Scholar 

  • Nguyen-Van-Phai. Automatic mesh generation with tetrahedron elements. Int J Numer Methods Eng. 1982;18(2):237–89.

    Article  Google Scholar 

  • Nordsletten D, Smith NP. Triangulation of p-order parametric surfaces. J Sci Comput. 2008;34(3):308–35.

    Article  MathSciNet  Google Scholar 

  • 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 

  • 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.

    Article  Google Scholar 

  • Peraire J, Vahdati M, Morgan K, Zienkiewicz OC. Adaptive remeshing for compressible flow computations. J Comp Phys. 1987;72(2):449–66.

    Article  Google Scholar 

  • Peraire J, Peiro J, Morgan K. Adaptive remeshing for three-dimensional compressible flow computations. J Comp Phys. 1992;103(2):269–85.

    Article  Google Scholar 

  • Polak E. On the mathematical foundations of nondifferentiable optimization in engineering design. SIAM Rev. 1987;29(1):21–89.

    Article  MathSciNet  Google Scholar 

  • Prenter PM. Splines and variational methods. New York: Wiley; 1975.

    MATH  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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 

  • Shi JY, Cai WL. Visualization in scientific computing: algorithm and system. Beijing: Science Press; 1996 (in Chinese).

    Google Scholar 

  • Sloan SW, Houlsby GT. An implementation of Watson’s algorithm for computing 2-dimensional Delauney triangulations. Adv Eng Softw. 1984;6(4):192–7.

    Article  Google Scholar 

  • 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 

  • Thacker WC. A brief review of techniques for generating irregular computational grids. Int J Numer Methods Eng. 1980;15(7):1335–41.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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 

  • Watson DF. Computing the n-dimensional Delaunay tesselation with application to Voronoi polytopes. Comput J. 1981;24(2):167–72.

    Article  MathSciNet  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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 

  • 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 

  • Xu H, Newman TS. An angle-based optimization approach for 2D finite element mesh smoothing. Finite Elem Anal Des. 2006;42(13):1150–64.

    Article  MathSciNet  Google Scholar 

  • 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.

    Article  MathSciNet  Google Scholar 

  • Yerry MA, Shepard MS. Automatic 3-dimensional mesh generation by the modified octree technique. Int J Numer Methods Eng. 1984;20(11):1965–90.

    Article  Google Scholar 

  • 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 

  • Zavattieri P, Dari EA, Buscaglia GC. Optimization strategies in unstructured mesh generation. Int J Numer Methods Eng. 1996;39(12):2055–71.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Zienkiewicz OC, Zhu JZ. Adaptive and mesh generation. Int J Numer Methods Eng. 1991;32(4):783–810.

    Article  Google Scholar 

  • Zienkiewicz OC, Taylor RL, Zhu JZ. The finite element method—its basis & fundamentals. 6th ed. Oxford: Elsevier Butterworth-Heinemann; 2005.

    Google Scholar 

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Authors and Affiliations

  1. School of Water Resources and Hydropower Engineering, Wuhan University, Wuhan, Hubei, P.R. China

    Sheng-Hong Chen

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Chen, SH. (2019). Geometrical Description and Discretization of Hydraulic Structures. In: Computational Geomechanics and Hydraulic Structures. Springer Tracts in Civil Engineering . Springer, Singapore. https://doi.org/10.1007/978-981-10-8135-4_3

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  • DOI: https://doi.org/10.1007/978-981-10-8135-4_3

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