整体叶盘建模及其四面体网格的自动生成研究
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摘要
有限元网格生成技术是工程科学与计算机科学的一个重要研究领域,随着计算机技术和信息技术的广泛应用和飞速发展,网格生成技术已成功应用于计算力学、有限元分析等工程领域,成为解决数值解析与模拟等复杂问题的强有力手段。
整体叶盘是现代航空发动机的一种新型结构部件。整体叶盘已经被列为新型航空发动机、火箭发动机的重大改进部件,为达到对其进行优化设计的目的,针对性地对其进行建模及网格自动生成的系统开发,具有十分重要的工程应用价值。
本文对基于OpenCASCADE的整体叶盘建模方法和四面体网格自动生成的相关技术进行了研究和探讨,主要内容包括:
研究了OpenCASCADE的建模模块,包括拓扑数据结构、数据类型、拓扑关系、模型显示、文件存储等。以整体叶盘为例,并结合发动机整体叶盘的结构特点,将OpenCASCADE开发平台引入到航空发动机整体叶盘的建模过程中,实现了基于OpenCASCADE发动机整体叶盘建模。
研究了限定Delaunay四面体生成的BFS方法,包括限定条件的表示方法及其规范化要求、规范化算法。介绍了BFS方法的思路、算法介绍和BFS方法的效率分析,给出了薄元问题解决方法。
在上述研究的基础上,讨论了四面体网格的质量标准,对各种四面体网格生成方法做了比较,采用C/C++结合OpenCASCADE,利用TCL/TK脚本语言开发界面,实现了基于OpenCASCADE的整体叶盘建模和限定的Delaunay四面体网格生成,并给出了实例。
Finite element method is an effective means in solving complex engineering problem.Finite element mesh generation method is a crucial step of finite element numerical simulation and it has a direct impact on the accuracy of follow-up analysis results.
Blisk has been classified as a new aviation engine and rocket engine components significant improvements to achieve optimum design of its purpose, the targeted development of blisk’s modeling and automatic mesh generation system,it would have a very important project value.
In this thesis, based on the OpenCASCADE blisk modeling methods and automatic generation of tetrahedral mesh related technologies were studied and discussed, the main contents include:
Research on OpenCASCADE modeling module,including data type,topology,model,data storage,and so on.According to the structural characteristics of blisk,completed blisk modeling based on the OpenCASCADE.
BFS(Boundary Facet Subdivide) methods in Constraint-based Delaunay tetrahedral mesh generation,including restrictive conditions and standardized requirements, standardized algorithm. Introduced the idea of BFS method, the algorithm and the efficiency analysis method.Using C++ and OpenCASCADE realized constraint delaunay tetrahedral mesh generation algorithm.
Discussed the tetrahedral mesh quality standards,using C++ binding OpenCASCAD and TCL/TK achivethe blisk modeling and constraint delaunay tetrahedral mesh generation, and gives examples.
整体叶盘是现代航空发动机的一种新型结构部件。整体叶盘已经被列为新型航空发动机、火箭发动机的重大改进部件,为达到对其进行优化设计的目的,针对性地对其进行建模及网格自动生成的系统开发,具有十分重要的工程应用价值。
本文对基于OpenCASCADE的整体叶盘建模方法和四面体网格自动生成的相关技术进行了研究和探讨,主要内容包括:
研究了OpenCASCADE的建模模块,包括拓扑数据结构、数据类型、拓扑关系、模型显示、文件存储等。以整体叶盘为例,并结合发动机整体叶盘的结构特点,将OpenCASCADE开发平台引入到航空发动机整体叶盘的建模过程中,实现了基于OpenCASCADE发动机整体叶盘建模。
研究了限定Delaunay四面体生成的BFS方法,包括限定条件的表示方法及其规范化要求、规范化算法。介绍了BFS方法的思路、算法介绍和BFS方法的效率分析,给出了薄元问题解决方法。
在上述研究的基础上,讨论了四面体网格的质量标准,对各种四面体网格生成方法做了比较,采用C/C++结合OpenCASCADE,利用TCL/TK脚本语言开发界面,实现了基于OpenCASCADE的整体叶盘建模和限定的Delaunay四面体网格生成,并给出了实例。
Finite element method is an effective means in solving complex engineering problem.Finite element mesh generation method is a crucial step of finite element numerical simulation and it has a direct impact on the accuracy of follow-up analysis results.
Blisk has been classified as a new aviation engine and rocket engine components significant improvements to achieve optimum design of its purpose, the targeted development of blisk’s modeling and automatic mesh generation system,it would have a very important project value.
In this thesis, based on the OpenCASCADE blisk modeling methods and automatic generation of tetrahedral mesh related technologies were studied and discussed, the main contents include:
Research on OpenCASCADE modeling module,including data type,topology,model,data storage,and so on.According to the structural characteristics of blisk,completed blisk modeling based on the OpenCASCADE.
BFS(Boundary Facet Subdivide) methods in Constraint-based Delaunay tetrahedral mesh generation,including restrictive conditions and standardized requirements, standardized algorithm. Introduced the idea of BFS method, the algorithm and the efficiency analysis method.Using C++ and OpenCASCADE realized constraint delaunay tetrahedral mesh generation algorithm.
Discussed the tetrahedral mesh quality standards,using C++ binding OpenCASCAD and TCL/TK achivethe blisk modeling and constraint delaunay tetrahedral mesh generation, and gives examples.
引文
[1]孙家广,计算机图形学,清华大学出版社,北京,1999.6.
[2] S Owen.Meshing Software Survey. http://www.andrew.cmu.edu/user/sowen/softsurv.html, 2008.1.3
[3] W C Thacker.A brief review of techniques for generating irregular computational grids.International Journal for Numerical Methods in Engineering,1980,(15):1335~1341.
[4] Ken Ho-Le.Finite element mesh generation methods:a review and classification.Computer-Aided Design,1988,20(1):27~38.
[5] M S Shephard.Approaches to the automatic generation and control of finite element meshes.Applied Mechanics Review,1988,41(4): 169~185.
[6] P L George.Automatic mesh generation: Applications to Finite Element Methods.New York,John Wiley and Sons, 1991.
[7] S J Owen.A Survey of Unstructured Mesh Generation Technology.Proc, 7th International Meshing Roundtable,1998: 239~267.
[8]关振群,宋超,顾元宪,等.有限元网格生成方法研究的新进展[J],计算机辅助设计与图形学学报,2003,15(1):1~14.
[9]胡恩球,张新访,向文,等.有限元网格生成方法发展综述[J],计算机辅助设计与图形学学报,1997,9(4):378~383.
[10] E L Wilson.Automation of the Finite Element Method:A Personal Historical View.Finite Element Analysis Design,1993,13:91~104.
[11] O C Zienkiewicz,D V Phillips.An automatic mesh generation scheme for plane and curved surfaces by isoparametric coordinates. International Journal for Numerical Methods in Engineering,1971, 3: 519~528.
[12] W J Gordon,C A Hall.Construction of curvilinear coordinate systems and applications to mesh generation.International Journal for Numerical Methods in Engineering,1973, 7: 461~477.
[13]R E Barnhill,G Birkhoff,W J Gordon.Smooth interpolation in triangles. Journalof Approximation theory,1973, 8: 114~128.
[14]C A Hall.Transfinite interpolation and applications to engineering problems.Theory of approximation,1976: 308~331.
[15]F T Tracy.Graphics pre-and post-processor for two dimensional finite element method.Computer Graphics Proceedings,1977,11(1):8~12.
[16]T K H Tam,C G Armstrong. Finite element control by integer programming. International Journal for Numerical Methods in Engineering,1993, 36:2581~2605.
[17]J Suhara,J Fukuda. Automatic mesh generation for finite element analysis.J T Oden,R W Clough,Y Yamamoto.Advances in computational methods in structure mechanics and design.Huntsville,Alabama,UAH Press,1972,607~624.
[18]J C Cavendish.Automatic triangulation of arbitrary planar domains for the finite element method. International Journal for Numerical Methods in Engineering,1974,8: 679~696.
[19]C L Lawson.Software for C1 Surface Interpolation. Mathematical Software,1997:161~194.
[20]D F Watson.Computing the Delaunay Tesselation with Application to Voronoi Polytopes,The Computer Journal,1981,24:167~172.
[21]T J Baker.Automatic Mesh Generation for Complex Three-Dimensional Regions Using a Constrained Delaunay Triangulation, Engineering With Computers,1989:161~175.
[22]N P Weatherill,O Hassan.Efficient Three Dimensional Delaunay Triangulation with Automatic Point Creation and Imposed Boundary constraints.International Journal for Numerical Methods in Engineering,1994: 2005~2039.
[23]L R Herrmann.Laplacian-isoparametric grid generation scheme. Journal of the Engineering Mechanics Division of the American Society of Civil Engineers,1976,102:749~756.
[24]B Wordenweber.Volume Triangulation,Cambridge.University ofCambridge,CAD Group Document,1980.
[25] B Wordenweber.Finite Element Mesh Generation. Computer Aided Design, 1984,16:285~291.
[26]R Haber,M S Shephard,J F Abeletal.A General Two-Dimensional, Graphical Finite Element Preprocessor Utilizing Discrete Transfinite Mappings.International Journal for Numerical Methods in Engineering, 1981,17:1015~1044.
[27] E A Heighway.A mesh generator for automatically subdiving irregular polygons into quadrilaterals.IEEE transactions on Magnetic,1983, 19:2535~2538.
[28]S H Lo.Generating Quadrilateral Elements on Plane and Over Curved Surfaces.Computers and Structures,1989, 31:421~426.
[29]B P Johnston,J M Sullivan,A Kwasnik.Automatic Conversion of Triangular Finite Element Meshes to Quadrilateral Elements. International Journal for Numerical Methods in Engineering,1991, 31: 67~84.
[30] C K Lee,S H Lo.A New Scheme for the Generation of a Graded Quadrilateral Mesh.Computers and Structures,1994,52:847~857.
[31]W C Thacker,A Gonzalez,G E Putland.A method for automating the construction of irregular computational grids for stormsurge forecast models.Journal of Computational Physics,1980,37:371~387.
[32]M A Yerry,M S Shephard. A modified quadtree approach to finite element mesh generation.IEEE Computer Graphics & Applications,1983,3:39~46.
[33]H Samet.The quadtree and related hierarchical data structure.ACM Computing Survey,1984,16:187~260.
[34]A Bykat.Design of a recursive shape controlling mesh generator. International Journal for Numerical Methods in Engineering,1983,19: 1375~1390.
[35]S H L,T S Lau. Finite Element Mesh Generation Over Analytical Surfaces. Computers and Structures,1996, 59: 301~309.
[36]T C Woo,T Thomasma.An algorithm for generating solid elements in objects with holes.Computer&Structure,1984,18:333~342.
[37]M S Shephard,M K Georges.Three-Dimensional Mesh Generation by Finite Octree Technique.International Journal for Numerical Methods in Engineering,1991,32: 709~749.
[38]M A Yerry,M S Shephard.Three-Dimensional Mesh Generation by Modified Octree Technique.International Journal for Numerical Methods in Engineering,1984,20:1965~1990.
[39]J Amresh.Morden methods for automatic FE mesh generation.The American Society of Civil Engineers,1986:19~28.
[40]International Meshing Roundtable,http://www.imr.sandia.gov/.
[41]黄春峰,现代航空发动机整体叶盘及其制造技术[J],航空制造技术,2006,04
[42]J E Goodman and J O'Rourke,Handbook on Discrete and Computational Geometry,CRC Press,2002.
[43] C M Hoffmann,Geometric and Solid Modeling,Morgan Kaufmann,1989.
[44] B G Baumgart,A Polyhedron representation for computer vision,Proc. AFIPS National Computer Conference,1975:589-596.
[45] K Weiler,The Radial-Edge Structure:A Topological Representation for Non-Manifold Geometric Boundary Representations,Geometric Modelling for CAD Applications,1988(3-36).
[46] Modeling Algorithms User's Guide. Version 6.1 / March 2006 by Open CASCADE S.A.S.
[47] Visualization User's Guide. Version 6.1 / March 2006 by Open CASCADE S.A.S.
[48]Modeling Data User's Guide User's Guide Version 6.1/March 2006 by Open CASCADE S.A.S
[49]施法中,计算机辅助几何设计与非均匀有理B样条,高等教育出版社,北京, 2001.
[50]JurgenM.Anders and Jorg Haamerey A Parametric Blade Design System(Part I +II). BMW Rolls-Royce GmbH,Dahlewitz,Germany.
[51]聂春戈,刘剑飞,孙树立,四面体网格质量度量准则的研究[J],计算机力学学报,2003.05
[52]R.Sibson,Locally Equiangular Triangulations,Computer J,1978, 21(3):243-245
[53] L iu A,Joe B. Relationship between tetrahedron shape measures[J]. B IT,1994,34:268-287.
[54] D. V. P. C.Zienkiewica, An Automatic Mesh Generation Scheme for Plane and Curved Surfaces by Isoparamatic Coordinates,Int.J.Num.Meth. Eng,1971,3:519-528.
[55] M.S.H.W.J.Gorden,Construction of Curcilinear Coordinate System and Applications to Mesh Generation,Int.J.Num.Meth.Eng,1973,5:461-477.
[56] R.Sibson,Locally Equiangular Triangulations,Computer J,1978, 21(3):243-245.
[57] R.Lohner,Progress in Grid Generation via the Advancing Front Technique.Engineering with Computers,1996,12:186-210.
[58] S.H.Lo,Volume Discretization into Tetrahedral Verifiacation and Orientation of Boundary Surfaces,Computers and Structures,1991, 39(5):493-500.
[59] George P L,Seveno E.The advanceing-front mesh generation method revisited.International Journal for Numberical Methods in Engineering.1994,37(21):3605-3619.
[60] S. M.A.Yerry and M.S, Three-Dimensional Mesh Generation by Modified Octree Technique, International Journal for Numerical Methods in Engineering, 1984, 20:1965-1990.
[61] C.J.H.etal,Quadtree/Octree meshing with adaptive analysis, Numerical Grid Generation in Computational Fluid mechanicsPineridge Press,Swansea,1988:633-642.
[62] M.S.S.a.M.A.Yerry, Approaching the automatic generation of finite element meshes,Computers in Mesh Engng,1983,1(4):49-56.
[63]白双强,三维边界一致约束DT四面体有限元网格生成,[硕士学位论文],大连,大连理工大学,2006.
[64]宋超,关振群,顾元宪,三维限定Delaunay三角化的边界恢复和薄元消除方法[J],计算机力学学报,2004,21(2):169-175.
[65]杨钦,限定Delaunay三角网格剖分技术,电子工业出版社,北京,2005.
[2] S Owen.Meshing Software Survey. http://www.andrew.cmu.edu/user/sowen/softsurv.html, 2008.1.3
[3] W C Thacker.A brief review of techniques for generating irregular computational grids.International Journal for Numerical Methods in Engineering,1980,(15):1335~1341.
[4] Ken Ho-Le.Finite element mesh generation methods:a review and classification.Computer-Aided Design,1988,20(1):27~38.
[5] M S Shephard.Approaches to the automatic generation and control of finite element meshes.Applied Mechanics Review,1988,41(4): 169~185.
[6] P L George.Automatic mesh generation: Applications to Finite Element Methods.New York,John Wiley and Sons, 1991.
[7] S J Owen.A Survey of Unstructured Mesh Generation Technology.Proc, 7th International Meshing Roundtable,1998: 239~267.
[8]关振群,宋超,顾元宪,等.有限元网格生成方法研究的新进展[J],计算机辅助设计与图形学学报,2003,15(1):1~14.
[9]胡恩球,张新访,向文,等.有限元网格生成方法发展综述[J],计算机辅助设计与图形学学报,1997,9(4):378~383.
[10] E L Wilson.Automation of the Finite Element Method:A Personal Historical View.Finite Element Analysis Design,1993,13:91~104.
[11] O C Zienkiewicz,D V Phillips.An automatic mesh generation scheme for plane and curved surfaces by isoparametric coordinates. International Journal for Numerical Methods in Engineering,1971, 3: 519~528.
[12] W J Gordon,C A Hall.Construction of curvilinear coordinate systems and applications to mesh generation.International Journal for Numerical Methods in Engineering,1973, 7: 461~477.
[13]R E Barnhill,G Birkhoff,W J Gordon.Smooth interpolation in triangles. Journalof Approximation theory,1973, 8: 114~128.
[14]C A Hall.Transfinite interpolation and applications to engineering problems.Theory of approximation,1976: 308~331.
[15]F T Tracy.Graphics pre-and post-processor for two dimensional finite element method.Computer Graphics Proceedings,1977,11(1):8~12.
[16]T K H Tam,C G Armstrong. Finite element control by integer programming. International Journal for Numerical Methods in Engineering,1993, 36:2581~2605.
[17]J Suhara,J Fukuda. Automatic mesh generation for finite element analysis.J T Oden,R W Clough,Y Yamamoto.Advances in computational methods in structure mechanics and design.Huntsville,Alabama,UAH Press,1972,607~624.
[18]J C Cavendish.Automatic triangulation of arbitrary planar domains for the finite element method. International Journal for Numerical Methods in Engineering,1974,8: 679~696.
[19]C L Lawson.Software for C1 Surface Interpolation. Mathematical Software,1997:161~194.
[20]D F Watson.Computing the Delaunay Tesselation with Application to Voronoi Polytopes,The Computer Journal,1981,24:167~172.
[21]T J Baker.Automatic Mesh Generation for Complex Three-Dimensional Regions Using a Constrained Delaunay Triangulation, Engineering With Computers,1989:161~175.
[22]N P Weatherill,O Hassan.Efficient Three Dimensional Delaunay Triangulation with Automatic Point Creation and Imposed Boundary constraints.International Journal for Numerical Methods in Engineering,1994: 2005~2039.
[23]L R Herrmann.Laplacian-isoparametric grid generation scheme. Journal of the Engineering Mechanics Division of the American Society of Civil Engineers,1976,102:749~756.
[24]B Wordenweber.Volume Triangulation,Cambridge.University ofCambridge,CAD Group Document,1980.
[25] B Wordenweber.Finite Element Mesh Generation. Computer Aided Design, 1984,16:285~291.
[26]R Haber,M S Shephard,J F Abeletal.A General Two-Dimensional, Graphical Finite Element Preprocessor Utilizing Discrete Transfinite Mappings.International Journal for Numerical Methods in Engineering, 1981,17:1015~1044.
[27] E A Heighway.A mesh generator for automatically subdiving irregular polygons into quadrilaterals.IEEE transactions on Magnetic,1983, 19:2535~2538.
[28]S H Lo.Generating Quadrilateral Elements on Plane and Over Curved Surfaces.Computers and Structures,1989, 31:421~426.
[29]B P Johnston,J M Sullivan,A Kwasnik.Automatic Conversion of Triangular Finite Element Meshes to Quadrilateral Elements. International Journal for Numerical Methods in Engineering,1991, 31: 67~84.
[30] C K Lee,S H Lo.A New Scheme for the Generation of a Graded Quadrilateral Mesh.Computers and Structures,1994,52:847~857.
[31]W C Thacker,A Gonzalez,G E Putland.A method for automating the construction of irregular computational grids for stormsurge forecast models.Journal of Computational Physics,1980,37:371~387.
[32]M A Yerry,M S Shephard. A modified quadtree approach to finite element mesh generation.IEEE Computer Graphics & Applications,1983,3:39~46.
[33]H Samet.The quadtree and related hierarchical data structure.ACM Computing Survey,1984,16:187~260.
[34]A Bykat.Design of a recursive shape controlling mesh generator. International Journal for Numerical Methods in Engineering,1983,19: 1375~1390.
[35]S H L,T S Lau. Finite Element Mesh Generation Over Analytical Surfaces. Computers and Structures,1996, 59: 301~309.
[36]T C Woo,T Thomasma.An algorithm for generating solid elements in objects with holes.Computer&Structure,1984,18:333~342.
[37]M S Shephard,M K Georges.Three-Dimensional Mesh Generation by Finite Octree Technique.International Journal for Numerical Methods in Engineering,1991,32: 709~749.
[38]M A Yerry,M S Shephard.Three-Dimensional Mesh Generation by Modified Octree Technique.International Journal for Numerical Methods in Engineering,1984,20:1965~1990.
[39]J Amresh.Morden methods for automatic FE mesh generation.The American Society of Civil Engineers,1986:19~28.
[40]International Meshing Roundtable,http://www.imr.sandia.gov/.
[41]黄春峰,现代航空发动机整体叶盘及其制造技术[J],航空制造技术,2006,04
[42]J E Goodman and J O'Rourke,Handbook on Discrete and Computational Geometry,CRC Press,2002.
[43] C M Hoffmann,Geometric and Solid Modeling,Morgan Kaufmann,1989.
[44] B G Baumgart,A Polyhedron representation for computer vision,Proc. AFIPS National Computer Conference,1975:589-596.
[45] K Weiler,The Radial-Edge Structure:A Topological Representation for Non-Manifold Geometric Boundary Representations,Geometric Modelling for CAD Applications,1988(3-36).
[46] Modeling Algorithms User's Guide. Version 6.1 / March 2006 by Open CASCADE S.A.S.
[47] Visualization User's Guide. Version 6.1 / March 2006 by Open CASCADE S.A.S.
[48]Modeling Data User's Guide User's Guide Version 6.1/March 2006 by Open CASCADE S.A.S
[49]施法中,计算机辅助几何设计与非均匀有理B样条,高等教育出版社,北京, 2001.
[50]JurgenM.Anders and Jorg Haamerey A Parametric Blade Design System(Part I +II). BMW Rolls-Royce GmbH,Dahlewitz,Germany.
[51]聂春戈,刘剑飞,孙树立,四面体网格质量度量准则的研究[J],计算机力学学报,2003.05
[52]R.Sibson,Locally Equiangular Triangulations,Computer J,1978, 21(3):243-245
[53] L iu A,Joe B. Relationship between tetrahedron shape measures[J]. B IT,1994,34:268-287.
[54] D. V. P. C.Zienkiewica, An Automatic Mesh Generation Scheme for Plane and Curved Surfaces by Isoparamatic Coordinates,Int.J.Num.Meth. Eng,1971,3:519-528.
[55] M.S.H.W.J.Gorden,Construction of Curcilinear Coordinate System and Applications to Mesh Generation,Int.J.Num.Meth.Eng,1973,5:461-477.
[56] R.Sibson,Locally Equiangular Triangulations,Computer J,1978, 21(3):243-245.
[57] R.Lohner,Progress in Grid Generation via the Advancing Front Technique.Engineering with Computers,1996,12:186-210.
[58] S.H.Lo,Volume Discretization into Tetrahedral Verifiacation and Orientation of Boundary Surfaces,Computers and Structures,1991, 39(5):493-500.
[59] George P L,Seveno E.The advanceing-front mesh generation method revisited.International Journal for Numberical Methods in Engineering.1994,37(21):3605-3619.
[60] S. M.A.Yerry and M.S, Three-Dimensional Mesh Generation by Modified Octree Technique, International Journal for Numerical Methods in Engineering, 1984, 20:1965-1990.
[61] C.J.H.etal,Quadtree/Octree meshing with adaptive analysis, Numerical Grid Generation in Computational Fluid mechanicsPineridge Press,Swansea,1988:633-642.
[62] M.S.S.a.M.A.Yerry, Approaching the automatic generation of finite element meshes,Computers in Mesh Engng,1983,1(4):49-56.
[63]白双强,三维边界一致约束DT四面体有限元网格生成,[硕士学位论文],大连,大连理工大学,2006.
[64]宋超,关振群,顾元宪,三维限定Delaunay三角化的边界恢复和薄元消除方法[J],计算机力学学报,2004,21(2):169-175.
[65]杨钦,限定Delaunay三角网格剖分技术,电子工业出版社,北京,2005.