空间结构参数曲面描述及网格划分算法
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摘要
空间结构具有优美的曲面形体,这些曲面可分为函数曲面和自由曲面。其中自由曲面具有自由生动的外形,故其运用日益广泛,但由于无法用解析函数表达式来表示,建模具有一定的难度。本文主要研究了空间结构中自由曲面的参数化描述及网格划分算法,并编制了相应的程序。
本文首先介绍了空间结构领域曲面造型技术的发展和现状,阐述了空间结构曲面造型和网格划分中所遇到的一些问题。
计算机辅助几何设计(CAGD)中对自由曲面的研究已较为成熟。本文介绍了CAGD中一些基本理论与概念,借鉴前人的研究成果,阐述了双三次B样条曲面插值算法的原理,为本文所探讨的曲面造型技术提供理论基础。
空间网格结构的曲面是由一系列的网格单元组成的。本文借鉴相关有限元理论,提出基于二次插值的映射法网格划分方法,应用于本文所探讨的曲面造型,并评估采用不同网格类型划分所得的曲面网格质量。
自然界中的贝壳不仅外观美丽而且结构构造也非常符合力学原理,但由于其复杂的曲面外形,给结构建模带来了很大的难度,目前空间结构领域也暂无针对其造型的专业软件,极大地影响了该类曲面的应用和推广。本文结合空间结构的实际情况对贝壳类进行形态仿生研究,将自由曲面造型技术应用于该类曲面造型,并采用合适的网格类型进行划分。
蒙皮法是目前市场上CAD系统中一种比较常见的曲面定义方法。本文研究了蒙皮曲面算法,并结合工程实际特点对传统蒙皮法进行改良,将其应用于曲面重构中。
与工程实际结合,基于能量法原理对贝壳曲面进行造型修正,从而得到既美观又符合实际工程要求的曲面造型。
另外,编制了面向空间结构的曲面造型程序,对上述曲面造型方法进行了算例验证与分析。
Spatial structure presents colorful shape surface, which can be classified as function surface and free surface. Free surface has been applied widely in spatial structure due to its vivid shape. However, modeling of free surface is difficult because it has no analytic expression. This paper mainly researched on parametric description and meshing algorithm for the free surface of spatial structure with the program development.First, development and actuality of surface modeling techniques in spatial structure were introduced, and some problems were also expounded.Research on free surface is mature in Computer Aided Geometric Design (CAGD). Some of basic theories and concepts in CAGD were presented. Based on the existing research finding, algorithm of Bicubic B-Spline Interpolation Surface was expounded as theoretical basis of this paper.Surface in Spatial Lattice Structure is comprised of grids. Drawing lessons from Finite Element Method (FEM), reflection mesh method base on reinterpolation was proposed and applied to the surface modeling discussing in this paper. Besides, grids with different types were evaluated, using the grid quality criterion.The shape of mussel is pretty and with good mechanical property. But it is hard to be generalized, because it is difficult for model building due to its complex shape and no professional software can be used. Considering features of spatial structure, the shape of mussel was studied using techniques of free surface modeling and mesh method with suitable grid type.Skinning is a common method of surface definition in the CAD system. In this paper, algorithm of skinning was studied and improved for the further application in surface reconstruction.In order to have a practical surface model, shelly surface can be optimized with energy method.A surface modeling program orient to spatial structure was developed. In this program, the surface modeling methods above were demonstrated by some examples.
本文首先介绍了空间结构领域曲面造型技术的发展和现状,阐述了空间结构曲面造型和网格划分中所遇到的一些问题。
计算机辅助几何设计(CAGD)中对自由曲面的研究已较为成熟。本文介绍了CAGD中一些基本理论与概念,借鉴前人的研究成果,阐述了双三次B样条曲面插值算法的原理,为本文所探讨的曲面造型技术提供理论基础。
空间网格结构的曲面是由一系列的网格单元组成的。本文借鉴相关有限元理论,提出基于二次插值的映射法网格划分方法,应用于本文所探讨的曲面造型,并评估采用不同网格类型划分所得的曲面网格质量。
自然界中的贝壳不仅外观美丽而且结构构造也非常符合力学原理,但由于其复杂的曲面外形,给结构建模带来了很大的难度,目前空间结构领域也暂无针对其造型的专业软件,极大地影响了该类曲面的应用和推广。本文结合空间结构的实际情况对贝壳类进行形态仿生研究,将自由曲面造型技术应用于该类曲面造型,并采用合适的网格类型进行划分。
蒙皮法是目前市场上CAD系统中一种比较常见的曲面定义方法。本文研究了蒙皮曲面算法,并结合工程实际特点对传统蒙皮法进行改良,将其应用于曲面重构中。
与工程实际结合,基于能量法原理对贝壳曲面进行造型修正,从而得到既美观又符合实际工程要求的曲面造型。
另外,编制了面向空间结构的曲面造型程序,对上述曲面造型方法进行了算例验证与分析。
Spatial structure presents colorful shape surface, which can be classified as function surface and free surface. Free surface has been applied widely in spatial structure due to its vivid shape. However, modeling of free surface is difficult because it has no analytic expression. This paper mainly researched on parametric description and meshing algorithm for the free surface of spatial structure with the program development.First, development and actuality of surface modeling techniques in spatial structure were introduced, and some problems were also expounded.Research on free surface is mature in Computer Aided Geometric Design (CAGD). Some of basic theories and concepts in CAGD were presented. Based on the existing research finding, algorithm of Bicubic B-Spline Interpolation Surface was expounded as theoretical basis of this paper.Surface in Spatial Lattice Structure is comprised of grids. Drawing lessons from Finite Element Method (FEM), reflection mesh method base on reinterpolation was proposed and applied to the surface modeling discussing in this paper. Besides, grids with different types were evaluated, using the grid quality criterion.The shape of mussel is pretty and with good mechanical property. But it is hard to be generalized, because it is difficult for model building due to its complex shape and no professional software can be used. Considering features of spatial structure, the shape of mussel was studied using techniques of free surface modeling and mesh method with suitable grid type.Skinning is a common method of surface definition in the CAD system. In this paper, algorithm of skinning was studied and improved for the further application in surface reconstruction.In order to have a practical surface model, shelly surface can be optimized with energy method.A surface modeling program orient to spatial structure was developed. In this program, the surface modeling methods above were demonstrated by some examples.
引文
[1] 董石麟,裘涛,罗尧治.空间结构.北京:中国计划出版社,2003
[2] 沈祖炎,陈扬骥.网架与网壳.上海:同济大学出版社,1997
[3] 董石麟.新型网壳结构的应用与发展.工程力学(增刊),1996
[4] 蓝天,刘枫.中国空间结构的20年.第十届空间结构学术会议论文集,北京:中国建材工业出版社,2002
[5] 刘锡良,董石麟.20年来中国空间结构形式创新.第十届空间结构学术会议论文集,北京:中国建材工业出版社,2002
[6] 张其林.索和膜结构.上海:同济大学出版社,2002
[7] 杨庆山,姜忆南.张拉索—膜结构分析与设计.北京:科学出版社,2004
[8] 毛国栋.索膜结构设计方法研究.浙江大学博士学位论文,杭州:浙江大学,2004
[9] Nooshin H, Disney P. Formex Configuration Processing. International Journal of Space Structures, Vol 15 No.1 2000,Vol 16 No.1 2001 and Vol 17 No.1 2002
[10] I. S. Hodmann, Ing. -Buro Braun & Partner GbR, Pforzheim, Germany. The Concept of Pellevation for Shaping of Structural Forms. Space Structures 5, Volumel, 2002, p.433-442
[11] G. N. Pavlov, Nizhny Novgorod, University of Architecture and Civil Engineering, Russian Federation. Methods of virtual architecture used for the design of geodesic domes and multi-petal shells. Space Structures 5, Volume 1, 2002, p.673-681
[12] D. J. Anderson TekStar International Corporation, Longwood FL, USA, W. R. WENDEL, Stamet International Corporation, Longwood FL, USA, V. GANE HOK Aviation Division, Orlando FL, USA. TekCAD A new system for creating space structures. Space Structures 5, Volumel, 2002, p.775-784
[13] 罗尧治.空间网格结构分析软件MSTCAD使用手册.浙江大学空间结构研究中心,2003
[14] 王国瑾,汪国昭,郑建民.计算机辅助几何设计.北京:高等教育出版社:海德堡:施普林格出版社,2001
[15] 张浩.空间结构曲面造型算法及程序实现.浙江大学硕士学位论文,杭州:浙江大学, 2005
[16] 罗尧治,公晓莺.基于双三次B样条插值的空间结构自由曲面.空间结构,2004,10(2):30-34
[17] 公晓莺.空间结构曲面生成与网格划分技术研究.浙江大学硕士学位论文,杭州:浙江大学,2004
[18] 公晓莺,罗尧治.面向空间结构自由曲面重建技术.第五届全国现代结构工程学术研讨会论文集,广州,2005,7:628-636
[19] 郑志镇,李尚健,李志刚.曲面网格划分算法的分类与比较.计算机辅助工程,1998,1:53-58
[20] 潘子杰,杨文通.有限元四边形网格划分的两种算法.机械设计与制造,2002,4:50-51
[21] 窦一康.用逐点插入法自动生成全四边形的自适应有限元网格.计算力学学报,1997,14(3):317-323
[22] 郑志镇,李尚健,李志刚.复杂曲面的四边形网格生成方法.计算机辅助设计与图形学学报,1999,11(6):521-524
[23] 施法中.计算机辅助几何设计与非均匀有理B样条(CAGD&NURBS).北京航空航天大学出版社,1994
[24] Curry, H. B. and Schoenberg, I. J., On Spline Distributions and Their Limits: The Polya Distribution Functions, Abstract 330t, Bull. American Mathematical Soc., Vol.53, 1947, 1114
[25] de Boor, C., On Calculating with B-Spline, J. Approx. Theory, Vol.6, 1972: 50-62
[26] Cox, M. g., The Numerical Evaluation of B-Splines, Report No. NPL-DNACS-4, National Physical Laboratory, 1971
[27] Bezier P. Numerical Control-Mathematics and Applications, Forrest trans. Wiley, London, 1972
[28] Farin, G. Curvature continuity and offsets for piecewise conics, ACM Trans. On graphics, 8, 2, 1989
[29] 吴骏恒,施法中,蒋钰.计算机辅助几何设计.北京:北京航空航天大学讲义,1988
[30] 李有法.数值计算方法.北京:高等教育出版社,1996
[31] 卓新,董石麟.基于仿生学的空间结构形体设计.空间结构,2003,9(3):3-5
[32] 卓新,董石麟.海洋贝类仿生建筑的结构形体研究.空间结构,2004,10(4):19-22
[33] 张冰.大跨度空间结构建造过程中吊点和支撑位置合理性研究.浙江大学硕士学位论 文,杭州:浙江大学,2006
[34] 肖纪美,朱逢吾.材料能量学,M.上海科学技术出版社,1999年
[35] 盛平等.北京植物园展览温室钢结构设计.建筑结构,2001,31(2):10-12
[36] 李保峰.仿生学的启示,建筑学报,2002,9:24-26
[37] 张东声.自由曲面薄壳屋面造型研究.西北工业大学硕士学位论文,西安:西北工业大学,2004
[38] David J. Kruglinski and Scot Wingo. Visual C++ 6.0 技术内幕.北京:希望电子出版社,1999
[2] 沈祖炎,陈扬骥.网架与网壳.上海:同济大学出版社,1997
[3] 董石麟.新型网壳结构的应用与发展.工程力学(增刊),1996
[4] 蓝天,刘枫.中国空间结构的20年.第十届空间结构学术会议论文集,北京:中国建材工业出版社,2002
[5] 刘锡良,董石麟.20年来中国空间结构形式创新.第十届空间结构学术会议论文集,北京:中国建材工业出版社,2002
[6] 张其林.索和膜结构.上海:同济大学出版社,2002
[7] 杨庆山,姜忆南.张拉索—膜结构分析与设计.北京:科学出版社,2004
[8] 毛国栋.索膜结构设计方法研究.浙江大学博士学位论文,杭州:浙江大学,2004
[9] Nooshin H, Disney P. Formex Configuration Processing. International Journal of Space Structures, Vol 15 No.1 2000,Vol 16 No.1 2001 and Vol 17 No.1 2002
[10] I. S. Hodmann, Ing. -Buro Braun & Partner GbR, Pforzheim, Germany. The Concept of Pellevation for Shaping of Structural Forms. Space Structures 5, Volumel, 2002, p.433-442
[11] G. N. Pavlov, Nizhny Novgorod, University of Architecture and Civil Engineering, Russian Federation. Methods of virtual architecture used for the design of geodesic domes and multi-petal shells. Space Structures 5, Volume 1, 2002, p.673-681
[12] D. J. Anderson TekStar International Corporation, Longwood FL, USA, W. R. WENDEL, Stamet International Corporation, Longwood FL, USA, V. GANE HOK Aviation Division, Orlando FL, USA. TekCAD A new system for creating space structures. Space Structures 5, Volumel, 2002, p.775-784
[13] 罗尧治.空间网格结构分析软件MSTCAD使用手册.浙江大学空间结构研究中心,2003
[14] 王国瑾,汪国昭,郑建民.计算机辅助几何设计.北京:高等教育出版社:海德堡:施普林格出版社,2001
[15] 张浩.空间结构曲面造型算法及程序实现.浙江大学硕士学位论文,杭州:浙江大学, 2005
[16] 罗尧治,公晓莺.基于双三次B样条插值的空间结构自由曲面.空间结构,2004,10(2):30-34
[17] 公晓莺.空间结构曲面生成与网格划分技术研究.浙江大学硕士学位论文,杭州:浙江大学,2004
[18] 公晓莺,罗尧治.面向空间结构自由曲面重建技术.第五届全国现代结构工程学术研讨会论文集,广州,2005,7:628-636
[19] 郑志镇,李尚健,李志刚.曲面网格划分算法的分类与比较.计算机辅助工程,1998,1:53-58
[20] 潘子杰,杨文通.有限元四边形网格划分的两种算法.机械设计与制造,2002,4:50-51
[21] 窦一康.用逐点插入法自动生成全四边形的自适应有限元网格.计算力学学报,1997,14(3):317-323
[22] 郑志镇,李尚健,李志刚.复杂曲面的四边形网格生成方法.计算机辅助设计与图形学学报,1999,11(6):521-524
[23] 施法中.计算机辅助几何设计与非均匀有理B样条(CAGD&NURBS).北京航空航天大学出版社,1994
[24] Curry, H. B. and Schoenberg, I. J., On Spline Distributions and Their Limits: The Polya Distribution Functions, Abstract 330t, Bull. American Mathematical Soc., Vol.53, 1947, 1114
[25] de Boor, C., On Calculating with B-Spline, J. Approx. Theory, Vol.6, 1972: 50-62
[26] Cox, M. g., The Numerical Evaluation of B-Splines, Report No. NPL-DNACS-4, National Physical Laboratory, 1971
[27] Bezier P. Numerical Control-Mathematics and Applications, Forrest trans. Wiley, London, 1972
[28] Farin, G. Curvature continuity and offsets for piecewise conics, ACM Trans. On graphics, 8, 2, 1989
[29] 吴骏恒,施法中,蒋钰.计算机辅助几何设计.北京:北京航空航天大学讲义,1988
[30] 李有法.数值计算方法.北京:高等教育出版社,1996
[31] 卓新,董石麟.基于仿生学的空间结构形体设计.空间结构,2003,9(3):3-5
[32] 卓新,董石麟.海洋贝类仿生建筑的结构形体研究.空间结构,2004,10(4):19-22
[33] 张冰.大跨度空间结构建造过程中吊点和支撑位置合理性研究.浙江大学硕士学位论 文,杭州:浙江大学,2006
[34] 肖纪美,朱逢吾.材料能量学,M.上海科学技术出版社,1999年
[35] 盛平等.北京植物园展览温室钢结构设计.建筑结构,2001,31(2):10-12
[36] 李保峰.仿生学的启示,建筑学报,2002,9:24-26
[37] 张东声.自由曲面薄壳屋面造型研究.西北工业大学硕士学位论文,西安:西北工业大学,2004
[38] David J. Kruglinski and Scot Wingo. Visual C++ 6.0 技术内幕.北京:希望电子出版社,1999