六面体有限元网格自动剖分技术研究
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摘要
本文首先对有限元前处理技术进行了分析和综合，指出了六面体网格在有限元分析中的优点及六面体网格剖分的难点和现状。随后论证了四面体转换法全自动生成六面体网格的可行性，并在紫瑞CAE软件前处理模块的基础上，研制开发了八节点和二十节点六面体网格的全自动剖分程序。最后，通过考题和实例说明本程序的可靠性和正确性。本文的主要工作包括如下几个方面：
(1)研究了在紫瑞CAE基础上采用四面体转换法进行六面体网格全自动剖分的可行性并对约束和载荷的处理提出了一套可行的方案。
(2)在紫瑞CAE软件基础上，以Mechanical Desktop 3.0为开发平台，利用ARX二次开发技术和Visual C++ 6.0、Fortran PowerStation version
4.0等开发工具，采用面向对象技术、动态链接技术、混合语言编程方法等技术开发了六面体网格全自动剖分程序，并对节点坐标进行了优化处理。
(3)通过有理论解的算例和工程实例验证表明，本程序采用的六面体网格剖分算法是可行的、程序编制是正确的。所剖分的六面体单元的
－计算精度和计算效率都高于四面体单元。工程实例表明，本程序适合于
工程计算。
g u）本程序是在商品化的紫瑞 CAE基础上开发的，与采用四面体
单元进行计算相比，用户要采用六面体单元进行计算，只需增加一跟
＿择操作，所以本程序保持了紫瑞CAE操作简单的特点。
Summarize and analyze on the preprocessor of the finite element method firstly was carried through in this paper. It was then pointed out the advantage of hexahedron mesh on analyze with the finite element method and the difficulty of the automatic generation technique of hexahedron mesh. It was later demonstrated the possibility to get hexahedron mesh through tetrahedron conversion method. Basing on the preprocessor module of ZRCAE software,a program system has been developed with which hexahedron mesh can be automatically generated. The main contributions of the dissertation are as follow:
(1) The possibility of generation hexahedron mesh through tetrahedron conversion method was studied,and a set of feasible method to deal with the boundary condition of constraint and loads has been brought forward.
(2) Basing on ZRCAE software and on development bench of Mechanical Desktop 3.0 and using the ARX second level development
technique a program system by which hexahedron mesh can be automatically generated had been developed. During the process of developing some tools such as Visual C++ 6.0,Fortran PowerStation version 4.0 and techniques such as object-oriented programmer technique,dynamic link library technique,mixed-language programming method was used. The nodes coordinate had been optimized.
(3) Some examples with theoretical answer and engineering-oriented instance show that the arithmetic of this program system is feasible and this program system has been correctly written. The calculation accuracy and the calculation efficiency of hexahedron mesh generated by author are higher than tetrahedron element. This engineering-oriented instance also indicated that this program system was fit for applications of engineering.
(4) This program was developed on the base of the ZRCAE software,comparing with the process of calculation with tetrahedron element,only one additional choice operation was needed if the user want using hexahedron element. So the characteristic for simple operation of the ZRCAE software was kept.
(1)研究了在紫瑞CAE基础上采用四面体转换法进行六面体网格全自动剖分的可行性并对约束和载荷的处理提出了一套可行的方案。
(2)在紫瑞CAE软件基础上，以Mechanical Desktop 3.0为开发平台，利用ARX二次开发技术和Visual C++ 6.0、Fortran PowerStation version
4.0等开发工具，采用面向对象技术、动态链接技术、混合语言编程方法等技术开发了六面体网格全自动剖分程序，并对节点坐标进行了优化处理。
(3)通过有理论解的算例和工程实例验证表明，本程序采用的六面体网格剖分算法是可行的、程序编制是正确的。所剖分的六面体单元的
－计算精度和计算效率都高于四面体单元。工程实例表明，本程序适合于
工程计算。
g u）本程序是在商品化的紫瑞 CAE基础上开发的，与采用四面体
单元进行计算相比，用户要采用六面体单元进行计算，只需增加一跟
＿择操作，所以本程序保持了紫瑞CAE操作简单的特点。
Summarize and analyze on the preprocessor of the finite element method firstly was carried through in this paper. It was then pointed out the advantage of hexahedron mesh on analyze with the finite element method and the difficulty of the automatic generation technique of hexahedron mesh. It was later demonstrated the possibility to get hexahedron mesh through tetrahedron conversion method. Basing on the preprocessor module of ZRCAE software,a program system has been developed with which hexahedron mesh can be automatically generated. The main contributions of the dissertation are as follow:
(1) The possibility of generation hexahedron mesh through tetrahedron conversion method was studied,and a set of feasible method to deal with the boundary condition of constraint and loads has been brought forward.
(2) Basing on ZRCAE software and on development bench of Mechanical Desktop 3.0 and using the ARX second level development
technique a program system by which hexahedron mesh can be automatically generated had been developed. During the process of developing some tools such as Visual C++ 6.0,Fortran PowerStation version 4.0 and techniques such as object-oriented programmer technique,dynamic link library technique,mixed-language programming method was used. The nodes coordinate had been optimized.
(3) Some examples with theoretical answer and engineering-oriented instance show that the arithmetic of this program system is feasible and this program system has been correctly written. The calculation accuracy and the calculation efficiency of hexahedron mesh generated by author are higher than tetrahedron element. This engineering-oriented instance also indicated that this program system was fit for applications of engineering.
(4) This program was developed on the base of the ZRCAE software,comparing with the process of calculation with tetrahedron element,only one additional choice operation was needed if the user want using hexahedron element. So the characteristic for simple operation of the ZRCAE software was kept.
引文
1 王勖成，邵敏 编著．有限元法基本原理和数值方法．北京：清华大学出版社，1997
2 Courant R. Variational Method for Solutions of Problems of Equilibrim and Vibrations. Bull. Am. Math. Soc. 1943,49 1～23
3 Turner M J, Clough R W, Martin H C, Topp L C. Stiffness and Deflection Analysis of Complex Structures J.Aero. Sci, 1956,23,805～823
4 Caeslaw, H. S, and Janger J. C. Conduction of Heat in Solid. Oxford University Press, 1959
5 刘剑飞．有限元前置处理的研究和实现．北京：北京航空航天大学博士论文，1991
6 Tam T. K. H. and Armstrong C. G.. Finite element mesh control by integer programming. International Journal for Numerical Methods in Engineering, 1993, 36:2581～2605
7 Lee Y. K. and Yang D.Y. A new automatic mesh generation technique and its application to the finite element analysis of practical forging process. Advanced Plasity Technology, 1996, Ⅱ :409～413
8 Schneiders R. A-grid based algorithm for the generation of hexahedral element meshes. Engineering with computers, 1996,12:168～177
9 Blacker T. D. Meyers R. J. Seams and wedges in plastering: A 3-D hexahedral mesh generation algorithm. Engineering with computers, 1993,9:83～93
10 Taniguchi T. Fillion E. and Sauty J. P. Fast mesh generation for groungwater flow analysis in 3D structure system. In: Proceedings of Numerical Grid Generation in computational Fluid Dynamics, Swansea, 1994, 374～378
11 Parthasarathy V. N. and Kodiyalam S. A constrained optimization approach to finite element mesh smoothing. Finite Elements in Analysis and Design, 1991, 9:309～320
12 Denayer. A automatic generation of finite element meshes. Computer & Struc. 1978 9:359～364
13 Cavendish, J. C. Automatic trangulation of arbitrary planar domains for the finite element method. Int.j.Number. Meth. Eng, 1974, Vo18, 679～696
14 Heighway, E. A. and Biddlecombe. Two-dimensional automatic triangular mesh generation for the finite element electromagnetics package PE2D. IEEE Trans. On Nag. Vol MAG-18 No 2, pp594～598
15 D.M.马依泽尔著，王君健译．弹性理论的温度场问题．北京：科学出版社，1959
16 俞昌铭 编著．热传导及其数值分析．北京：清华大学出版社，1981
17 MSC.Marc 软件技术报告．北京：MSC公司，2000
18 紫瑞CAE技术报告．郑州：郑州紫瑞软件有限公司．2001．1
19 范钦珊．轴对称问题应力分析．北京：高等教育出版社，1985
20 龚国庆，刘寒冰等．结构动力分析自适应有限元方法综述．计算力学学报，2000，30(3)：332～342
21 郭书祥．自适应有限元方法及其工程应用．力学进展，1997，27(4)：479～488
22 左旭，卫原平等．三维六面体有限元网格自动划分中的一种单元转换优化算法．计算力学学报，1999，16(3)：343～347
23 杨名生，吴京宁．基于四叉数树法的有限元网格自动生成及凝聚方法．计算力学学报，1995，12(4)：409～416
24 魏红宁，周本宽．基于四叉树法的自适应有限元局部网格加密研究．计算力学学报，1997，14(3)：324～331
25 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
26 郭书祥．自适应有限元方法及其工程应用．力学进展，1997 24(4)：479～488
27 徐志强，张丕辛，郑冒勖．基于几何造型的有限元前处理技术．全国第六届CAD／CG学术会议(1990)
28 孙国平，阮雪榆．一种基于实体造型系统的网格自动划分算法．全国第六届CAD／CG学术会议(1990)
29 余俊，周济等著．优化方法程序库OPB-1——原理及使用说明．北京：机械工业出版社，1989
30 K.J.巴斯编著，付子智 译．工程分析中的有限元法．北京：机械工业出版社，1991
31 谭浩强，田淑清 等著．FORTRAN77结构化程序设计．北京：清华大学出版社，1990
32 桂良进，王军等著．Fortran Powerstation 使用与编程．北京：航空航天大学出版社，1999
33 杨晓辉 编著．Fortran Powerstation程序员指南．长沙：湖南科学技术出版社，1999
34 左正兴，陈世红等译．AutoCAD R13技术精粹．北京：清华大学出版社，1996
35 David Bennett著，徐军等译．Visual C++5.0开发指南．北京：机械工业出版社，1998
36 童秉枢 等著．机械CAD技术基础．北京：清华大学出版社，1996
37 童秉枢，李学志，吴志军，张春凤著．机械设计CAD技术基础．北京：清华大学出版社，1996
38 Richard C.Leincker 著，廖安棣 等译．Visual C++开发工具实用指南．北京：机械工业出版社，1997
39 严蔚敏，吴伟民 编著．数据结构．北京：清华大学出版社，1992
40 郑雪明．Visual C++基础类库参考大全．北京：学苑出版社，1994
41 将华 等著．VC++6.0编程技术．北京：航空航天大学出版社，1998
42 丁香荣 主编．Visual C++4.1编程技巧指南．电子科技大学出版社，1997．6
43 沈纪新 编著．Visual C++使用速成．北京：清华大学出版社，1996
44 Chris H.Pappas,William H.Murray,Ⅲ.THE VISUAL C++ HANDBOOK.北京：学苑出版社，1994
45 韩成果，谭超 等著．ARX在AutoCAD中二次开发的研究．机械设计与研究，1998，No．2
46 汪成为，郑小军，彭木昌等．面向对象分析、设计及应用．国防工业出版社，1992
47 王福军．AutoCAD R12／R13应用C程序设计．电子工业出版社，1995
48 木林森 等编著．Windows95实用编程与范例．清华大学出版社，1997，6
49 丁香荣主编．Visual C++4.1编程技巧指南．电子科技大学出版社，1997，6
50 刘鸿文 主编．材料力学．北京：高等教育出版社，1995，9
51 蒋智翔，杨小昭 编著．锅炉及压力容器受压元件强度．北京：机械工业出版社，1999
52 赵少汴，王忠保 编著．抗疲劳设计——方法与数据．北京：机械工业出版社，1997．1
作者在攻读硕士学位期间发表的论文：
1．梁醒培，李延龄．紫瑞CAE稳态温度场及热应力的计算精度．《智能化CAD／CAE学术交流研讨会》，青岛，2001．8
2．李延龄，梁醒培．六面体网格自动剖分方法及软件研制．力学与工程应用．第九卷，2002(已录用，待发表)
2 Courant R. Variational Method for Solutions of Problems of Equilibrim and Vibrations. Bull. Am. Math. Soc. 1943,49 1～23
3 Turner M J, Clough R W, Martin H C, Topp L C. Stiffness and Deflection Analysis of Complex Structures J.Aero. Sci, 1956,23,805～823
4 Caeslaw, H. S, and Janger J. C. Conduction of Heat in Solid. Oxford University Press, 1959
5 刘剑飞．有限元前置处理的研究和实现．北京：北京航空航天大学博士论文，1991
6 Tam T. K. H. and Armstrong C. G.. Finite element mesh control by integer programming. International Journal for Numerical Methods in Engineering, 1993, 36:2581～2605
7 Lee Y. K. and Yang D.Y. A new automatic mesh generation technique and its application to the finite element analysis of practical forging process. Advanced Plasity Technology, 1996, Ⅱ :409～413
8 Schneiders R. A-grid based algorithm for the generation of hexahedral element meshes. Engineering with computers, 1996,12:168～177
9 Blacker T. D. Meyers R. J. Seams and wedges in plastering: A 3-D hexahedral mesh generation algorithm. Engineering with computers, 1993,9:83～93
10 Taniguchi T. Fillion E. and Sauty J. P. Fast mesh generation for groungwater flow analysis in 3D structure system. In: Proceedings of Numerical Grid Generation in computational Fluid Dynamics, Swansea, 1994, 374～378
11 Parthasarathy V. N. and Kodiyalam S. A constrained optimization approach to finite element mesh smoothing. Finite Elements in Analysis and Design, 1991, 9:309～320
12 Denayer. A automatic generation of finite element meshes. Computer & Struc. 1978 9:359～364
13 Cavendish, J. C. Automatic trangulation of arbitrary planar domains for the finite element method. Int.j.Number. Meth. Eng, 1974, Vo18, 679～696
14 Heighway, E. A. and Biddlecombe. Two-dimensional automatic triangular mesh generation for the finite element electromagnetics package PE2D. IEEE Trans. On Nag. Vol MAG-18 No 2, pp594～598
15 D.M.马依泽尔著，王君健译．弹性理论的温度场问题．北京：科学出版社，1959
16 俞昌铭 编著．热传导及其数值分析．北京：清华大学出版社，1981
17 MSC.Marc 软件技术报告．北京：MSC公司，2000
18 紫瑞CAE技术报告．郑州：郑州紫瑞软件有限公司．2001．1
19 范钦珊．轴对称问题应力分析．北京：高等教育出版社，1985
20 龚国庆，刘寒冰等．结构动力分析自适应有限元方法综述．计算力学学报，2000，30(3)：332～342
21 郭书祥．自适应有限元方法及其工程应用．力学进展，1997，27(4)：479～488
22 左旭，卫原平等．三维六面体有限元网格自动划分中的一种单元转换优化算法．计算力学学报，1999，16(3)：343～347
23 杨名生，吴京宁．基于四叉数树法的有限元网格自动生成及凝聚方法．计算力学学报，1995，12(4)：409～416
24 魏红宁，周本宽．基于四叉树法的自适应有限元局部网格加密研究．计算力学学报，1997，14(3)：324～331
25 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
26 郭书祥．自适应有限元方法及其工程应用．力学进展，1997 24(4)：479～488
27 徐志强，张丕辛，郑冒勖．基于几何造型的有限元前处理技术．全国第六届CAD／CG学术会议(1990)
28 孙国平，阮雪榆．一种基于实体造型系统的网格自动划分算法．全国第六届CAD／CG学术会议(1990)
29 余俊，周济等著．优化方法程序库OPB-1——原理及使用说明．北京：机械工业出版社，1989
30 K.J.巴斯编著，付子智 译．工程分析中的有限元法．北京：机械工业出版社，1991
31 谭浩强，田淑清 等著．FORTRAN77结构化程序设计．北京：清华大学出版社，1990
32 桂良进，王军等著．Fortran Powerstation 使用与编程．北京：航空航天大学出版社，1999
33 杨晓辉 编著．Fortran Powerstation程序员指南．长沙：湖南科学技术出版社，1999
34 左正兴，陈世红等译．AutoCAD R13技术精粹．北京：清华大学出版社，1996
35 David Bennett著，徐军等译．Visual C++5.0开发指南．北京：机械工业出版社，1998
36 童秉枢 等著．机械CAD技术基础．北京：清华大学出版社，1996
37 童秉枢，李学志，吴志军，张春凤著．机械设计CAD技术基础．北京：清华大学出版社，1996
38 Richard C.Leincker 著，廖安棣 等译．Visual C++开发工具实用指南．北京：机械工业出版社，1997
39 严蔚敏，吴伟民 编著．数据结构．北京：清华大学出版社，1992
40 郑雪明．Visual C++基础类库参考大全．北京：学苑出版社，1994
41 将华 等著．VC++6.0编程技术．北京：航空航天大学出版社，1998
42 丁香荣 主编．Visual C++4.1编程技巧指南．电子科技大学出版社，1997．6
43 沈纪新 编著．Visual C++使用速成．北京：清华大学出版社，1996
44 Chris H.Pappas,William H.Murray,Ⅲ.THE VISUAL C++ HANDBOOK.北京：学苑出版社，1994
45 韩成果，谭超 等著．ARX在AutoCAD中二次开发的研究．机械设计与研究，1998，No．2
46 汪成为，郑小军，彭木昌等．面向对象分析、设计及应用．国防工业出版社，1992
47 王福军．AutoCAD R12／R13应用C程序设计．电子工业出版社，1995
48 木林森 等编著．Windows95实用编程与范例．清华大学出版社，1997，6
49 丁香荣主编．Visual C++4.1编程技巧指南．电子科技大学出版社，1997，6
50 刘鸿文 主编．材料力学．北京：高等教育出版社，1995，9
51 蒋智翔，杨小昭 编著．锅炉及压力容器受压元件强度．北京：机械工业出版社，1999
52 赵少汴，王忠保 编著．抗疲劳设计——方法与数据．北京：机械工业出版社，1997．1
作者在攻读硕士学位期间发表的论文：
1．梁醒培，李延龄．紫瑞CAE稳态温度场及热应力的计算精度．《智能化CAD／CAE学术交流研讨会》，青岛，2001．8
2．李延龄，梁醒培．六面体网格自动剖分方法及软件研制．力学与工程应用．第九卷，2002(已录用，待发表)