摘要
经过近三十年的研究发展,塑料注射成型模拟(CAE)技术已经相当成熟,但是有限元网格技术却一直是CAE技术实施的瓶颈。在当今主流的双面流技术中,表面网格的信息配置技术更是其实施困难的关键所在。本文基于网格划分算法中已经十分成熟的映射法,提出了表面网格生成、信息配置和表面网格优化一整套解决方案,并提出了注塑模领域的网格质量标准,为全面解决注射模拟领域的网格问题提供了一条思路。
本文着重研究了基于超面技术的表面网格生成技术。通过表面三角形拼合处理、删除尖角、删除短边、消除内外环连接错误和解开多边形自相交错误等操作得到超面描述模型,降低了原始模型错误的影响。又经过超面类型判断和后续的具体单元信息判断出单元类型,使网格模型更符合分析模型的需求。然后通过映射法,将超面投影到平面进行平面域Delaunay三角剖分,再把网格反投影到超面上,生成表面三角形网格模型。
本文提出了基于超面技术的节点单元配对和厚度计算技术,大大地提高了配对算法的效率,为网格模型配置了注塑分析所必需的配对和厚度信息。提出了二次配对和候选择优的配对算法,兼顾了分析模型的需求和配对的准确率。
最后本文提出了表面网格优化技术的三个层次:无错层次、整体层次和单元层次,并针对各个层次的不同要求设计了具体的算法。设计了统一的表面网格错误识别模型和错误修复技术。提出了基于超面的节点移动技术,优化了网格整体的配对情况。针对单元层次提出了形态优化技术,并对两种典型的形态很差的单元设计了优化算法。
Numerical simulation for plastic injection molding is improved rapidly in the last decades. But mesh processing technology is always the critical and difficult point. Especially in the dominating double-surface simulation technology, the surface mesh information setting technology becomes the obstacle of being put into practice. In this paper, a method base on the mature Mesh Mapping Generation technology is presented, including mesh generation, mesh information setting and mesh optimization as a whole problem solution. And also, a suit of mesh standard for plastic injection simulation is proposed to point a way towards the mesh problem solving.
The main point of this paper is a mesh generation method base on super-face technology. Through uniting original triangles, deleting short edges and removing small angles to build super-face model, it greatly improves the result mesh quality. Mesh-type technology is also used here therefore the mesh model is more approach the analyzed model. After that, the Mesh Mapping Generation technology is presented in order to use the perfect 2-D Delaunay mesh generation.
Mesh information setting technology is the main difference between plastic injection simulation and other technologies. In this paper, an algorithm called TWICE PAIR is presented to supply the necessary information for analyzing.
Mesh optimization technology is the last part of this paper. It summarizes the mesh standard as three levels: error repair level, mesh entire level and triangle level. A unified error repair model is presented for the first level, and also a method called MESH NODE MOVING for the second level. For the third level, it divides the bad-shape triangle as two parts and presents optimization algorithms for each.
引文
[1]张玉峰,朱以文.有限元网格自动生成的典型方法与研究前瞻.武汉大学学报, 2005,38(2): 54~55
[2]周华民,成学文,刘芬,李德群. STL文件错误的修复算法研究.计算机辅助设计与图形学学报,2005,17(4): 761-767
[3]何发祥,刘浩吾.有限元法前处理技术的发展.水利水电科技进展,2000,20(6): 15~17
[4]韩西,钟厉,李博.有限元分析在结构分析和计算机仿真中的应用.重庆交通学院学报,2001,20(3): 124~126
[5]李卫民.有限元网格生成算法的评述.泰州职业技术学院学报,2004,4(1):12~14
[6] Brown P R. A non-interactive method for the automatic generation of finite element meshes using the Schwarz-Christoffel transformation [J]. Computer methods in applied mechanics and engineering, 1981, 25(1): 101 ~126
[7] Baldwin K H, Schreyer H L, Automatic generation of quadrilateral elements by a conformal mapping [J]. Engineering with Computers, 1985, 2(3): 187~194
[8] Yang G W, E Q, Li F W. Use of conformal mapping in grid generation for complex two- and three-dimensional configurations. ACTA Aerodynamic SINICA, 1997, 15(3): 378~385
[9] Thompson J F, Thames F C, Martin C W. Automatic numerical generation of body-fitted curvilinear coordinates system for field containing and number of arbitrary two-dimensional bodies [J]. Journal of Computational Physics, 1974, 15: 299~319
[10] Thompson J F, Warsi Z U A, Martin C W. Boundary-fitted coordinate systems for numerical solution of partial differential equations– A review. Journal of Computational Physics, 1982, 47: 1~108
[11] Thompson J F, Warsi Z U A, Martin C W. Numerical Grid Generation: Foundations and Applications [M]. New York: Elsevier, 1985
[12] Thompson J F. A composite grid generation code for general 3D regions– The EAGLE code [J]. AIAA Journal, 1988, 26(3): 271~272
[13] Hsu K, Lee S L. A numerical technique for two-dimensional grid generation with grid control at all of the boundaries [J]. Journal of Computational Physics, 1991, 96(2): 451~469
[14] Spekreijse S P. Elliptic grid generation based on Laplace equations and algebraic transformations [J]. Journal of Computational Physics, 1995, 118(1): 38~61
[15] Gordon W J, Hall C A. Construction of curvilinear coordinate systems and applications to mesh generation [J]. Inter-national Journal for Numerical Methods in Engineering, 1973, 7: 461~477
[16] Eriksson L E. Generation of boundary conforming grids around wing-body configurations using transfinite interpolation [J]. AIAA Journal, 1982, 20(10): 1313~1320
[17] Yang W J, Bao Z X, Fu M F, et al. Mapping applied for Hexahedral mesh generation [J]. Journal of Nanchang University(Engineering & Technology), 1999, 21(4): 39~43
[18] Kadivar M H, Sharifi H. Double mapping of isoparameteric mesh generation [J]. Computer & Structure, 1996, 59(3): 471~477
[19]周华民.塑料注射成型三维真实感流动保压过程模拟及实验研究: [博士学位论文].武汉:华中科技大学,2001
[20]黄建科.基于CAE的虚拟注射成型系统关键技术的研究: [硕士学位论文].武汉:华中科技大学,2004
[21] Gao F, Zhao C. Melt temperature profile prediction for thermoplastic injection molding. Polymer Engineering and Science, 1999, 12: 51~54
[22] Palit K, Chen I J. How to Access CAE Injection Mold Design Softwares for Production Applications. SPE ANTEC Tech. Papers, 1989, 35: 356~359
[23] K. Bourdon. The Selection and Setting of Injection Molding Machines By Means of Process Simulation. SPE ANTEC Tech. Papers, 1989, 35: 308
[24] Y M Deng, Y C lam, S B Tor, et al. A CAD-CAE Integrated Injection Molding Design System. Engineering with Computers, 2002, 18: 80~92
[25]周华民,李德群.基于成形模拟的注塑件熔接缝确定与评价.中国机械工程,2004,15(21): 1962-1966
[26]周华民,李德群.基于型腔表面模型的塑料注射成形的充填保压模拟.中国机械工程,2002,13(16): 1382-1384
[27]周华民,李德群.基于注射成型CAE模拟的熔合纹确定与评价:(I)熔合纹的确定.塑料工业,2002,30(2): 32-33
[28]李德群.基于注射成型CAE模拟的熔合纹确定与评价:(II)熔合纹的评价.塑料工业,2002,30(3): 37-39
[29]叶福源,黄志高,周华民,李德群.冰箱抽屉注射成形的CAE优化.电加工与模具,2004,(3): 50-51
[30]李德群,陈兴,张宜生等.注射模软件的三个发展阶段.模具工业,1998,208(6): 3~6
[31]耿铁,李德群,周华民.注塑成型流动模拟技术发展的三个阶段.塑料科技,2002,151(5): 1~4
[32]周华民,李德群.基于型腔表面模型的塑料注射成形的充填保压模拟.中国机械工程,2002,13(16): 1382-1384
[33]周华民,张宜生,李德群.基于表面模型的注射成型充填模拟.自然科学进展,2001,11(3): 288-292
[34]崔树标,周华民,李德群.基于表面模型的注射模冷却过程模拟.模具工业,2005,(5): 10-14
[35]崔树标,周华民,李德群.注塑模冷却过程模拟关键算法研究.中国塑料,2005,19(4): 95-99
[36]耿铁,李德群,周华民.全三维注塑成型流动模拟有限元模型的研究.中国机械工程,2006,17(5): 505-509
[37]耿铁,李德群,周华民,邵玉杰.注塑充模过程中温度场的全三维数值模拟.化工学报,2005,56(9): 1612-1617
[38]耿铁,李德群,周华民.三维注射成型流动模拟的研究.中国塑料,2003,17(7): 78-81
[39]周华民,张云,李巍毅,李德群.塑料注射成型CAE集成系统的设计与实现.华中科技大学学报(自然科学版),2006,34(11): 15-18
[40]周华民,李德群,燕立唐,刘来英.集成环境下的智能化塑料注射成型CAE分析.华中科技大学学报,2002,30(3): 37-39
[41] Yao Zheng, Roland W. Lewis, David T. Gethin. Three- dimensional unstructured mesh generation: Part 1. Fundamental aspects of triangulation and point creation. Computer methods in applied mechanics and engineering, 1996, 134: 249~268
[42] Yao Zheng, Roland W. Lewis, David T. Gethin. Three- dimensional unstructured mesh generation: Part 2. Fundamental aspects of triangulation and point creation.Computer methods in applied mechanics and engineering, 1996, 134: 269~284
[43] Yao Zheng, Roland W. Lewis, David T. Gethin. Three- dimensional unstructured mesh generation: Part 3. Fundamental aspects of triangulation and point creation. Computer methods in applied mechanics and engineering, 1996, 134: 285~310
[44]成学文,李德群,周华民,崔树标.基于哈希表的STL面片冗余顶点快速滤除算法.华中科技大学学报,2004,32(6): 69~71
[45]崔树标,张宜生,梁书云等. STL面片中冗余顶点的快速滤除算法及应用.中国机械工程,2001,12(2): 173~176
[46]熊英,胡于进,赵建军.基于映射法和Delaunay方法的曲面三角网格划分算法.计算机辅助设计与图形学学报,2002,14(1): 56~60
[47]杨晓东,冯晓峰,申长雨.注塑模CAE用实体模型的表面网格模型生成方法.塑料工业,2004,32(5): 26~28
[48]成学文.塑性注射成型模拟系统的研究与开发: [博士学位论文].武汉:华中科技大学,2005
[49]熊英,胡于进.一种新的曲面有限元三角网格划分方法.华中科技大学学报,2001,29(4): 40~43
[50]刘春太,杨晓东,申长雨,陈静波.任意平面域的变尺寸有限元网格划分,计算力学学报. 2000,17(1): 107~108
[51]张修忠,金生.任意平面区域三角网格的全自动生成算法.计算力学学报, 2000,17(3): 313~319
[52]黄晓东,杜群贵.二维有限元网格的局部加密方法.华南理工大学学报(自然科学版),2004,32(12): 56~59
[53]金晶,吴新跃.有限元网格划分相关问题分析研究.计算机辅助工程,2005,14(2): 75~78
[54]杜平安.有限元网格划分的基本原则.机械设计与制造,2000,1: 34~36
[55]黄志超,包忠诩,周天瑞等.有限元网格划分技术研究.南昌大学学报(工科版), 2001,23(4): 25~30
[56] Steven J. Owen, Sunil Saigal. Surface mesh sizing control. International journal for numerical methods in engineering, 2000, 47: 497~511
[57]李娅,赵文.有限元网格自动剖分及优化方法.四川工业学院学报,2003,22(3): 104~106
[58]许晶,李桂荣. 2-D有限元网格优化新方法.德州学院学报,2003,19(6): 18~19
[59]温建昌,董湘怀,李赞.基于STL文件的有限元模拟模具自动生成技术.华中科技大学学报(自然科学版),2002,30(2): 27~29
[60]成学文,周华民,李德群,刘芬. STL文件错误修复算法的研究与应用.机械科学与技术(增刊),2005, 17(4): 761~766
[61]张世学,吴恩华.基于特征保持与三角形优化的网格简化.长春理工大学学报, 2005,28(2): 52~56
[62]李梅娥,周进雄.任意平面域的高质量有限元网格自动剖分.应用力学学报, 2004,21(3): 125~128
[63]王弘,王昌凌,袁铭辉.一种曲面网格优化的通用算法.华中科技大学学报, 2001,29(1): 41~43