基于自定义单元法的自由曲面网格划分研究*
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（浙江大学建筑工程学院, 杭州 310058）［摘要］为实现对任意自由曲面的建筑网格划分，采用自定义单元法，以网格节点为对象，以“代”为整体进行节点推进。首先，根据节点的演化规律进行网格单元自定义。其次，在节点推进过程中，根据曲面特征进行单元选择生成下代节点，自适应曲面尺寸变化，将每一推进步单元“组装”，建立网格拓扑的参数化表达；采用黎曼度量表征单元节点参数距离，考虑适应曲面曲率特征，确定节点参数坐标。最后，参数网格映射到自由曲面形成空间网格结构。结果表明，自定义单元法能够通过参数选择实现对网格规模和形式的量化控制，为自由曲面提供多样化网格划分方案，生成的网格杆件均匀、线条流畅、形式多样。［关键词］自由曲面; 自定义单元法; 黎曼度量; 映射法; 网格划分中图分类号：TU311.41 文献标识码：A 文章编号：1002-848X(2015)05-0044-05Research on free-form surface meshing based on self-defined element methodJiang Cun, Gao Boqing(College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, China)Abstract: To realize the meshing of any free-form surface, the node was taken as the object and node in the same generation was taken as a whole to realize the advancing based on self-defined element method. Firstly, grid elements were defined based on the evolutional law of nodes. Besides, proper elements were selected automatically according to the surface feature to generate the nodes of next generation in the advancing process of nodes. In this way, it could be adaptive to change in surface size and elements in each step were assembled to establish parametric expression of grid topology. Riemannian metric was used to represent the parametric distance in consideration of curvature variation on surface and parametric coordinates of nodes were determined accordingly. Finally, the parametric grid was mapped back onto surface to form spatial grid. The results show that self-defined element method can control the scale and form of grid quantitatively through the selection of parameters and offer diverse meshing plans for free-form surface. Grid generated by the method has uniform rods, fluent lines and multiple forms.Keywords: free-form surface; self-defined element method; Riemannian metric; mapping method; meshing*国家自然科学基金项目（51378457）。作者简介：江存，硕士，Email: cunjiangg@163.com。参考文献［1］关振群, 宋超. 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.［2］李承铭, 卢旦. 自由曲面单层网格的智能布局设计研究［J］. 土木工程学报, 2011, 44(3): 1-7.［3］SU LIANG，ZHU SHUNLAI. An automatic grid generation approach over free-form surface for architectural design ［J］. Journal of Central South University, 2014, 21(6): 2444-2453.［4］危大结, 舒赣平. 自由曲面网格的划分与优化方法［J］. 建筑结构, 2013,43(19): 48-53.［5］崔昌禹, 王有宝, 姜宝石. 自由曲面单层网壳结构形态创构方法研究［J］. 土木工程学报, 2013, 46(4): 57-63.［6］HERNANDEZ-MONTES E, JURADO-PINA R. Topological mapping for tension structures ［J］. Journal of Structural Engineering, 2006, 132(6): 970-977.［7］PIEGL L, TILLER W. 非均匀有理B样条［M］.2版. 赵罡,译. 北京: 清华大学出版社, 2010.［8］彭家贵，陈卿.微分几何［M］.北京：高等教育出版社，2002.
