基于自定義單元法的自由曲面網(wǎng)格劃分研究*
江存，高博青
- 摘 要
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（浙江大學(xué)建筑工程學(xué)院, 杭州 310058）［摘要］為實(shí)現(xiàn)對(duì)任意自由曲面的建筑網(wǎng)格劃分，采用自定義單元法，以網(wǎng)格節(jié)點(diǎn)為對(duì)象，以“代”為整體進(jìn)行節(jié)點(diǎn)推進(jìn)。首先，根據(jù)節(jié)點(diǎn)的演化規(guī)律進(jìn)行網(wǎng)格單元自定義。其次，在節(jié)點(diǎn)推進(jìn)過程中，根據(jù)曲面特征進(jìn)行單元選擇生成下代節(jié)點(diǎn)，自適應(yīng)曲面尺寸變化，將每一推進(jìn)步單元“組裝”，建立網(wǎng)格拓?fù)涞膮?shù)化表達(dá)；采用黎曼度量表征單元節(jié)點(diǎn)參數(shù)距離，考慮適應(yīng)曲面曲率特征，確定節(jié)點(diǎn)參數(shù)坐標(biāo)。最后，參數(shù)網(wǎng)格映射到自由曲面形成空間網(wǎng)格結(jié)構(gòu)。結(jié)果表明，自定義單元法能夠通過參數(shù)選擇實(shí)現(xiàn)對(duì)網(wǎng)格規(guī)模和形式的量化控制，為自由曲面提供多樣化網(wǎng)格劃分方案，生成的網(wǎng)格桿件均勻、線條流暢、形式多樣。［關(guān)鍵詞］自由曲面; 自定義單元法; 黎曼度量; 映射法; 網(wǎng)格劃分中圖分類號(hào)：TU311.41 文獻(xiàn)標(biāo)識(shí)碼：A 文章編號(hào)：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*國(guó)家自然科學(xué)基金項(xiàng)目（51378457）。作者簡(jiǎn)介：江存，碩士，Email: cunjiangg@163.com。參考文獻(xiàn)［1］關(guān)振群, 宋超. 有限元網(wǎng)格生成方法研究的新進(jìn)展［J］. 計(jì)算機(jī)輔助設(shè)計(jì)與圖形學(xué)學(xué)報(bào), 2003, 15(1): 1-14.［2］李承銘, 盧旦. 自由曲面單層網(wǎng)格的智能布局設(shè)計(jì)研究［J］. 土木工程學(xué)報(bào), 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］危大結(jié), 舒贛平. 自由曲面網(wǎng)格的劃分與優(yōu)化方法［J］. 建筑結(jié)構(gòu), 2013,43(19): 48-53.［5］崔昌禹, 王有寶, 姜寶石. 自由曲面單層網(wǎng)殼結(jié)構(gòu)形態(tài)創(chuàng)構(gòu)方法研究［J］. 土木工程學(xué)報(bào), 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. 非均勻有理B樣條［M］.2版. 趙罡,譯. 北京: 清華大學(xué)出版社, 2010.［8］彭家貴，陳卿.微分幾何［M］.北京：高等教育出版社，2002.
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