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   喬  磊¹，  趙樂之²
   （1 城市建設(shè)研究院，北京 100120；2 北京市市政工程設(shè)計(jì)研究總院，北京 100082）

[摘要] 索膜結(jié)構(gòu)有限元分析計(jì)算速度歸結(jié)為大規(guī)模線性方程組KU =P的求解速度。通過RCM算法，對有限元網(wǎng)格節(jié)點(diǎn)編號進(jìn)行優(yōu)化，從而減小總剛度矩陣K的帶寬與輪廓來減少數(shù)據(jù)存儲量及浮點(diǎn)運(yùn)算次數(shù)，提高了線性方程組直接法的求解速度。另外，在大型索膜結(jié)構(gòu)有限元計(jì)算中，傳統(tǒng)的RCM算法計(jì)算過程存在兩方面問題，一方面沒有考慮網(wǎng)格規(guī)模造成的計(jì)算內(nèi)存負(fù)擔(dān)，影響計(jì)算速度；另一方面不能適應(yīng)索膜結(jié)構(gòu)中存在混合節(jié)點(diǎn)自由度的實(shí)際情況。因此，改進(jìn)了傳統(tǒng)RCM算法，使其能夠高效應(yīng)用于索膜結(jié)構(gòu)有限元分析。算例表明，改進(jìn)的RCM算法能夠顯著提高索膜結(jié)構(gòu)有限元計(jì)算速度。
[關(guān)鍵詞] 索膜結(jié)構(gòu)；節(jié)點(diǎn)編號；線性方程組求解；RCM算法；求解速度
中圖分類號：TU311.4    文獻(xiàn)標(biāo)識碼：A  文章編號：1002-848X(2012) Sl-0665-04

Application of RCM algorithm in cable-membrane structural FEM analysis
Qiao Lei¹,  Zhao Lezhi²
(1 Urban Construction Design & Research Institute, Beijing 100120, China; 2 Beijing General Municipal Engineering Design & Research Institute, Beijing 100082, China)

Abstract: The calculation speed of finite element analysis of cable-membrane structures is attributed to the solving speed oflarge-scale linear equation KU=P.Using the RCM algorithm, the node number optimization of the finite element mesh was conducted to reduce the bandwidth and contour of the total stiffness matrix [ K].  Then, the data storage capacity and the number of floating point operations were decreased and the speed of the direct method of solving linear equations was improved. In addition, in the finite element method of the large cable-membrane structures, there are two drawbacks of the traditional RCM algorithm calculation process. The first one is the calculation speed is influenced by neglecting the burden of computer memory caused by grid scale. The other one is that this method can not be adapted to the mixed node degrees of freedom of the cable-membrane structures. Therefore, the improvement of traditional RCM algorithm was efficiently applied to finite element analysis of cable-membrane structure.  Examples illustrate that the modified RCM algorithm can significantly improve the finite element calculation speed of the cable-membrane structures.
Keywords: cable-membrane structures; node number; solution oflinear equations; RCM algorithm; solving speed