乔  磊¹，  赵乐之²
   （1 城市建设研究院，北京 100120；2 北京市市政工程设计研究总院，北京 100082）

[摘要] 索膜结构有限元分析计算速度归结为大规模线性方程组KU =P的求解速度。通过RCM算法，对有限元网格节点编号进行优化，从而减小总刚度矩阵K的带宽与轮廓来减少数据存储量及浮点运算次数，提高了线性方程组直接法的求解速度。另外，在大型索膜结构有限元计算中，传统的RCM算法计算过程存在两方面问题，一方面没有考虑网格规模造成的计算内存负担，影响计算速度；另一方面不能适应索膜结构中存在混合节点自由度的实际情况。因此，改进了传统RCM算法，使其能够高效应用于索膜结构有限元分析。算例表明，改进的RCM算法能够显著提高索膜结构有限元计算速度。
[关键词] 索膜结构；节点编号；线性方程组求解；RCM算法；求解速度
中图分类号：TU311.4    文献标识码：A  文章编号：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