一种基于代数图论的有限元模型节点排序方法

A Finite Element Nodal Ordering with Algebraic Graph Theory

提出了一种基于有限元模型中节点自由度构造赋权单元团图的方法,根据代数图论的理论,应用赋权单元团图的拉普拉斯矩阵的Fiedler向量,对有限元模型的节点进行排序,以达到减少结构刚度矩阵的半带宽和外形的目的.该方法不但能适用于一般有限元模型,而且适用于包含不同类型单元、具有不同自由度节点的混合节点模型.对于混合节点模型,该方法比基于单元团图的拉普拉斯矩阵的代数图论方法能够取得更加满意的结果.据此编制的前处理程序,可以对任意编号的模型进行优化处理.数值算例结果表明本方法是有效的.

A new methodology is proposed for construction of weighted element clique graph（WECG） based on nodal degrees of freedom.The Fiedler vector of the Laplacian Matrix of WECG is used for reduction of the bandwidth and profile of stiffness matrix in finite element analysis.The present method is not only suitable for common finite element models,but also for models including different nodal degrees of freedom of element in number and usually leads to better results for the latter models compared with common methodology of algebraic graph theory based on Laplacian Matrix of element clique graph.A pre-processing routine based on the present method is embedded in a finite element program,which can reduce the generation task of finite element model without consideration of nodal ordering.The numerical experiments show that the present method is efficient.