有限元模型中自由度层次的带宽优化算法

Bandwidth Optimization Algorithm of Finite Element Models at Level of Degree of Freedom

为提高有限元分析的计算速度,针对有限元模型中节点在整体结构自由度向量中参与自由度个数不等的情况,建立了自由度层次的带宽优化算法.根据自由度的邻接关系设置邻接矩阵,由邻接矩阵建立树层次结构,并利用顶点可移动判据对树宽进行优化,对树层次结构中的同层顶点按照未编号下层度的升序编号.该方法无需人工干预也能获得Burgess算法的最优带宽,能解决有限元模型中同时使用多种单元、主从节点或非节点连接技术引起的带宽优化问题.

Based on the fact that the numbers of degree of freedom （DOF） of nodes participating in the DOF vector of structures are not the same, an algorithm was proposed to optimize the bandwidth of finite element models at the level of DOF to raise the calculation speed of finite element analyses. In this algorithm, the tree level structure is established from an abutting matrix based on the abutting relationship among DOFs. When the width of the tree structure is optimized, criterions are put forward to judge whether a vertex is movable. The vertices at the same level are numbered by their unnumbered degrees at the next level. In two investigated examples, the proposed optimization algorithm gets the same bandwidths as Burgess＇s bandwidths without manual intervention. The proposed algorithm at the level of DOF can be used to solve the problems induced by various types of elements, host-subordinate nodes or non-nodal connection method.