有限元刚度矩阵的压缩存贮及组集

来源期刊：中南大学学报(自然科学版)2006年第4期

论文作者：姚松 田红旗

文章页码：826 - 830

关键词：细胞元;组集;非零元素;稀疏直接求解法;预处理共轭梯度法

Key words：cell element; assembly; non-zero element; sparse direct solver method; preconditioned conjugate gradient method

摘    要：基于细胞元索引存贮方案,提出一种仅组集有限元刚度矩阵中非零元素的方法,该方法最突出的特点是计算所需内存空间与有限元网格节点和单元的编号模式无关,适于进行自适应网格细化有限元分析。针对刚度矩阵的一维压缩存贮格式,对稀疏矩阵直接解法和预处理共轭梯度法进行探讨,并编制相应的计算机程序对某地铁车辆有限元模型进行分析,计算结果与ANSYS5.7的计算结果相比相对误差不超过2%,说明提出的存贮方案和求解方法是正确、可靠的。

Abstract: A procedure to assemble only non-zero element of a global stiffness matrix of finite element analysis in a one-dimensional array was proposed, which utilizes cell element index storage scheme. One of the important characteristics of the scheme is that the storage and solution requirements are independent of the numbering pattern of nodes and elements in finite element mesh, which is suitable for self-adaptively refined finite element analysis. For one-dimension compressed format of sparse structure matrix, two solution methods for large sparse matrix equations were discussed, including sparse direct solver and preconditioned conjugate gradient method. The procedure was implemented in a computer program. At last a finite element model of a subway car-body was carried out by using the program. The difference of the results between the presented method and commercial FEA codes ANSYS5.7 does not exceed 2%, which shows that the storage scheme and solution method proposed are correct and reliable.