结构静态重分析的改进预条件Lanczos方法  

MODIFY PRECONDITIONING LANCZOS ALGORITHM FOR STRUCTURAL STATIC REANALYSIS

作　　者：徐涛[1] 程飞[1] 郭桂凯[1] 李亦文[1] 陈静波[1] 

机构地区：[1]吉林大学机械学院力学系,长春130022

出　　处：《机械强度》2009年第3期425-431,共7页Journal of Mechanical Strength

基　　金：教育部博士点基金项目(20050183018);吉林大学"985汽车工程"项目资助~~

摘　　要：通过引入Jordan约化变换及广义模态理论,对预条件Lanczos算法进行优化修正,建立一种新的结构拓扑修改静态重分析方法。该方法适用于拓扑修改中的三种情况,并易于上机实现。该方法根据初始分析结果,对拓扑修改的三种情况分别选取预条件子,并对相应预条件系统的系数矩阵进行改进,得到改进后预条件子,经过预条件及预条件子改进处理后系统系数矩阵条件数显著减小,收敛速度得到大幅提高,应用该改进的预条件Lanczos迭代算法计算拓扑修改后结构响应。将此算法与直接Lanczos算法分别应用于数值算例,比较预条件前后迭代收敛速度。同时分析该方法时间复杂度,并分别和组合近似方法(combined approximations,CA)与直接解法进行对比,对比表明本文提出的方法计算成本显著降低,计算结果验证了该算法的正确性和有效性。A new method for structural static reanalysis of topological modifications is presented by introducing Jordan method and generalized model theory. The proposed procedure is easy to implement and suit for three cases of topological modifications. According to the analysis result of original system, three suitable preconditioner are selected and modified. After preconditioning and modifying the preconditioner, the condition number of the system matrix is decreased remarkably. Tne response of modified structure is gained by mod- ified preconditioning Lanczos algorithm. Both the present method and the Lanczos algorithm are applied to numerical examples, respectively. The convergence of the two methods are compared. The time complexity of present method and CA（ combined approximations） are compared also. The computational cost is significantly reduced by the proposed method. The numerical results show the exactitude and effectiveness of the reanalysis algorithm.

关 键 词：拓扑修改 结构静态重分析 LANCZOS算法 预条件子 有限元系统 

分 类 号：O302[理学—力学]