基于预条件Lanczos算法的结构拓扑修改静态重分析方法

New method for structural static reanalysis of topological modifications based on preconditioning Lanczos algorithm

提出了一种新的结构拓扑修改静态重分析方法。该方法易于实现并且适用于拓扑修改中的3种情况:自由度不变化;自由度减少;自由度增加。根据初始分析结果,对拓扑修改的3种情况分别选取了适当的预条件子,应用Lanczos迭代算法得到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,比较了预条件前后迭代收敛速度。应用本文提出的方法计算成本显著降低,计算结果显示了该算法的正确性和有效性。

A new method for structural static reanalysis of topological modifications was presented.The proposed procedure was easy to implement and suit for three cases of modifications： the number of Degree of Freedom （DOFs） is unchanged; the number of DOFs is decreased; the number of DOFs is increased. According to the analysis result of original system, three suitable preconditioner were selected and the response of modified structure was gained by Lanczos algorithm. Both the present method and the Lanczos algorithm without preconditioning were applied to numerical examples, respectively. The Convergence of the two methods were compared. The computational cost is significantly reduced by the proposed method. The numerical results show the exactitude and effectiveness of the reanalysis algorithm.