结构拓扑修改动力学重分析的单步摄动逆迭代法

提出了一种结构动力学拓扑重分析的单步摄动逆迭代方法:首先将新增加的自由度通过动力缩减方法凝聚到原始自由度上;然后用单步摄动法求出初始结构自由度和增加自由度上的修正特征向量;再用瑞利-商逆迭代法对整个自由度的近似特征向量进行逆迭代,并最终采用瑞利商获得修改结构的近似特征值。数值算例的结果表明:该方法计算编程简单易行,且具有较高精度,适合用于结构拓扑修改自由度增加时的动力学重分析。

A New Method for Dynamical Reanalysis of Topological Modifications of Structures

Purpose.Both Ref.2 and Ref.3 can be used to perform dynamical reanalysis of topological modifications of structure.We now present a new and,we believe,better method.Our new method first improves the single step perturbation method of Refs.4 and 5,and then combines the improved single step perturbation method with the Rayleigh-Quotient inverse iteration method of Ref.6 to perform better the dynamical reanalysis of topological modifications of structure.Eqs.(14) through(28),derived by us in the full paper,summarize mathematically our new method.Finally,we give two numerical examples,whose results are given respectively in Table 1 of the full paper.The numerical results show that our new method yields high precision for topological modifications of structures even if amount of topological modification is great;our new method is easy to implement on a mini-computer.Usually the convergence of inverse iterations was achieved after two iterations.Thus,the computational effort is significantly reduced.