Epsilon算法在结构模态重分析中的应用

Applications of Epsilon-algorithm in eigensolution reanalysis of structures

基于Neumann级数和Epsilon算法,提出了一种模态重分析的新算法。在求解过程中,利用Neumann级数产生基向量,然后用Epsilon算法求出近似特征向量,最后用Rayleigh商分析,求出了修改后结构的近似特征值和特征向量。数值算例表明,所提出的算法比K irsch组合近似法精度更高,计算速度更快。

Based on the Neumann series and Epsilon-algorithm, a new eigensolution reanalysis method was developed. In the solution process, the basis vectors can be obtained from the matrix perturbation or the Neumann series, and then the Epsilon-algorithm was used to obtain the approximate eigenvectors. The approximate eigenvalues are computed from the Rayleigh quotients. The solution steps are straightforward and easy to implement with the general finite element analysis system. The computational effort is much smaller than the effort needed for the full analysis of the modified structures. A numerical example of a 40-story frame was given to demonstrate the applications of the present method. Comparing with the exact solutions and the Kirsch combined approximate solutions, it was shown that the excellent results were obtained efficiently for large changes in the design parameters.