基于逆迭代法的结构动力缩聚技术

有限元模型的动力缩聚法已被广泛地应用到大阶系统的特征分析、试验－分析模型的相关分析等领域中。本文从逆迭代法出发，导出了一种有限元模型动力缩聚迭代方法。该方法具有三个显著的优点：其一是收敛速度远远超过现有的动力缩聚迭代法；若干是该迭代法收敛的可以从理论上得到保证，其三是由于没有必要的在每次迭代中都去计算降阶系数的刚度矩阵、质量矩阵和特征问题，因而可减少计算工作量，尤其在主自由度数较大的情况下。

A dynamic condensation technique via inverse iteration method

Dynamic condensation methods for finite element models have been broadly applied in eigenvalue problems of large structures, test analysis model correlation and so on. Based on the inverse iteration method, an iterative technique for dynamic condensation of finite element models has been derived in this paper. The approach has three advantages. Firstly, the convergent rate is much higher than all the iterative methods for dynamic condensation proposed in the past, especially when the approximate values of the reduced model are close to the full model. Second, the convergence can be proven simply according to the subspace iteration method. Finally, it is unnecessary to calculate the stiffness, mass matrices and eigenproblem of the condensed model in every iteration. This makes the proposed method more computationally efficient than the usual ones, especially when the number of the master degrees of freedom are large.