基于多重多级动力子结构的Lanczos算法

提出利用多重多级子结构技术与Lanczos方法求解超大型复杂结构动力特性的子结构算法。该算法利用子结构周游树技术，分别对每个子结构进行Lanczos迭代，通过累加各个子结构的正交化系数组成全局三对角矩阵，最后求解得到整体结构的特征值。算法能够计算超大型结构特征值和特征向量，计算效率高；消耗计算机资源少，稳定性高。由于考虑了各子结构内部自由度对整体求解的贡献，算法精度得到显著提高，并与不作凝聚的单一整体结构分析具有相同的计算精度，计算结果不受复杂子结构划分方式的限制。数值算例验证了所提出算法的正确与有效性。

Lanczos algorithm based on multi-level dynamic substructures

A combined method based on multi-level substructuring technique and Lanczos algorithm was proposed for solving dynamic characteristics of large-scale and complicate structures.In implementation of the method,a total tridiagonal matrix was given by accumulating the orthogonal coefficients of each substructure,and the eigenvalues corresponding to the whole structure were solved.The method was able to solve eigenvalue and eigenvector problems for super large-scale structures and had good computational efficiency and stability,and less computational cost.Since the contribution of all internal DOF of each substructure to the dynamic characteristics of the whole structure was considered,the accuracy was improved significantly and the same as the result achieved by directly solving the whole structure without condensation process.It was found that the partitioning scheme of substructure does not affect numerical results,and the finite element modeling has great flexibility.The numerical results showed that the solutions obtained by the proposed multi-level substructuring method are effective and valid.