基于Lanczos算法的模态重分析法及其在车身结构设计中的应用

A Lanczos-based modal reanalysis method and its application for car body structural design

模态重分析是指在结构修改之后不需要重新求解广义特征值方程,仅需要根据初始计算结果对修改后的问题进行求解,并能够在保证精度的前提下,提高计算速度。随着结构复杂度和修正量的增加,传统重分析方法的求解精度和稳定性随之下降。为此,利用初始结构模态分析结果,结合Lanczos算法和投影技术,采用缩减基方法求解修改结构的特征值和特征向量,使其同时具备了Lanczos向量快速收敛的优点和基于全局近似的缩减基向量的高精度。为了验证该方法的性能和准确性,对本文方法基于扩展基向量和瑞利-里兹分析的模态重分析法以及改进的单步摄动瑞利商逆迭代法进行了测试。测试结果表明,该方法具有最高的计算精度。同时,将该方法成功用于车架和车门的前期设计中,计算结果表明,该方法具备处理计算规模大、拓扑修改变化量大的结构分析问题的潜力。

Modal reanalysis is used for analyzing the modified structure according to the initial analysis results,which can be instead of full eigenvalue solver. Compared with the full analysis,modal reanalysis can achieve enough accurate result efficiently. With the increasing of the complexity and change of the original structure,the accuracy and stability of reanalysis can not be promised. Therefore, the suggested method combines Lanczos algorithm and projection techniques and solves the eigenproblem for the modi- fied structure utilizing the obtained eigenvectors with reduced basis algorithm. Compared with the Lanc- zos and modal reanalysis method, high accuracy of reduced basis due to global optimization and fast convergence could be maintained simultaneously. To validate the performance and accuracy of the suggested method, a test is performed by the suggested method, Rayleigh-Litz analysis with extend vector and improved single step perturbation Rayleigh quotient inverse iteration method. It demonstrated that the Lanczos-based modal reanalysis method has the best performance. Meanwhile, the proposed method was successfully applied to the preliminary design of the frame and door. The results also demon- strated that the Lanczos-based modal reanalysis method is capable of handling large-scale structural anal- ysis problem in which topological modifications change a lot.