Abstract:

In topological optimization,the structures were often required to make some modifications,and it was very important for improving the effciency of optimization that the low-order eigenvalues could be calculated accurately and quickly. The Lanczos-based modal reanalysis method was applied to topological modification.The presented method which combined Lanczos  algorithm and projection techniques,solved the natural frequency and mode shapes for the modified structures utilizing the already obtained eigenvectors with reduced-basis algorithm.The major advantages laid that the fast convergence of Lanczos vector and high-accuracy of reduced-basis method based on global approximations.A stiff frame example was demonstrated the high accuracy of the reanalysis method.The optimization results of the clamped square plate and vehicle frame indicate that the method can also ensure the calculation accuracy and optimization iteration speed to a certain extent.

Key words: Lanczos algorithm, modal reanalysis, topological optimization, frequency optimization

摘要：

在拓扑优化中,经常要求对结构进行修改,快速准确地计算修改后结构的低阶特征值对于提高整个结构优化的效率非常重要。将基于Lanczos算法的模态重分析法应用于拓扑优化过程中,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固有频率和振型, 则该方法同时具备了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。刚架算例验证了该重分析法的高精度。固支方形板和车架结构优化结果表明,该方法在保证求解精度的同时能够在一定程度上提高优化迭代速度。

关键词: Lanczos算法, 模态重分析, 拓扑优化, 频率优化