中国机械工程
中國機械工程
중국궤계공정
CHINA MECHANICAl ENGINEERING
2015年
11期
1516-1520,1526
,共6页
Lanczos 算法%模态重分析%拓扑优化%频率优化
Lanczos 算法%模態重分析%拓撲優化%頻率優化
Lanczos 산법%모태중분석%탁복우화%빈솔우화
Lanczos algorithm%modal reanalysis%topological optimization%frequency optimization
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。
在拓撲優化中，經常要求對結構進行脩改，快速準確地計算脩改後結構的低階特徵值對于提高整箇結構優化的效率非常重要。將基于 Lanczos 算法的模態重分析法應用于拓撲優化過程中，利用初始結構模態分析結果，結閤 Lanczos 算法和投影技術，採用縮減基方法求解脩改結構的固有頻率和振型，則該方法同時具備瞭 Lanczos 嚮量快速收斂的優點和基于全跼近似的縮減基嚮量的高精度。剛架算例驗證瞭該重分析法的高精度。固支方形闆和車架結構優化結果錶明，該方法在保證求解精度的同時能夠在一定程度上提高優化迭代速度。
재탁복우화중，경상요구대결구진행수개，쾌속준학지계산수개후결구적저계특정치대우제고정개결구우화적효솔비상중요。장기우 Lanczos 산법적모태중분석법응용우탁복우화과정중，이용초시결구모태분석결과，결합 Lanczos 산법화투영기술，채용축감기방법구해수개결구적고유빈솔화진형，칙해방법동시구비료 Lanczos 향량쾌속수렴적우점화기우전국근사적축감기향량적고정도。강가산례험증료해중분석법적고정도。고지방형판화차가결구우화결과표명，해방법재보증구해정도적동시능구재일정정도상제고우화질대속도。
In topological optimization,the structures were often required to make some modifica-tions,and it was very important for improving the effciency of optimization that the low-order eigen-values could be calculated accurately and quickly.The Lanczos-based modal reanalysis method was ap-plied to topological modification.The presented method which combined Lanczos algorithm and pro-jection 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 approxi-mations.A stiff frame example was demonstrated the high accuracy of the reanalysis method.The op-timization results of the clamped square plate and vehicle frame indicate that the method can also en-sure the calculation accuracy and optimization iteration speed to a certain extent.
