动力凝聚技术的新算法

A New Approach to the Dynamic Condensation Technique

本文提出了缩减特征方程的一种新方法。这一新算法兼有以Guyan法为基础的凝聚技术和子空间迭代法的的优点而又避免了两者的缺点,无需求逆,也不会占据过大的内存。采用这一方法,可判断凝聚到最后一个自由度的动力刚度值κ_n是否为零,能快速地在某一范围内搜索相应的特征值。这一新算法比行列式法运算简便得多;与Strum系列法相比,应用范围也大得多。

This paper suggests a new approach to the reduction of eigen-equation, it shares the advantages of condensation technique based on Guyan's reduction as well as that of subspace iteration method, while eliminates their disadvantages: the troublesome matrix inversions and the gain of accuracy at the expense of computer's internal storage. A new method is also presented which is able to search for all eigenvalues in a fixed range by simply judging the value of k(?) -the dynamic stiffness of the whole system after being condensed down to its last d.o.f-to see if it is zero. This method is more convenient in term of operation, compaired with the conventional determinant method, and also of wide applicability, compared with Strum Sequence.