用有限元法计算特征值问题的一种新的动态凝聚方法

A NEW DYNAMIC CONDENSATION METHOD USING FINITE ELEMENT APPROACH TO CALCULATE EIGENVALUE PROBLEM

有限元法是常用的建模方法,由于所建模型具有较大的自由度,通常需要进行降阶处理.一般来讲,模型前几阶特征值和特征向量可以较精确地得到,利用所得到的特征值和主振型分量(在特征向量中与所给定的主自由度对应的振型分量),本文提出了一种新的动态凝聚方法,该方法是通过迭代方式,利用所得到的特征值和主振型分量对Guyan降阶法所得到的降阶模型进行修正.与同类方法相比,本文方法具有较高的计算精度和很小的计算量,且迭代收敛的稳定性很好.最后本文给出了一个计算实例.

Finite element method is an usual model-built method, in which the reduction transaction is necessary for the acquired model as it has a larger degrees of freedom（d, o. f. ）, and generally speaking, the first several eigenvalues and eigenvectors can be accurately gained. In the paper, a new dynamic condensation method is presented based on the eigenvalues and master-mode-part （the parts corresponding to master d. o. f. in eigenvectors）,and the reduction model obtained by Guyan reduction can be updated by aid of an iterative method, the eigenvalues and master-mode-part. Compared with congeneric other methods, the presented method has a higher calculation precision, smaller calculation efforts and better calculation stability. In the last, an example is given to show the effectiveness of the presented algorithms.