New Structural Dynamic Condensation Method for Finite Element Models

A new iterative method is proposed for the reduction of finite element models arising in test-analysis correlation, model updating, finite element modeling, vibration control, structural dynamic optimization, and so on. Based on the modified eigenvalue equation and the eigenvalue shifting technique, two constraint equations for the dynamic condensation matrix, which relates the deformations associated with the master and slave degrees of freedom, are derived. Two iterative schemes are presented for solving the constraint equations. In the second constraint equation, because the dynamic condensation matrix has nothing to do with the eigenpairs of the reduced model, it is unnecessary to calculate them in every iteration. This makes the iterative scheme more computationally efficient than the usual scheme, especially when the number of the master degrees of freedom is large. The accuracy of eigenvalues and eigenvectors of the reduced model is examined in every iterative step. The comparison of the present method with some typical iterative schemes proposed in the past shows that the new one has the highest accuracy. Numerical examples are also presented to show the efficiency of the proposed method.