Element-Based Node Selection Method for Reduction of Eigenvalue Problems

For the condensation of degrees of freedom in large structure problems, various methods have been proposed to approximate the lower eigenvalues that represent the global behavior of the structures. One of the dynamic condensation methods was introduced by Guyan [1]. This method involves elimination of the degrees of freedom which do not give any significant influence on the solution field. O’Callahan has improved the Guyana’s method by considering the first order approximation in the transformation formula of slave degrees of freedom [2]. Zhang has proposed the successive-level approximate reduction method [3]. While these techniques could greatly reduce computational effort by eliminating degrees of freedom, they suffer from nontrivial flaws. Because they ignore several higher order terms, results of these methods are highly dependent on the choice of master degrees of freedom. For this reason, several techniques have been proposed to select the master degrees of freedom effectively. The one of the most effective technique is the sequential elimination of the degrees of freedom of which the ratio of stiffness to mass in the diagonal terms of mass and stiffness matrices is highest. This method has been proposed by Shah and Raymund [4]. Shah method shows the effective selection of master degrees of freedom among others and the prediction of lower mode eigenvalue is very reliable. However, it takes considerable computing time in selecting the master degrees of freedom which is required.