A DEGREE SELECTION METHOD OF MATRIX CONDENSATIONS FOR EIGENVALUE PROBLEMS

A new and automatic degree selection technique based on the approximate modal energy has been derived and developed for matrix condensations in this paper. The method is used to condense the number of degrees of the matrix when dealing with eigenvalue problems. By defining a new basis in the vicinity of the original space, the individual modal energy gradients can be evaluated. The primary degrees of freedom are then determined according to the variation of the energies in the neighborhood. In case the energy variation of a degree tends to increase in that neighborhood, the degree is classified as secondary since it relatively provides energy to the nodes nearby. On the other hand, if the energy variation is decreasing, then it is primary. All the classification criteria are finally mapped to one parameter, which is called the index of classification. That is, by examining the magnitude of the index of classification, one is able to determine the primary and secondary degrees. The new selection method is demonstrated and verified by a well-known cantilever beam problem in addition to the error bound estimation.