Energy method for selection of degrees of freedom in condensation

An analytical method is presented for the selection of degrees of freedom i n condensation of eigenproblems. The method is based on the energies associ ated with the degrees of freedom in the eigenmodes of structural systems. F or the energy estimation Ritz vectors are calculated, using the stiffness a nd mass matrices. The energies added through the modes or the weighted row sum of the energy distribution matrix can be used as an effective guideline on which degrees of freedom should be retained in the analysis. Another ap proach of sequential selection can be employed, in which a finite number of new degrees of freedom with the largest energy are taken in each mode and the final union becomes the analysis set. The energy of the selected degree s of freedom or the column sum of the matrix can be used to predict the sol ution accuracy in each mode. The error analysis shows that the perturbation in eigenvalue is related with the energy of the degrees of freedom. The ro w and column sums indicate the completeness of the selected set and give a clue to how many degrees of freedom to be included. The energy criterion ha s shown that the conventional practice of choosing translational degrees of freedom is appropriate only for the lowest modes. Numerical investigations were performed to test the convergence criterion. The energy method proved to work well for typical example problems.