Energy Method for Selection of Degrees of Freedom in Condensation

An analytical method is presented for the selection of degrees of freedom in condensation of eigenproblems. The method isbasedon theenergiesassociatedwiththedegrees offreedom in theeigenmodesofstructuralsystems. For theenergyestimationRitzvectorsarecalculated,usingthestiffnessandmassmatrices.Theenergiesaddedthrough themodesortheweighted rowsum oftheenergy distribution matrix can be used asan effective guideline on which degrees of freedom should be retained in the analysis. Another approach of sequential selection can be employed, in which a e nite number of new degrees of freedom with the largest energy are taken in each mode and the e nal union becomes the analysis set. The energy of the selected degrees of freedom or the column sum of the matrix can beused to predict thesolution accuracy in each mode. The erroranalysisshowsthattheperturbation in eigenvalue is related with the energy of the degrees of freedom. The row 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 has 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.