Optimal Ritz vectors for component mode synthesis using the singular value decomposition

A fundamental property of the Rayleigh-Ritz method is that a reduced model gives exact predictions if the solutions lie in the range of the reduction basis. For cases with and without rigid-body modes, it is shown that the strain energy norm can he used to define optimal projections of both loads and displacements onto the exactly represented subspace of a given reduced model. In practice, multiple loads or displacements are considered, and variants of the singular value decomposition based on the strain and kinetic energy norms are shown to provide ways to select important contributions. The proposed framework is used to define two new methods for optimal reduction and reduced model correction. The validity and usefulness of the proposed methods are illustrated for the example of two square plates assembled at a right angle with two very different plate thickness configurations.