On the finite element model reduction methods in structural dynamics

Abstract

Finite element model reduction methods have been widely used to reduce the computational costs of structural analysis and design. Using model reduction methods, global (original) models can be approximated by reduced models with much smaller matrix size. Although various model reduction methods such as dynamic condensation and component mode synthesis (CMS) have been proposed over the last several decades, many challenging issues still must still be addressed to improve the solution accuracy and computational efficiency of reduced models. The work in this thesis focuses on the development of enhanced model reduction, general mode selection, and accurate error estimation methods to overcome the known disadvantages and limitations of existing model reduction methods.In this work, we first develop a new component mode synthesis enhancing the Craig-Bampton (CB) method, the most popular model reduction method. To develop the enhanced CB method, the original transformation matrix in the CB method is enhanced considering the residual flexibility that contains the residual substructural modal effect, and the unknown eigenvalue in the enhanced transformation matrix is approximated by using O`callahan`s approach to Guyan reduction. Using the newly defined transformation matrix, global FE models can be more accurately approximated. We demonstrate its performance through numerical examples.In model reduction methods, only a small proportion of the dominant degree of freedoms (DOFs) or the substructural modes is retained in the reduced model. Therefore, the accuracy of the reduced model highly depends on the choice of the retained dominant DOFs or substructural modes. In this work, we develop a new mode selection method for CMS methods. In contrast to the frequency cut-off mode selection method, in which substructural modes in sequence from the lowest substructural frequency to a cut-off frequency are retained, the proposed method selects the dominant substructural modes i...