On the finite element model reduction methods in structural dynamics = 유한요소 구조동역학 모델의 축소기법 개발

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 in accordance with the contribution of the substructural modes to the target global modes. Therefore, the new mode selection method enables the analyst to select substructural modes that can better represent the target global modes in the resulting reduced model. We then validate its performance and feasibility for both stiffnessand flexibility-based CMS (F-CMS) methods using a variety of numerical examples. We also provide a simple strategy to detect inaccurately approximated global modes in the reduced model, the correction of which leads to improved reduced models. A major obstacle of model reduction methods has been the absence of a good methodology for estimating the reliability of reduced models. To resolve this issue, we develop a robust error estimator to accurately predict the relative eigenvalue errors. Derivation procedures show that the proposed error estimator is a direct approximation of the relative eigenvalue error. Therefore, using this new error estimator, the reliability of reduced models can be efficiently and precisely evaluated. In this work, we develop new error estimators for Guyan reduction, the CB method, and the F-CMS method. Here, we also propose a high-fidelity formulation for interface reduction in the F-CMS method. Using the new formulation, we can construct more compact reduced models without significant loss of accuracy. Eigenvector relations between the global and reduced models are clearly defined in the interface reduction level. The performance of the present formulation is validated using numerical examples.