Study on the model reduction for flexible structure based on clustering algorithm and DOFs concentration

A model reduction method by which the concentration of dynamical similar DOFs is auto-conducted with k-means clustering algorithm is proposed. Considering the space distribution of the dynamic loads, the method to select important modes of original model based on modal participation factor is proposed, and the omission of DOFs in the secondary directions is discussed. According to the similarity of the mode shape values in important modes the DOFs are auto-clustered using clustering algorithm. Starting from the definition of the entries in flexibility matrix, the flexible reduction common formula is induced with the explicit original model, and the positive definiteness, symmetry and orthogonality relationship of the reduced matrices are proved. At last, an example reducing a 40-storey concrete frame containing 240 DOFs to a model containing 8 DOFs shows the efficiency of the reduction method and the reasonability of the assessment indices.