THE MULTI-LEVEL SUBSTRUCTURING METHOD BASED ON PROPER ORTHOGONAL DECOMPOSITION

This paper proposes a novel multi-level substructuring method based on proper orthogonal decomposition (POD) to address the high computational cost associated with the dynamic analysis of large-scale structures. The method introduces a two-level independent POD reduction scheme, building upon the framework of traditional static condensation, which reduces internal degrees of freedom to boundary master degrees of freedom. The first level of reduction involves constructing a reduced-order basis by combining low-order vibration modes and POD-generated high-order approximation modes. This composite basis is employed to approximate the numerical basis functions (e.g., constraint modes) within the static condensation process and to capture the essential characteristics of the reduced internal dynamic behavior, thereby significantly decreasing storage requirements. The second level, which is crucial for enabling the efficient assembly of multiple substructures, applies singular value decomposition (SVD) to the reduced boundary modes obtained from all individual substructures. This critical step generates a common set of orthogonal interface bases, ensuring that the boundary deformations of all substructures can be consistently represented within the same linear space. This universal representation greatly simplifies the substructure assembly process and substantially increases the overall computational speed. Furthermore, the paper elaborates on specific strategies for the reduced-order treatment of complex topological boundaries and discusses methods to eliminate the adverse impact of zero eigenvalues associated with rigid body modes on computational stability. A rigorous quantitative analysis of the algorithm's complexity demonstrates its superiority over traditional substructuring methods in terms of both time and space complexity. Finally, the effectiveness and reliability of the proposed method are confirmed through numerical examples. The results indicate that the computational accuracy and efficiency improve steadily as the number of orthogonal bases increases, demonstrating good numerical precision, convergence behavior, and computational reliability. The method presents a robust and efficient framework for the model order reduction of complex structural systems.