Efficient topology optimization of multicomponent structure using substructuring-based model order reduction method

Abstract

This study develops a novel model reduction (MR) scheme called the multi-substructure multi-frequency quasi-static Ritz vector (MMQSRV) method to compute dynamic responses and sensitivity values with adequate efficiency and accuracy for topology optimization (TO) of dynamic systems with multiple substructures. The calculation of structural responses of dynamic excitation using the framework of the finite element (FE) procedure usually requires a significant amount of computation time. The ever-increasingly complex phenomena of FE models with many degrees of freedom make it difficult to calculate FE responses in the time or frequency domain. To overcome this difficulty, model reduction schemes can be utilized to reduce the size of the dynamic stiffness matrix. This paper presents a new model order reduction method called MMQSRV, based on the quasi-static Ritz vector method, with Krylov subspaces spanned at multiple angular velocities for efficient TO. Through several analysis and design examples, we validate the efficiency and reliability of the model reduction schemes for TO.