Structural topology optimization for frequency response problem using model reduction schemes

Abstract

This study uses model reduction (MR) schemes such as the mode superposition (MS), Ritz vector (RV), and quasi-static Ritz vector (QSRV) methods, which reduce the size of the dynamic stiffness matrix of dynamic structures, to calculate dynamic responses and sensitivity values with adequate efficiency and accuracy for topology optimization in the frequency domain. The calculation of structural responses to dynamic excitation using the framework of the finite element (FE) procedure usually requires a significant amount of computation time; that is mainly attributable to repeated inversions of dynamic stiffness matrices depending on time or frequency intervals, which hastens the dissemination of the MR schemes in the analysis. However, using well-established MR schemes in topology optimization has not been prevalent. Therefore, this study conducted a comprehensive investigation to highlight the drawbacks and advantages of these MR schemes for topology optimization. In the results, the MS method, which generates reduction bases by considering some of the lowest eigenmodes, can lose the accuracy in both approximated structural responses and sensitivity values due to locally vibrating eigenmodes and higher mode truncation in the solid isotropic material with penalization (SIMP) approach. In addition, the RV and QSRV methods, which generate reduction bases by considering the external force, mass, and stiffness matrices of a structure, can be used as alterative model reduction schemes for stable optimization. Through several analysis and design examples, the efficiency and reliability of the model reduction schemes for topology optimization are compared and validated.