An Eigenfrequency-Constrained Topology Optimization Method with Design Variable Reduction

Abstract

The dynamic response of structures heavily relies on eigenfrequency, so the optimization of eigenfrequency is valuable in various working conditions. The bi-directional evolutionary structural optimization (BESO) method has been widely applied due to its ability to eliminate grayscale elements. Based upon BESO, this paper introduces a topology optimization method that incorporates eigenfrequency constraints and reduces the number of design variables. In this method, the optimization objective was to minimize compliance. The Lagrange multiplier was used to introduce eigenfrequency constraints, allowing for coordinated control of compliance and eigenfrequency. To prevent oscillation during the optimization process, the sensitivity was normalized. Additionally, to achieve faster convergence, the variables were reduced after meeting volume constraints. The numerical examples demonstrate the effectiveness of this method in increasing the eigenfrequency of the structure and avoiding resonance.