An Improved Bi-directional Evolutionary Topology Optimization Method for Frequencies

This paper presents a topology optimization method for dynamic problems with an improved bi-directional evolutionary structural optimization (BESO) technique. The sensitivity derivation for the frequency optimization problem in the case of multiple eigenvalues and for the stiffness–frequency optimization problem is proposed. Algorithms for a filter scheme, sensitivity history-averaging, and sensitivity global-ranking are used in the present method. Techniques for adaptively removing alternative elements and eliminating singular and single-hinged elements are proposed. Solution-convergence and localized modes are discussed through numerical examples. Results show that the improved BESO method is capable of solving the frequency optimization problem and the multi-objective optimization problem for stiffness and frequency effectively.