An improved bi-directional evolutionary topology optimization method for frequencies

This paper presents a topology optimization method for dynamic problems with an improved bidirectional 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.