Optimal topological design of periodic structures for natural frequencies

This paper proposes a method for topology optimization of periodic structures on dynamic problems by using an improved bidirectional evolutionary structural optimization (BESO) technique. Frequency optimization and frequency-stiffness optimization are formulated for periodic continuum structures at the macroscopic level under arbitrary loadings and boundaries. Numerical instabilities that occur in common topological frequency optimization are dealt with by eliminating singular and single-hinged elements and removing alternative element groups in case of sudden drops of the relevant frequency. Layout periodicity of the optimal design is guaranteed by creating a representative unit cell (RUC) on the basis of a user-defined cell mode and averaging the sensitivities from all unit cells into the RUC. The capability and effectiveness of the proposed approach are demonstrated by numerical experiments with various cell modes.