Topology optimization for minimum dynamic compliance using an antiresonant frequency constraint

As studied in previous works, dynamic compliance presents widespread antiresonances in its spectrum, which could trap gradient-based topology optimization for minimum dynamic compliance and cause the optimization procedure to converge prematurely. In order to solve this problem, a novel method for predicting the frequencies that correspond to points of antiresonance in dynamic compliance spectrum is presented in this paper. By leveraging this eigenvalue formulation method, a strategy for introducing antiresonant frequency constraint is developed to solve one-material topology design for minimum dynamic compliance under high-frequency (above the first resonance of the initial design) excitations. In order to facilitate the exploitation of antiresonances, accurate track and eigenvalue sensitivity analysis for the prescribed antiresonant frequency are also discussed in detail. Numerical results show that the proposed method can achieve well-defined topologies with excellent dynamic performance.