Multi-objective and Multi-load-Conditions Topology Optimization Model for Designing Metamaterial Vibration Isolator with Customized Stiffness

Metamaterial vibration isolation, as a promising technology for reducing and controlling vibration, can achieve mechanical properties that natural materials do not have through the microstructural design of uniformly and periodically distributed unit cells of the metamaterial isolator. However, cell patterns of existing metamaterial isolators are relatively fixed, which leads to the limited design range of three-direction stiffnesses of the isolator. Under some harsh working conditions, the internal strain will be too large for the common unit cell structure. This work develops a topology optimization model based on SIMP (solid isotropic material with penalization) method for designing metamaterial vibration isolator with customized three-direction stiffnesses. It uses the three-direction stiffnesses and strain energies as the optimization objectives. And different direction stiffnesses are calculated under different loading conditions. To simplify the design process, one unit cell with periodic boundaries and equivalent loads is optimized. The overall three-dimensional structure of the vibration isolator is eventually periodically modelled from the optimized cell structure, and its stiffnesses are compared to the customized values to verify the effectiveness of the optimization model. The load–displacement curves of the overall isolator show that the obtained stiffnesses meet well with the target stiffnesses, and the maximum deviation is only 0.12%.