A heuristic approach to design lightweight metamaterials with novel configurations and arbitrary Poisson’s ratio is studied by using the functional element topology optimization (FETO) method. Mathematical model of the optimization problem is established, where the minimization of the mass is set as the objective, then a series of metamaterials with Poisson’s ratio ranging from −1.0 to +1.0 are designed by solving this model. The deformation resistance and vibration reduction performance of the novel metamaterials and conventional honeycomb are compared by numerical simulations. Specific stiffness analysis shows that the novel metamaterials are 5.6 to 21.0 times more resistant to deformation than that of the honeycomb, and frequency response shows about 60% improvement in vibration reduction performance. Finally, the lightweight effects of the novel metamaterials on deformation resistance and vibration reduction performance are analyzed, and further analysis reflects that the lightweight effects increase with the increase of the absolute value of the Poisson’s ratio.
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