Maximization of the fundamental eigenfrequency of micropolar solids through topology optimization

Aim of this work is the maximization of the fundamental eigenfrequency of 2D bodies made of micropolar (or Cosserat) materials using a topology optimization approach. A classical SIMP–like model is used to approximate the constitutive parameters of the micropolar medium. A suitable penalization is introduced for both the linear and the spin inertia of the material, to avoid the occurrence of undesired local modes. The robustness of the proposed procedure is investigated through numerical examples; the influence of the material parameters on the optimal material layouts is also discussed. The optimal layouts for Cosserat solids may differ significantly from the truss–like solutions typical of Cauchy solids, as the intrinsic flexural stiffness of the material can lead to curved beam-like material distributions. The numerical simulations show that the results are quite sensitive to the material characteristic length and the spin inertia.