  A level set topology optimization approach that uses an auxiliary density
field to nucleate holes during the optimization process and achieves minimum
feature size control in optimized designs is explored. The level set field
determines the solid-void interface, and the density field describes the
distribution of a fictitious porous material using the solid isotropic material
with penalization. These fields are governed by two sets of independent
optimization variables which are initially coupled using a penalty for hole
nucleation. The strength of the density field penalization and projection are
gradually increased through the optimization process to promote a 0-1 density
distribution. This treatment of the density field combined with a second
penalty that regulates the evolution of the density field in the void phase,
mitigate the appearance of small design features. The minimum feature size of
optimized designs is controlled by the radius of the linear filter applied to
the density optimization variables. The structural response is predicted by the
extended finite element method, the sensitivities by the adjoint method, and
the optimization variables are updated by a gradient-based optimization
algorithm. Numerical examples investigate the robustness of this approach with
respect to algorithmic parameters and mesh refinement. The results show the
applicability of the combined density level set topology optimization approach
for both optimal hole nucleation and for minimum feature size control in 2D and
3D. This comes, however, at the cost of a more advanced problem formulation and
additional computational cost due to an increased number of optimization
variables.

Optimization and Control