  Two approaches that use a density field for seeding holes in level set
topology optimization are proposed. In these approaches, the level set field
describes the material-void interface while the density field describes the
material distribution within the material phase. Both fields are optimized
simultaneously by coupling them through either a single abstract design
variable field or a penalty term introduced into the objective function. These
approaches eliminate drawbacks of level set topology optimization methods that
rely on seeding the initial design domain with a large number of holes.
Instead, the proposed approaches insert holes during the optimization process
where beneficial. The dependency of the optimization results on the initial
hole pattern is reduced, and the computational costs are lowered by keeping the
number of elements intersected by the material interface at a minimum. In
comparison to level set methods that use topological derivatives to seed small
holes at distinct steps in the optimization process, the proposed approaches
introduce holes continuously during the optimization process, with the hole
size and shape being optimized for the particular design problem. The proposed
approaches are studied using the extended finite element method for spatial
discretization, and the solid isotropic material with penalization for material
interpolation using fictitious densities. Their robustness with respect to
algorithmic parameters, dependency on the density penalization, and performance
are examined through 2D and 3D benchmark linear elastic numerical examples, and
a geometrically complex mass minimization with stress constraint design
problem.
