  In this paper we present a mixed projection- and density-based topology
optimization approach. The aim is to combine the benefits of both
parametrizations: the explicit geometric representation provides specific
controls on certain design regions while the implicit density representation
provides the ultimate design freedom elsewhere. This approach is particularly
suited for structural assemblies, where the optimization of the structural
topology is coupled with the optimization of the shape of the interface between
the sub-components in a unified formulation. The interface between the
assemblies is defined by a segmented profile made of linear geometric entities.
The geometric coordinates of the nodes connecting the profile segments are used
as shape variables in the problem, together with density variables as in
conventional topology optimization. The variable profile is used to locally
impose specific geometric constraints or to project particular material
properties. Examples of the properties considered herein are a local volume
constraint, a local maximum length scale control, a variable Young's modulus
for the distributed solid material, and spatially variable minimum and maximum
length scale. The resulting optimization approach is general and various
geometric entities can be used. The potential for complex design manipulations
is demonstrated through several numerical examples.
