  This paper focuses on density-based topology optimization and proposes a
combined method to simultaneously impose Minimum length scale in the Solid
phase (MinSolid), Minimum length scale in the Void phase (MinVoid) and Maximum
length scale in the Solid phase (MaxSolid). MinSolid and MinVoid mean that the
size of solid parts and cavities must be greater than the size of a prescribed
circle or sphere. This is ensured through the robust design approach based on
eroded, intermediate and dilated designs. MaxSolid seeks to restrict the
formation of solid parts larger than a prescribed size, which is imposed
through local volume restrictions. In the first part of this article, we show
that by proportionally restricting the maximum size of the eroded, intermediate
and dilated designs, it is possible to obtain optimized designs satisfying,
simultaneously, MinSolid, MinVoid and MaxSolid. However, in spite of obtaining
designs with crisp boundaries, some results can be difficult to manufacture due
to the presence of multiple rounded cavities, which are introduced by the
maximum size restriction with the sole purpose of avoiding thick solid members
in the structure. To address this issue, in the second part of this article we
propose a new geometric constraint that seeks to control the minimum separation
distance between two solid members, also called the Minimum Gap (MinGap).
Differently from MinVoid, MinGap introduces large void areas that do not
necessarily have to be round. 2D and 3D test cases show that simultaneous
control of MinSolid, MinVoid, MaxSolid and MinGap can be useful to improve the
manufacturability of maximum size constrained designs.
