  Topology optimization using gradient search with negative and positive
elliptical masks and honeycomb tessellation is presented. Through a novel
skeletonization algorithm for topologies defined using filled and void
hexagonal cells/elements, explicit minimum and maximum length scales are
imposed on solid states in the solutions. An analytical example is presented
which suggests that for a skeletonized topology, optimal solutions may not
always exist for any specified volume fraction, minimum and maximum length
scales, and that there may exist implicit interdependence between them. A
Sequence for Length Scale (SLS) methodology is proposed wherein solutions are
sought by specifying only the minimum and maximum length scales with volume
fraction getting determined systematically. Through four benchmark problems in
small deformation topology optimization, it is demonstrated that solutions
by-and-large satisfy the length scale constraints though the latter may get
violated at certain local sites. The proposed approach seems promising, noting
especially that solutions, if rendered perfectly {\it black and white} with
minimum length scale explicitly imposed and boundaries smoothened, are quite
close in performance compared to the parent topologies. Attaining {\it volume
distributed} topologies, wherein members are more or less of the same
thickness, may also be possible with the proposed approach.
