  With the goal of identifying optimal elastic single-scale microstructures for
multiple loading situations, the paper shows that qualified starting guesses,
based on knowledge of optimal rank-3 laminates, significantly improves chances
of convergence to near optimal designs. Rank-3 laminates, optimal for a given
set of anisotropic loading conditions, are approximated on a single scale using
a simple mapping approach. We demonstrate that these mapped microstructures
perform relatively close to theoretical energy bounds. Microstructures with
performance even closer to the bounds can be obtained by using the approximated
rank-3 structures in a further step as starting guesses for inverse
homogenization problems. Due to the non-convex nature of inverse homogenization
problems, the starting guesses based on rank-3 laminates outperform classical
starting guesses with homogeneous or random material distributions.
Furthermore, the obtained single-scale microstructures are relatively simple,
which enhances manufacturability. Results, obtained for a wide range of loading
cases, indicate that microstructures with performance within 5-8% of the
theoretical optima can be guarantied, as long as feature sizes are not limited
by minimium size constraints.
