Comparing optimal material microstructures with optimal periodic structures

Topology optimisation of manufacturable microstructural details without length scale separation using a spectral coarse basis preconditioner

“…This trend was also observed in [16] for the same problem, although the optimised designs differ. This difference in topology is likely due to a difference in the effective length scale of the current approach and that of [16]; the former using density filtering combined with a projection at η = 0.5 and the latter using BESO.…”

“…It is observed that the microstructure converges very fast and the overall topology does not qualitatively change for M x > 4, therefore only a select few have been shown out of the investigated set, M x ∈ {2, 4, 6, 8, 12, 16, 32, 64}. This trend was also observed in [16] for the same problem, although the optimised designs differ. This difference in topology is likely due to a difference in the effective length scale of the current approach and that of [16]; the former using density filtering combined with a projection at η = 0.5 and the latter using BESO.…”

“…For the optimised structures shown in figure 10, it is observed that the compliance increases as the number of unit cells is increased. This is attributed to the increased restriction of the design freedom imposed through the increased periodicity and is also observed in [16]. It is also seen that the MsFEM-GMRES approach gives qualitatively the same topologies as when using a direct solver, however, slight deviations are observed in the compliance values.…”

“…Comparing the microstructures in figure 15 to those presented in [16], an important difference is the vertical bar at the right-hand side of the unit cell. This vertical bar is needed for the unit cells in contact with the distributed load and due to the imposed periodicity it exist in all unit cells within the beam, as seen in figures 15f and 15g.…”

“…This paper restricts itself to a single-scale optimisation approach, where the periodic microstructural details filling a given domain are optimised for the macroscale response. The complete macroscopic structure and its response is considered, while resolving all microstructural details as compared to the homogenisation approach common to all of the above papers, except [15,16]. The approach takes boundary conditions into account and ensures connected and macroscopically optimised microstructures regardless of the difference in micro-and macroscopic length scales.…”