One-shot procedures for efficient minimum compliance topology optimization

In this paper, a one-shot approach for minimum compliance topology optimization is investigated. In the convex case of variable thickness sheet optimization, an optimality criteria scheme with a single step of an iterative state solver converges to the same solutions as an accurate procedure. This remarkable behavior is explained by the crucial role of the geometric multigrid preconditioner that generates accurate design sensitivities on a coarse scale. When applied to SIMP-based topology optimization, a one-shot procedure yields designs with the same primary load-transferring features as an accurate procedure. The difference is in the absence and presence of thin features that have a relatively minor impact on the objective. Several practical remedies are suggested that can close the small performance gaps between the one-shot procedure and an accurate one. The solution scheme is directly applicable to large-scale problems executed on parallel computers, allowing for significant computational savings.