Designing Variable Thickness Sheets for Additive Manufacturing Using Topology Optimization with Grey-Scale Densities

Topology optimization is a powerful tool to automatically generate optimal geometries for Additive Manufacturing (AM). However, to ensure manufacturability, e.g. by material extrusion-based AM (MEX) or Laser-Beam Powder-Bed-Fusion of Metals (PBF-LB/M), a minimum structure thickness has often to be maintained. In this paper, a simple interpolation scheme for penalizing grey-scale densities in topology optimization is applied. It locally reduces the stiffness-to-weight ratio of elements in the variable thickness sheet problem for densities between zero and a critical density. A cantilever beam is optimized, confirming that less penalization produces stiffer structures. Results for the optimization of an L-shaped bell crank are 12% stiffer (and only 4% less stiff) than the design based on conventional (and no) penalization. Simulating and printing the hinge using MEX and PBF-LB/M confirm enhanced manufacturability. In regions of load concentrations, where stresses vary significantly, the results show a general potential for performance improvement, when switching from conventional designs (e.g. sheet metals) to more complex designs that would require advanced manufacturing methods, such as AM.