Space-time topology optimization for additive manufacturing

The design of optimal structures and the planning of (additive manufacturing) fabrication sequences have been considered typically as two separate tasks that are performed consecutively. In the light of recent advances in robot-assisted (wire-arc) additive manufacturing which enable addition of material along curved surfaces, we present a novel topology optimization formulation which concurrently optimizes the structure and the fabrication sequence. For this, two sets of design variables, i.e., a density field for defining the structural layout, and a time field which determines the fabrication process order, are simultaneously optimized. These two fields allow to generate a sequence of intermediate structures, upon which manufacturing constraints (e.g., fabrication continuity and speed) are imposed. The proposed space-time formulation is general, and is demonstrated on three fabrication settings, considering self-weight of the intermediate structures, process-dependent critical loads, and time-dependent material properties.