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.

We study linearity assumptions in the transient macroscale mechanical aspect of additive manufacturing (AM) process simulation. Linearity assumptions are often resorted to in combination with calibrated inelastic deformation components to arrive at computationally tractable yet reasonably accurate AM process models. We point out that linearity assumptions permit the independent computation of the response increment in each step of the AM process, and the total mechanical response is the superposition of all the process-step increments. In effect, process-step increments are computed with respect to the stress-free reference configuration in each step. The implication is that the mechanical response increment in each linearised AM process step may be computed in parallel. Trivial process-step-wise parallel computability breaks down, however, if nonlinearity (i.e. geometric or material) is modelled. In our investigation the influence of geometric nonlinearity on part distortion is small (but this is of course part-geometry specific), and more realistic stresses are obtained by imposing a nonlinear elastoplastic material law after the parallel computation and superposition of the linear AM response increments. It is demonstrated that simulation wall-clock time is reduced by exploiting process-step parallel computability in the linear regime. Moreover, numerical experiments suggest that process-step parallelization scales better (in wall-clock time) than conventional parallelization in the sequential computation of each response increment.