Recent Advances in Space-Time Topology Optimization for Multi-Axis Additive Manufacturing
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Space-time topology optimization is gaining significant interest in computational design for additive manufacturing as a rigorous method to bridge the gap between structural design and fabrication sequence planning. Traditionally, these two stages are performed sequentially, leading to optimized structures that cannot be manufactured or that suffer from a serious compromise in quality due to the neglect of critical process-dependent effects, such as thermomechanical distortions and residual stresses. To address this, we proposed a unified mathematical framework in which the fabrication sequence is optimized concurrently with the structural layout~\cite{wang2020space}. This is achieved by introducing a pseudo-time field to encode the deposition sequence in tandem with a pseudo-density field that defines the structural layout. The isocontours of this pseudo-time field segment the structure into a series of intermediate states, allowing for the explicit analysis and optimization of process-dependent loads. Since the conceptualization of this framework, we have refined and extended the formulation to address the specific challenges in Wire Arc Additive Manufacturing. In this talk, we discuss recent progress in improving the manufacturability of the simultaneously optimized structure and fabrication sequence. These developments include: \begin{itemize} \item PDE-based Sequence Reformulation: A transition to a partial differential equation (PDE) governing the pseudo-time field. This ensures a strictly monotonic fabrication sequence and effectively eliminates local minima in the pseudo-time field that violate the fabrication principles~\cite{wang2024se}. \item Geometric Constraints for Curved Layers: The introduction of thickness and curvature regularizations designed to maintain consistent bead morphology. These constraints ensure that the resulting non-planar toolpaths remain within the physical process window of the hardware~\cite{Wu2026}. \item Multi-Planar Printing Strategies: A reduced formulation that generates optimized multi-planar sequences. This approach balances structural performance with hardware complexity, thereby facilitating implementation on standard industrial robotic cells~\cite{mishra2026differentiable}. \end{itemize} These developments demonstrate an advancement from theoretical space-time frameworks toward robust, machine-ready strategies for complex multi-axis additiv
