  Additive manufacturing of metal parts involves phase transformations and high
temperature gradients which lead to uneven thermal expansion and contraction,
and, consequently, distortion of the fabricated components. The distortion has
a great influence on the structural performance and dimensional accuracy, e.g.,
for assembly. It is therefore of critical importance to model, predict and,
ultimately, reduce distortion. In this paper, we present a computational
framework for fabrication sequence optimization to minimize distortion in
multi-axis additive manufacturing (e.g., robotic wire arc additive
manufacturing), in which the fabrication sequence is not limited to planar
layers only. We encode the fabrication sequence by a continuous pseudo-time
field, and optimize it using gradient-based numerical optimization. To
demonstrate this framework, we adopt a computationally tractable yet reasonably
accurate model to mimic the material shrinkage in metal additive manufacturing
and thus to predict the distortion of the fabricated components. Numerical
studies show that optimized curved layers can reduce distortion by orders of
magnitude as compared to their planar counterparts.
