Sophia Michelle Boyce

Topology optimization is increasingly important for additive manufacturing because it enables lightweight structures with complex load paths, while process-induced variability can produce spatial heterogeneity in fatigue resistance. This study develops a distributionally robust fatigue-constrained topology optimization framework that distinguishes two sources of uncertainty: spatial variability in local fatigue strength and ambiguity in the probabilities assigned to sampled uncertainty realizations. Spatial variability is represented by a correlated fatigue-strength random field, while probability-model ambiguity is treated using a discrete Kullback–Leibler ambiguity set. The framework is evaluated using an Al 6061-T6 cantilever benchmark and transfer studies involving Ti-6Al-4V, an L-bracket geometry, and a three-dimensional benchmark. In the principal Al case, KL-DRO reduces independent out-of-sample fatigue exceedance from 17.56% to 12.88% and lowers the 95th-percentile fatigue measure from 1.999 to 1.685, with an approximately 2.2% increase in material relative to mean-risk optimization. Similar reductions are observed for the L-bracket and three-dimensional benchmarks, whereas Ti-6Al-4V and matched material studies show little or no advantage. The results therefore indicate that KL-DRO can improve out-of-sample fatigue-tail performance when fatigue risk is active and the empirical uncertainty support is sufficiently informative, but it does not universally outperform mean-risk optimization. The proposed framework provides a computational basis for incorporating spatially resolved fatigue-property uncertainty into topology optimization for additively manufactured structures.