Robust topology optimization accounting for uncertain micro-structural changes in metallic additive manufacturing

Abstract Additive Manufacturing (AM) can introduce defects in the material or variations in its properties, which can alter the mechanical performance of 3D-printed parts and lead to discrepancies between predicted and observed behavior. To mitigate this effect, it is essential to incorporate these variabilities into the design process to ensure optimal structural performance. Topology Optimization (TO) methods determine the optimal distribution of material within a design domain and often result in complex parts. AM is particularly relevant for manufacturing such parts. To reach robust designs, it is essential to consider material variability arising from AM in TO. Rather than relying on computationally expensive simulations to characterize these material variations, this study presents a new, practical, simplified, parametrized stochastic model that accounts for these variations in the AM process. This stochastic modeling directly optimizes performance in terms of average and variability. The work specifically focuses on variations in material properties along the build direction. More specifically, it addresses the transition from columnar grains (which have anisotropic properties) to equiaxed grains (which have isotropic properties) in metallic AM. This transforms the topology optimization problem into a robust topology optimization problem, yielding an optimal shape that reduces variability related to the AM process. TO is performed using the SIMP method. Gaussian quadrature is employed to reduce the computational cost of the statistical moments of the objective function. The influence of individual and combined transition stochastic model parameters is analyzed. The results demonstrate that the robust geometry systematically outperforms the deterministic ones, showing the effectiveness of the method in reducing performance variability. More specifically, for similar average properties, variability is substantially reduced. These findings support the integration of robust design strategies with AM.