Overhang angle and boundary oscillation control in topology optimization for multi-axis additive manufacturing through perturbation field-based non-planar slicing

Multi-axis additive manufacturing (AM) overcomes traditional limitations through non-planar slicing and local build direction control, enabling the fabrication of complex, support-free geometries. To fully exploit these capabilities, integrating features of multi-axis AM into the design phase is essential for exploring a broader design space and achieving high-performance designs. Existing methods for non-planar slicing often rely on solving auxiliary partial differential equations (PDEs) to define the fabrication sequence. This work proposes a simpler parameterization method, where the slicing field combines a Euclidean distance field (to maintain sequence) with a perturbation field (to adjust local layer profiles). The perturbation field is optimized concurrently with the density field to achieve self-supporting designs. Leveraging the spatial gradients of these fields, a global constraint is formulated to enforce local overhang angle control. To further address the boundary oscillations inherent to spatial-gradient-based formulations, an additional global constraint is introduced, which acts by regulating the local volume fraction along overhang boundaries. The efficacy of the proposed non-planar slicing and overhang control methods is validated through both 2D and 3D numerical examples in linear elasticity and heat conduction problems.