Topology Optimization for Multi-Axis Additive Manufacturing Considering Overhang and Anisotropy

TL;DR

This paper introduces a space-time topology optimization framework for multi-axis additive manufacturing that jointly optimizes material density, fabrication sequence, and build orientation to address overhang and anisotropy. By parameterizing intermediate structures with a pseudo-time field and using stage-wise deposition, Sobel-gradient-based overhang constraints, and an orthotropic material model aligned to build directions, the method yields manufacturable, high-performance designs. Numerical results on isotropic and anisotropic L-shaped beams and a cantilever with a cutout show that increasing the number of stages improves compliance toward unconstrained levels while maintaining overhang feasibility, and that stage-specific volume control further enhances performance. The framework demonstrates practical potential for integrating manufacturability and anisotropy into topology optimization for multi-axis AM, with opportunities to extend to 3D and more explicit collision handling in future work.

Abstract

Topology optimization produces designs with intricate geometries and complex topologies that require advanced manufacturing techniques such as additive manufacturing (AM). However, insufficient consideration of manufacturability during the optimization process often results in design modifications that compromise the optimality of the design. While multi-axis AM enhances manufacturability by enabling flexible material deposition in multiple orientations, challenges remain in addressing overhang structures, potential collisions, and material anisotropy caused by varying build orientations. To overcome these limitations, this study proposes a novel space-time topology optimization framework for multi-axis AM. The framework employs a pseudo-time field as a design variable to represent the fabrication sequence, simultaneously optimizing the density distribution and build orientations. This approach ensures that the overhang angles remain within manufacturable limits while also mitigating collisions. Moreover, by incorporating material anisotropy induced by diverse build orientations into the design process, the framework can take the scan path-dependent structural behaviors into account during the design optimization. Numerical examples demonstrate that the proposed framework effectively derives feasible and optimal designs that account for the manufacturing characteristics of multi-axis AM.

Figures (21)

• Figure 1: Design approaches for AM: (a) design with supports, where $\bar{\alpha}$ represents the overhang angle threshold and the red arrows $\bm{b}$ denote the build orientation, (b) designs considering overhang angles and build orientations, (c) designs for multi-axis AM with divided build orientations and paths, and (d) proposed space-time topology optimization for multi-axis AM, where red arrows indicate the build orientation and the blue lines represent the material orientation.
• Figure 2: The concept of space-time topology optimization for multi-axis AM. Each building stage has a different platform orientation, affecting the material's principal axis and overhang behavior. The red arrows denote the build orientation, while the blue lines indicate the material orientation at each stage.
• Figure 3: Calculated density gradients using the Sobel operator. The figure shows gradients with fixed magnitudes and the corresponding element-wise numbering for the highlighted region.
• Figure 4: (a) Build and material orientations in multi-axis AM, (b) Heaviside function defined over the time field for $N=5$, and (c) Young's modulus and shear modulus with respect to orientation angle for isotropic and anisotropic materials.
• Figure 5: Overhang angle constraint in multi-axis AM: (a) density distribution for the entire domain, (b) time field, (c) overhang angle constraint values for the entire domain, (d) density distribution at the stage $j$, (e) density difference between consecutive stages, and (f) overhang angle constraint values for the stage $j$, where the red lines in each element indicate the density boundaries.