Abstract
The primary driver for technological advancement in design methods is increasing part performance and reducing manufacturing cost. Design optimization tools, such as topology optimization, provide a mathematical approach to generate efficient and lightweight designs; however, integration of this design tool into industry has been hindered most notably by manufacturability. Innovative processes, such as additive manufacturing (AM), have significantly more design freedom than traditional manufacturing methods, providing a means to develop the complex designs produced by topology optimization. The layer-wise nature of AM leads to new design challenges such as the need for support material, influenced by part topology and build orientation. Previous works addressing approaches to limit support material often rely on the finite element discretization scheme, leading to a gap between solving academic and practical problems. This study presents an approach to simultaneously optimize part topology and build orientation with AM considerations. Utilizing the spatial density gradient in the topology optimization formulation, the dependence on the finite element discretization scheme is reduced. The proposed approach has the potential to significantly decrease support material, while having a minimal impact on structural performance. Both 2D and 3D academic test problems, as well as an aerospace industry example, demonstrate the proposed methodology is capable of generating high-quality designs.
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Replication of results
A pseudo code is provided in Appendix 3 to assist with the replication of the results presented in this paper. The pseudo code has been generalized for 2D and 3D.
Funding
This research was funded by the Natural Sciences and Engineering Research Council of Canada (NSERC).
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Appendices
Appendix 1. Sharpening effect
A sharpening step is completed to post-process each design to obtain discrete element values. This is completed using a bisection algorithm to ensure that the volume fraction constraint is satisfied. Figure 29 shows the effect of sharpening using the optimization 1 geometry of the 3D cantilever beam.
Sharpening effect: a 3D design showing cross-section location, b raw results for the cross-sectional slice, c sharpened results for the cross-sectional slice
Appendix 2. Convergence history
Figure 30 shows the convergence history for the proposed approach (optimization 4) for the 3D cantilever beam initialized at θx = 60; θz = 60. For the combined objective function, compliance, and build orientation design variables, the convergence is smooth and well suited for gradient-based optimization; however, the support material convergence history has unsmooth characteristics, due to the nature of how it is calculated. For example, when the build direction changes, entire support material columns can be added or subtracted to the total value.
3D cantilever beam convergence history. Optimization 4 initialized at θx = 60; θz = 60
Appendix 3. Pseudo code
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Olsen, J., Kim, I.Y. Design for additive manufacturing: 3D simultaneous topology and build orientation optimization. Struct Multidisc Optim 62, 1989–2009 (2020). https://doi.org/10.1007/s00158-020-02590-8
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DOI: https://doi.org/10.1007/s00158-020-02590-8