ABSTRACT
Topology optimization and additive manufacturing together enable the optimal design and direct fabrication of complex geometric parts with groundbreaking performance for diverse applications. However constraining the optimization to ensure that the generated object can be reliably manufactured via layer-by-layer 3D printing processes is challenging. The typical solution is to enforce design rules based only on geometric heuristics like overhang angles, minimum wall widths, and maximum bridge spans. Recent work has proposed instead to simulate the robustness of each partial object generated from bottom-to-top during the fabrication process as a more accurate, physics-aware printability assessment. However, this approach comes at the cost of an vast increase in the number of simulations run per design iteration, making existing implementations intractable at high resolution. We demonstrate that by developing a custom solver leveraging the close relationships between these many simulations, even voxel-level layer-by-layer simulations are feasible to incorporate into high-resolution 2D and 3D topology optimization problems on a single workstation.
- Grégoire Allaire, Charles Dapogny, Alexis Faure, and Georgios Michailidis. 2017. Shape optimization of a layer by layer mechanical constraint for additive manufacturing. Comptes Rendus Mathematique 355, 6 (2017), 699–717. https://doi.org/10.1016/j.crma.2017.04.008Google ScholarCross Ref
- Grégoire Allaire, Franccois Jouve, and Georgios Michailidis. 2016. Thickness control in structural optimization via a level set method. Structural and Multidisciplinary Optimization 53, 6(2016), 1349–1382.Google ScholarDigital Library
- Grégoire Allaire, François Jouve, and Anca-Maria Toader. 2004. Structural optimization using sensitivity analysis and a level-set method. J. Comput. Phys. 194, 1 (2004), 363–393. https://doi.org/10.1016/j.jcp.2003.09.032Google ScholarDigital Library
- Oded Amir, Niels Aage, and Boyan S Lazarov. 2014. On multigrid-CG for efficient topology optimization. Structural and Multidisciplinary Optimization 49, 5(2014), 815–829.Google ScholarDigital Library
- Oded Amir and Yoram Mass. 2018. Topology optimization for staged construction. Structural and Multidisciplinary Optimization 57, 4(2018), 1679–1694.Google ScholarDigital Library
- Jernej Barbič and Doug L James. 2005. Real-time subspace integration for St. Venant-Kirchhoff deformable models. ACM transactions on graphics (TOG) 24, 3 (2005), 982–990.Google Scholar
- Mohamad Bayat, Wen Dong, Jesper Thorborg, Albert C. To, and Jesper H. Hattel. 2021. A review of multi-scale and multi-physics simulations of metal additive manufacturing processes with focus on modeling strategies. Additive Manufacturing 47 (2021), 102278. https://doi.org/10.1016/j.addma.2021.102278Google ScholarCross Ref
- Martin Philip Bendsoe and Ole Sigmund. 2003. Topology optimization: theory, methods, and applications. Springer Science & Business Media.Google Scholar
- William Briggs, Van Henson, and Steve McCormick. 2000. A Multigrid Tutorial, 2nd Edition.Google ScholarDigital Library
- Tyler E Bruns and Daniel A Tortorelli. 2001. Topology optimization of non-linear elastic structures and compliant mechanisms. Computer methods in applied mechanics and engineering 190, 26-27(2001), 3443–3459.Google Scholar
- Michael Bruyneel and Pierre Duysinx. 2005. Note on topology optimization of continuum structures including self-weight. Structural and Multidisciplinary Optimization 29, 4(2005), 245–256.Google ScholarCross Ref
- Xiang Chen, Changxi Zheng, and Kun Zhou. 2016. Example-Based Subspace Stress Analysis for Interactive Shape Design. PP, 99 (2016).Google Scholar
- Elena Cherkaev and Andrej Cherkaev. 2008. Minimax optimization problem of structural design. Computers & Structures 86, 13-14 (2008), 1426–1435.Google ScholarDigital Library
- Charles Dapogny, Cécile Dobrzynski, and Pascal Frey. 2014. Three-dimensional adaptive domain remeshing, implicit domain meshing, and applications to free and moving boundary problems. Journal of computational physics 262 (2014), 358–378.Google ScholarDigital Library
- Nikan Doosti, Julian Panetta, and Vahid Babaei. 2021. Topology Optimization via Frequency Tuning of Neural Design Representations. In Symposium on Computational Fabrication. 1–9.Google ScholarDigital Library
- Tao Du, Kui Wu, Andrew Spielberg, Wojciech Matusik, Bo Zhu, and Eftychios Sifakis. 2020. Functional Optimization of Fluidic Devices with Differentiable Stokes Flow. ACM Trans. Graph. 39, 6, Article 197 (nov 2020), 15 pages. https://doi.org/10.1145/3414685.3417795Google ScholarDigital Library
- Carlos Faria, Jaime Fonseca, and Estela Bicho. 2020. FIBR3DEmul—an open-access simulation solution for 3D printing processes of FDM machines with 3+ actuated axes. The International Journal of Advanced Manufacturing Technology 106, 7(2020), 3609–3623.Google ScholarCross Ref
- Andrew T Gaynor and James K Guest. 2016. Topology optimization considering overhang constraints: Eliminating sacrificial support material in additive manufacturing through design. Structural and Multidisciplinary Optimization 54, 5(2016), 1157–1172.Google ScholarDigital Library
- Gaël Guennebaud, Benoît Jacob, 2010. Eigen v3. http://eigen.tuxfamily.org.Google Scholar
- G.A. Haveroth, C.-J. Thore, M.R. Correa, R.F. Ausas, S. Jakobsson, J.A. Cuminato, and A. Klarbring. 2022. Topology optimization including a model of the layer-by-layer additive manufacturing process. Computer Methods in Applied Mechanics and Engineering 398 (2022), 115203. https://doi.org/10.1016/j.cma.2022.115203Google ScholarCross Ref
- Intel. 2022. Intel® oneAPI Threading Building Blocks. https://github.com/oneapi-src/oneTBBGoogle Scholar
- Hokeun Kim, Yan Zhao, and Lihua Zhao. 2016. Process-level modeling and simulation for HP’s Multi Jet Fusion 3D printing technology. In 2016 1st international workshop on cyber-physical production systems (CPPS). IEEE, 1–4.Google ScholarCross Ref
- Matthijs Langelaar. 2017. An additive manufacturing filter for topology optimization of print-ready designs. Structural and multidisciplinary optimization 55, 3(2017), 871–883.Google Scholar
- Timothy Langlois, Ariel Shamir, Daniel Dror, Wojciech Matusik, and David IW Levin. 2016. Stochastic structural analysis for context-aware design and fabrication. ACM Transactions on Graphics (TOG) 35, 6 (2016), 226.Google ScholarDigital Library
- Haixiang Liu, Yuanming Hu, Bo Zhu, Wojciech Matusik, and Eftychios Sifakis. 2018. Narrow-Band Topology Optimization on a Sparsely Populated Grid. ACM Trans. Graph. 37, 6, Article 251 (dec 2018), 14 pages. https://doi.org/10.1145/3272127.3275012Google ScholarDigital Library
- Shinji Nishiwaki, Mary I Frecker, Seungjae Min, and Noboru Kikuchi. 1998. Topology optimization of compliant mechanisms using the homogenization method. International journal for numerical methods in engineering 42, 3(1998), 535–559.Google Scholar
- Timilehin Martins Oyinloye and Won Byong Yoon. 2021. Application of Computational Fluid Dynamics (CFD) Simulation for the Effective Design of Food 3D Printing (A Review). Processes 9, 11 (2021). https://doi.org/10.3390/pr9111867Google Scholar
- Julian Panetta, Abtin Rahimian, and Denis Zorin. 2017. Worst-Case Stress Relief for Microstructures. ACM Trans. Graph. 36, 4, Article 122 (jul 2017), 16 pages. https://doi.org/10.1145/3072959.3073649Google ScholarDigital Library
- Julian Panetta, Qingnan Zhou, Luigi Malomo, Nico Pietroni, Paolo Cignoni, and Denis Zorin. 2015. Elastic textures for additive fabrication. ACM Transactions on Graphics (TOG) 34, 4 (2015), 1–12.Google ScholarDigital Library
- Xiaoping Qian. 2017. Undercut and overhang angle control in topology optimization: a density gradient based integral approach. Internat. J. Numer. Methods Engrg. 111, 3 (2017), 247–272.Google ScholarCross Ref
- Christian Schumacher, Bernd Bickel, Jan Rys, Steve Marschner, Chiara Daraio, and Markus Gross. 2015. Microstructures to control elasticity in 3D printing. ACM Transactions on Graphics (Tog) 34, 4 (2015), 1–13.Google ScholarDigital Library
- Christian Schumacher, Jonas Zehnder, and Moritz Bächer. 2018. Set-in-Stone: Worst-Case Optimization of Structures Weak in Tension. ACM Trans. Graph. 37, 6, Article 252 (Dec. 2018), 13 pages. https://doi.org/10.1145/3272127.3275085Google ScholarDigital Library
- Eftychios Sifakis and Jernej Barbic. 2012. FEM simulation of 3D deformable solids: a practitioner’s guide to theory, discretization and model reduction. In Acm siggraph 2012 courses. 1–50.Google Scholar
- Ole Sigmund and Joakim Petersson. 1998. Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima. Structural optimization 16, 1 (1998), 68–75.Google Scholar
- M. Stolpe and K. Svanberg. 2001. An Alternative Interpolation Scheme for Minimum Compliance Topology Optimization. Struct. Multidiscip. Optim. 22, 2 (sep 2001), 116–124. https://doi.org/10.1007/s001580100129Google ScholarDigital Library
- Krister Svanberg. 2007. MMA and GCMMA-two methods for nonlinear optimization. vol 1(2007), 1–15.Google Scholar
- Adrien Treuille, Andrew Lewis, and Zoran Popović. 2006. Model reduction for real-time fluids. ACM Transactions on Graphics (TOG) 25, 3 (2006), 826–834.Google ScholarDigital Library
- Nico P Van Dijk, Kurt Maute, Matthijs Langelaar, and Fred Van Keulen. 2013. Level-set methods for structural topology optimization: a review. Structural and Multidisciplinary Optimization 48, 3(2013), 437–472.Google ScholarDigital Library
- Fengwen Wang, Boyan Stefanov Lazarov, and Ole Sigmund. 2011. On projection methods, convergence and robust formulations in topology optimization. Structural and Multidisciplinary Optimization 43, 6(2011), 767–784.Google ScholarDigital Library
- Weiming Wang, Dirk Munro, Charlie CL Wang, Fred van Keulen, and Jun Wu. 2020. Space-time topology optimization for additive manufacturing. Structural and Multidisciplinary Optimization 61, 1(2020), 1–18.Google ScholarDigital Library
- Jun Wu, Christian Dick, and Rüdiger Westermann. 2016. A System for High-Resolution Topology Optimization. IEEE Transactions on Visualization and Computer Graphics 22, 3(2016), 1195–1208. https://doi.org/10.1109/TVCG.2015.2502588Google ScholarDigital Library
- Hongyi Xu, Yijing Li, Yong Chen, and Jernej Barbič. 2015. Interactive material design using model reduction. ACM Transactions on Graphics (TOG) 34, 2 (2015), 1–14.Google ScholarDigital Library
- Suna Yan, Fengwen Wang, Jun Hong, and Ole Sigmund. 2019. Topology optimization of microchannel heat sinks using a two-layer model. International Journal of Heat and Mass Transfer 143 (2019), 118462.Google ScholarCross Ref
- Qingnan Zhou, Julian Panetta, and Denis Zorin. 2013. Worst-case structural analysis. ACM Trans. Graph. 32, 4, Article 137 (July 2013), 12 pages.Google ScholarDigital Library
Index Terms
- Efficient Layer-by-Layer Simulation for Topology Optimization
Recommendations
Two-layer particle swarm optimization for unconstrained optimization problems
In this article, a two-layer particle swarm optimization (TLPSO) is proposed to increase the diversity of the particles so that the drawback of trapping in a local optimum is avoided. In order to design the TLPSO, a structure with two layers (top layer ...
Residual layer lithography
Graphical abstractDisplay Omitted Combination of nanoimprint lithography of negative tone resist with a UV-flood exposure.Pattern definition in the remaining residual layer.Use of interference and diffraction effects along the imprinted edges to define ...
Microfabricated double layer octupoles for microcolumn applications
We report about a new process we have developed to fabricate miniaturized double layer octupoles that can be operated as electrostatic scanner/stigmators for charged particle beams. The fabrication process is based on deep reactive ion etching (DRIE) ...
Comments