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Multi-Material Topology Optimization: A Practical Approach and Application
ISSN: 0148-7191, e-ISSN: 2688-3627
Published April 03, 2018 by SAE International in United States
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The automotive industry is facing significant challenges for next-generation vehicle design as fuel economy regulations and tailpipe emission standards continue to strive for greater efficiency. In order to ensure vehicle design reaches these sustainability targets, lightweighting through multi-material design and topology optimization (TO) has been suggested as the leading method to reduce weight from conventional component and small assembly structures. More effective tools, techniques, and methodologies are now required to advance the development of multi-phase optimization tools beyond current commercial capability, and help automotive designers achieve critical efficiency improvements without sacrificing performance.
Presented here is a unique tool description and practical application of multi-material topology optimization (MMTO), a direct extension of the classical single-material problem statement (SMTO). In this implementation the TO problem is expanded to include material existence and selection design variables in the typical density method while utilizing the solid isotropic material with penalization (SIMP) interpolation scheme. Further improvements from the prior research include adoption of the method of moving asymptotes (MMA) for handling large-scale, high-resolution optimization problems.
Emphasized in this paper is a description of a multi-material topology optimization computational tool, an examination of single and multi-material solutions and comments for practical design. First, key equations and techniques that enable MMTO are presented, including interpolation schemes, sensitivity analysis, and filtering methods. Next, MMTO is applied to a practical automotive case study in a minimum compliance framework, and compared to other SMTO approaches. Lastly, an overview of practical design considerations is presented to discuss development of a final product from concept to validation.
CitationRoper, S., Li, D., Florea, V., Woischwill, C. et al., "Multi-Material Topology Optimization: A Practical Approach and Application," SAE Technical Paper 2018-01-0110, 2018, https://doi.org/10.4271/2018-01-0110.
- United States Environmental Protection Agency , “Regulations for Emissions from Vehicles and Engines,” Final Rule for Model Year 2012-2016 Light-Duty Vehicle Greenhouse Gas Emission Standards and Corporate Average Fuel Economy Standards,” Federal Register, Rev. Sept 2017.
- United States Environmental Protection Agency , “Regulations for Emissions from Vehicles and Engines,” Final Rule for Model Year 2017 and Later Light-Duty Vehicle Greenhouse Gas Emissions and Corporate Average Fuel Economy Standards, Federal Register, Rev. Sept 2017.
- International Energy Agency , “Global EV Outlook 2017,” https://www.iea.org/publications/freepublications/publication/GlobalEVOutlook2017.pdf, accessed 2017.
- United States Department of Energy , “Lightweight Materials R&D,” https://energy.gov/sites/prod/files/2016/09/f33/Lightweight%20Materials%20-%202015%20Annual%20Report.pdf, accessed 2017.
- Owens, E. , “Vehicle Technologies: Materials Technology,” U.S. Department of Energy, 2014.
- Li, C. and Kim, I.Y. , “Topology, Size and Shape Optimization of an Automotive Cross Car Beam,” Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering 229(10), 2014, doi:10.1177/0954407014561279.
- Li, C., Kim, I.Y., and Jeswiet, J. , “Conceptual and Detailed Design of an Automotive Engine Cradle by Using Topology, Shape, and Size Optimization,” Structural and Multidisciplinary Optimization 51(2):547-564, 2015, doi:10.1007/s00158-014-1151-6.
- Li, G., Xu, F., Huang, X., and Sun, G. , “Topology Optimization of an Automotive Tailor-Welded Blank Door,” Journal of Mechanical Design 137(5):055001-08, 2015, doi:10.1115/1.4028704.
- Cavazzuti, M., Baldini, A., Bertocchi, E., Costi, D. et al. , “High Performance Automotive Chassis Design: A Topology Optimization Based Approach,” Structural and Multidisciplinary Optimization 44(1):45-56, 2011, doi:10.1007/s00158-010-0578-7.
- Deaton, J.D. and Grandhi, R.V. , “A Survey of Structural and Multidisciplinary Continuum Topology Optimization: Post 2000,” Structural and Multidisciplinary Optimization 49(1):1-38, 2014, doi:10.1007/s00158-013-0956-z.
- Sigmund, O. and Maute, K. , “Topology Optimization approaches: A comparative review,” Structural and Multidisciplinary Optimization 48(6):1031-1055, 2013, doi:10.1007/s00158-013-0978-6.
- Sigmund, O. , “A 99 Line Topology Optimization Code Written in Matlab,” Structural and Multidisciplinary Optimization 21(2):120-127, 2001, doi:10.1007/s001580050176.
- Stolpe, M. and Svanberg, K. , “An Alternative Interpolation Scheme for Minimum Compliance Topology Optimization,” Structural and Multidisciplinary Optimization 22(2):116-124, 2001, doi:10.1007/s001580100129.
- Stolpe, M. and Stegmann, J. , “A Newton Method for Solving Continuous Multiple Material Minimum Compliance Problems,” Structural and Multidisciplinary Optimization 35(2):93-106, 2008, doi:10.1007/s00158-007-0131-5.
- Sigmund, O. and Torquato, S. , “Design of Materials with Extreme Thermal Expansion Using a Three-Phase Topology Optimization Method,” Journal of the Mechanics and Physics of Solids 33(6):401-424, 1997, doi:10.1007/s00158-006-0087-x.
- Zuo, W. and Saitou, K. , “Multi-Material Topology Optimization Using Ordered SIMP Interpolation,” Structural and Multidisciplinary Optimization, 2016, doi:10.1007/s00158-016-1513-3.
- Li, D., Roper, S., Woischwill, C., Carrick C., and Kim, I.Y. , "Multi-Material Lightweight Design by Topology Optimization," Presented at 26th Canadian Congress of Applied Mechanics, Canada, 29 May-1 Jun 2017.
- Ramani, A. , “Multi-Material Topology Optimization with Strength Constraints,” Structural and Multidisciplinary Optimization 43(5):597-615, 2011, doi:10.1007/s00158-010-0581-z.
- Bendsøe, M.P. , “Optimal Shape Design as a Material Distribution Problem,” Structural Optimization 1(4):193-202, 1989, doi:10.1007/BF01650949.
- Zhou, M. and Rozvany, G. , “The COC Algorithm, Part II: Topological, Geometrical and Generalized Shape Optimization,” 89:309-336, 1991, doi:10.1016/0045-7825(91)90046-9.
- Svanberg, K. , “The Method of Moving Asymptotes-A New Method for Structural Optimization,” 24(Jun 1986):359-373, 1987, doi:10.1002/nme.1620240207.
- Svanberg, K. , “A Class of Globally Convergent Optimization Methods Based on Conservative Convex Separable Approximations,” SIAM Journal of Optimization 12(2):555-573, 2002, doi:10.1137/S1052623499362822.
- Bendsoe, M. and Sigmund, O. , “Topology Optimization: Theory, Methods, and Applications,” (Heidelberg, Springer, 2003), 5-20, ISBN: 978-3-662-05086-6.
- Sigmund, O. , “Morphology-Based Black and White Filters for Topology Optimization,” Structural and Multidisciplinary Optimization 33(4-5):401-424, 2007, doi:10.1007/s00158-006-0087-x.