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Multi-Material Topology Optimization for Crashworthiness Using Hybrid Cellular Automata
ISSN: 0148-7191, e-ISSN: 2688-3627
Published April 2, 2019 by SAE International in United States
This content contains downloadable datasetsAnnotation ability available
Structures with multiple materials have now become one of the perceived necessities for automotive industry to address vehicle design requirements such as light-weight, safety, and cost. The objective of this study is to develop a design methodology for multi-material structures accountable for vehicle crash durability. The heuristic topology synthesis approach of Hybrid Cellular Automaton (HCA) framework is implemented to generate multi-material structures with the constraint on the volume fraction of the final design. The HCA framework is integrated with ordered-SIMP (solid isotropic material with penalization) interpolation, artificial material library, as well as statistical analysis of material distribution data to ensure a smooth transition between multiple practical materials during the topology synthesis. Since the proposed method does not rely on additional variables to represent material selection, the computational cost of this method is independent of the number of the phases in a multi-material design. The dynamic simulations of a sphere ball impacting an armor plate and the frontal crash on a car bumper are used to evaluate the proposed multi-material topology synthesis algorithm. The practical materials are the different grades of steels with the same elastic properties and different yield strength and plastic hardening. The crash performance measures such as peak acceleration-displacement profiles of multi-material designs are compared with binary designs obtained from HCA to conclude the results of the multi-material HCA framework.
CitationRaeisi, S., Tapkir, P., Tovar, A., Mozumder, C. et al., "Multi-Material Topology Optimization for Crashworthiness Using Hybrid Cellular Automata," SAE Technical Paper 2019-01-0826, 2019, https://doi.org/10.4271/2019-01-0826.
Data Sets - Support Documents
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- Elhedhli, S. and Merrick, R., “Green Supply Chain Network Design to Reduce Carbon Emissions,” Transportation Research Part D: Transport and Environment 17(5):370-379, 2012.
- Cui, X. et al., “Design of Lightweight Multi-Material Automotive Bodies Using New Material Performance Indices of Thin-Walled Beams for the Material Selection with Crashworthiness Consideration,” Materials & Design 32(2):815-821, 2011.
- Yamane, K. and Furuhama, S., “A Study on the Effect of the Total Weight of Fuel and Fuel Tank on the Driving Performances of Cars,” International Journal of Hydrogen Energy 23(9):825-831, 1998.
- Li, Y. et al., “Use of High Strength Steel Sheet for Lightweight and Crashworthy Car Body,” Materials & Design 24(3):177-182, 2003.
- Deb, A. et al., “Design of an Aluminium-Based Vehicle Platform for Front Impact Safety,” International Journal of Impact Engineering 30(8):1055-1079, 2004.
- Carle, D. and Blount, G., “The Suitability of Aluminium as an Alternative Material for Car Bodies,” Materials & Design 20(5):267-272, 1999.
- Mayer, R.R., Kikuchi, N., and Scott, R.A., “Application of Topological Optimization Techniques to Structural Crashworthiness,” International Journal for Numerical Methods in Engineering 39(8):1383-1403, 1996.
- Du Bois, P. et al., Vehicle Crashworthiness and Occupant Protection, 2004.
- Fang, H. et al., “A Comparative Study of Metamodeling Methods for Multiobjective Crashworthiness Optimization,” Computers & Structures 83(25-26):2121-2136, 2005.
- Fang, H., Solanki, K., and Horstemeyer, M., “Numerical Simulations of Multiple Vehicle Crashes and Multidisciplinary Crashworthiness Optimization,” International Journal of Crashworthiness 10(2):161-172, 2005.
- Zhou, S. and Wang, M.Y., “Multimaterial Structural Topology Optimization with a Generalized Cahn-Hilliard Model of Multiphase Transition,” Structural and Multidisciplinary Optimization 33(2):89, 2007.
- Mozumder, C. et al., “Thickness Based Topology Optimization for Crashworthiness Design Using Hybrid Cellular Automata,” in 12th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, 2008.
- Patel, N.M. et al., “Crashworthiness Design Using Topology Optimization,” Journal of Mechanical Design 131(6):061013, 2009.
- Ramani, A., “A Pseudo-Sensitivity Based Discrete-Variable Approach to Structural Topology Optimization with Multiple Materials,” Structural and Multidisciplinary Optimization 41(6):913-934, 2010.
- Wang, M.Y. and Wang, X., ““Color” Level Sets: A Multi-Phase Method for Structural Topology Optimization with Multiple Materials,” Computer Methods in Applied Mechanics and Engineering 193(6-8):469-496, 2004.
- Kim, Y.-I. and Park, G.-J., “Nonlinear Dynamic Response Structural Optimization Using Equivalent Static Loads,” Computer Methods in Applied Mechanics and Engineering 199(9-12):660-676, 2010.
- Bandi, P., Design of Crashworthy Structures with Controlled Behavior in HCA Framework, University of Notre Dame, 2012.
- Lee, H.-A. and Park, G.-J., “Nonlinear Dynamic Response Topology Optimization Using the Equivalent Static Loads Method,” Computer Methods in Applied Mechanics and Engineering 283:956-970, 2015.
- Forsberg, J. and Nilsson, L., “Topology Optimization in Crashworthiness Design,” Structural and Multidisciplinary Optimization 33(1):1-12, 2007.
- Liu, K., Detwiler, D., and Tovar, A., “Cluster-Based Optimization of Cellular Materials and Structures for Crashworthiness,” Journal of Mechanical Design 140(11):111412, 2018.
- Wang, M.Y. et al., “Design of Multimaterial Compliant Mechanisms Using Level-Set Methods,” Journal of Mechanical Design 127(5):941-956, 2005.
- Guo, X., Zhang, W., and Zhong, W., “Stress-Related Topology Optimization of Continuum Structures Involving Multi-Phase Materials,” Computer Methods in Applied Mechanics and Engineering 268:632-655, 2014.
- Cui, M., Chen, H., and Zhou, J., “A Level-Set Based Multi-Material Topology Optimization Method Using a Reaction Diffusion Equation,” Computer-Aided Design 73:41-52, 2016.
- Tavakoli, R. and Mohseni, S.M., “Alternating Active-Phase Algorithm for Multimaterial Topology Optimization Problems: A 115-Line MATLAB Implementation,” Structural and Multidisciplinary Optimization 49(4):621-642, 2014.
- Goede, M. et al., “Super Light Car-Lightweight Construction Thanks to a Multi-Material Design and Function Integration,” European Transport Research Review 1(1):5, 2009.
- Sakiyama, T. et al., “Dissimilar Metal Joining Technologies for Steel Sheet and Aluminum Alloy Sheet in Auto Body,” Nippon Steel Technical Report 103:91-98, 2013.
- Fiebig, S. et al., “Future Challenges for Topology Optimization for the Usage in Automotive Lightweight Design Technologies, in Advances in Structural and Multidisciplinary Optimization-Proceedings of the 11th World Congress on Structural and Multidisciplinary Optimization, Sydney, Australia, 2015.
- Falkenberg, P. et al., “Consideration of Adhesive Joints for a Multi-Material Topology Optimization Approach, in 20th International Conference on Composite Materials, Copenhagen, Denmark, 2015.
- Li, C. and Kim, I.Y., Multi-Material Topology Optimization for Automotive Design Problems,” in Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, 2017, 0954407017737901.
- Liu, K. et al., “Towards Nonlinear Multimaterial Topology Optimization Using Unsupervised Machine Learning and Metamodel-Based Optimization,” in ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, 2015, American Society of Mechanical Engineers.
- Liu, K., Detwiler, D., and Tovar, A., “Optimal Design of Nonlinear Multimaterial Structures for Crashworthiness Using Cluster Analysis,” Journal of Mechanical Design 139(10):101401, 2017.
- Tovar, A. et al., “Topology Optimization Using a Hybrid Cellular Automaton Method with Local Control Rules,” Journal of Mechanical Design 128(6):1205-1216, 2006.
- Tovar, A., Bone Remodeling as a Hybrid Cellular Automaton Optimization Process, 2004.
- Bochenek, B. and Tajs-Zielińska, K., “Novel Local Rules of Cellular Automata applied to Topology and Size Optimization,” Engineering Optimization 44(1):23-35, 2012.
- Tovar, A. et al., “Hybrid Cellular Automata with Local Control Rules: A New Approach to Topology Optimization Inspired by Bone Functional Adaptation,” in Proceedings of the 6th World Congress on Structural and Multidisciplinary Optimization (WCSMO6), Rio de Janeiro, Brazil, 2005.
- Tovar, A. et al., “Optimality Conditions of the Hybrid Cellular Automata for Structural Optimization,” AIAA Journal 45(3):673-683, 2007.
- Tapkir, P., Topology Design of Vehicle Structures for Crashworthiness Using Variable Design Time (Purdue University, 2017).
- Patel, N.M. et al., “Comparative Study of Topology Optimization Techniques,” AIAA Journal 46(8):1963-1975, 2008.
- Bendsøe, M.P. and Sigmund, O., “Material Interpolation Schemes in Topology Optimization,” Archive of Applied Mechanics 69(9-10):635-654, 1999.
- Zuo, W. and Saitou, K., “Multi-Material Topology Optimization Using Ordered SIMP Interpolation,” Structural and Multidisciplinary Optimization 55(2):477-491, 2017.