Topology optimization for crashworthiness of thin-walled structures under axial crash considering nonlinear plastic buckling and locations of plastic hinges

References

• Abramowicz, W., and N. Jones. 1984. “Dynamic Axial Crushing of Square Tubes.” International Journal of Impact Engineering 2 (2): 179–208. doi: 10.1016/0734-743X(84)90005-8
   Google Scholar
• Baleh, R., and A. Abdul-Latif. 2007. “Quasi-static Biaxial Plastic Buckling of Tubular Structures Used as an Energy Absorber.” Journal of Applied Mechanics 74 (4): 628. doi: 10.1115/1.2424470
   Web of Science ®Google Scholar
• Bendsøe, M. P., and O. Sigmund. 2003. Topology Optimization: Theory, Methods and Applications. 2nd ed. Berlin: Springer.
   Google Scholar
• Cavazzuti, M., A. Baldini, E. Bertocchi, D. Costi, E. Torricelli, and P. Moruzzi. 2011. “High Performance Automotive Chassis Design: A Topology Optimization Based Approach.” Structural and Multidisciplinary Optimization 44 (1): 45–56. doi: 10.1007/s00158-010-0578-7
   Web of Science ®Google Scholar
• Choi, W. S., and G. J. Park. 2002. “Structural Optimization Using Equivalent Static Loads at All Time Intervals.” Computer Methods in Applied Mechanics and Engineering 191 (19–20): 2105–2122. doi: 10.1016/S0045-7825(01)00373-5
   Web of Science ®Google Scholar
• Christensen, J., C. Bastien, and M. V. Blundell. 2012. “Effects of Roof Crush Loading Scenario upon Body in White Using Topology Optimisation.” International Journal of Crashworthiness 17 (1): 29–38. doi: 10.1080/13588265.2011.625640
   Web of Science ®Google Scholar
• Duddeck, F., S. Hunkeler, P. Lozano, E. Wehrle, and D. Zeng. 2016. “Topology Optimization for Crashworthiness of Thin-Walled Structures Under Axial Impact Using Hybrid Cellular Automata.” Structural and Multidisciplinary Optimization 54 (3): 415–428. doi: 10.1007/s00158-016-1445-y
   Web of Science ®Google Scholar
• Forsberg, J., and L. Nilsson. 2006. “Topology Optimization in Crashworthiness Design.” Structural and Multidisciplinary Optimization 33 (1): 1–12. doi: 10.1007/s00158-006-0040-z
   Web of Science ®Google Scholar
• Furusako, S., A. Uenishi, and Y. Miyazaki. 2007. “Improvement of Crashworthiness by Application of High Strength Steel.” Nippon Steel Technical Report 95: 35–38.
   Google Scholar
• Griskevicius, P., and A. Ziliukas. 2003. “The Crash Energy Absorption of the Vehicles Front Structures.” Transport 18 (2): 97–101.
   Google Scholar
• Guler, M. A., M. E. Cerit, B. Bayram, B. Gerceker, and E. Karakaya. 2010. “The Effect of Geometrical Parameters on the Energy Absorption Characteristics of Thin-Walled Structures Under Axial Impact Loading.” International Journal of Crashworthiness 15 (4): 377–390. doi: 10.1080/13588260903488750
   Web of Science ®Google Scholar
• Hayduk, R. J., and T. Wierzbicki. 1982. “Extensional Collapse Modes of Structural Members.” In Proceedings of Symposia Advances and Trends in Structural and Solid Mechanics, 405–434. Hampton, VA: NASA Langley Research Center.
   Google Scholar
• Hooputra, H., H. Gese, H. Dell, and H. Werner. 2004. “A Comprehensive Failure Model for Crashworthiness Simulation of Aluminium Extrusions.” International Journal of Crashworthiness 9 (5): 449–464. doi: 10.1533/ijcr.2004.0289
   Web of Science ®Google Scholar
• Jang, H. H., H. A. Lee, J. Y. Lee, and G. J. Park. 2012. “Dynamic Response Topology Optimization in the Time Domain Using Equivalent Static Loads.” AIAA Journal 50 (1): 226–234. doi: 10.2514/1.J051256
   Web of Science ®Google Scholar
• Kim, Y. I., and G. J. Park. 2010. “Nonlinear Dynamic Response Structural Optimization Using Equivalent Static Loads.” Computer Methods in Applied Mechanics and Engineering 199 (9–12): 660–676. doi: 10.1016/j.cma.2009.10.014
   Web of Science ®Google Scholar
• Lee, S., H. A. Lee, S. Yi, D. Kim, H. Yang, and G. Park. 2013. “Design Flow for the Crash Box in a Vehicle to Maximize Energy Absorption.” Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering 227 (2): 179–200.
   Web of Science ®Google Scholar
• Lee, H. A., and G. J. Park. 2015. “Nonlinear Dynamic Response Topology Optimization Using the Equivalent Static Loads Method.” Computer Methods in Applied Mechanics and Engineering 283: 956–970. doi: 10.1016/j.cma.2014.10.015
   Web of Science ®Google Scholar
• Lee, Y., and G. J. Park. 2017. “Non-linear Dynamic Response Structural Optimization for Frontal-Impact and Side-Impact Crash Tests.” Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering 231 (5): 600–614.
   Web of Science ®Google Scholar
• Mayer, R. R., N. Kikuchi, and R. A. Scott. 1996. “Application of Topological Optimization Techniques to Structural Crashworthiness.” International Journal for Numerical Methods in Engineering 39 (8): 1383–1403. doi: 10.1002/(SICI)1097-0207(19960430)39:8<1383::AID-NME909>3.0.CO;2-3
   Web of Science ®Google Scholar
• Mozumder, C., J. Renaud, and A. Tovar. 2012. “Topometry Optimisation for Crashworthiness Design Using Hybrid Cellular Automata.” International Journal of Vehicle Design 60 (1/2): 100–120. doi: 10.1504/IJVD.2012.049160
   Web of Science ®Google Scholar
• Ortmann, C., and A. Schumacher. 2013. “Graph and Heuristic Based Topology Optimization of Crash Loaded Structures.” Structural and Multidisciplinary Optimization 47 (6): 839–854. doi: 10.1007/s00158-012-0872-7
   Web of Science ®Google Scholar
• Patel, N., B. Kang, J. Renaud, and A. Tovar. 2009. “Crashworthiness Design Using Topology Optimization.” ASME Journal of Mechanical Design 131 (6): 61013-1-12.
   Web of Science ®Google Scholar
• Pedersen, C. 2003a. “Topology Optimization Design of Crushed 2D-Frames for Desired Energy Absorption History.” Structural and Multidisciplinary Optimization 25 (5): 368–382. doi: 10.1007/s00158-003-0282-y
   Web of Science ®Google Scholar
• Pedersen, C. 2003b. “Topology Optimization for Crashworthiness of Frame Structures.” International Journal of Crashworthiness 8: 29–39. doi: 10.1533/ijcr.2003.0218
   Web of Science ®Google Scholar
• Schumacher, A., M. Seibel, M. Schafer, and H. Zimmer. 2005. “New Optimization Strategies for Crash Design.” LS-DYNA Anwenderforum, Bamberg, A-II-1–13.
   Google Scholar
• SIMULIA. 2012. ABAQUS/Standard Version 6.12 User’s Manual. Providence, RI: Abaqus, Inc.
   Google Scholar
• Sun, G., G. Li, S. Zhou, H. Li, S. Hou, and Q. Li. 2011. “Crashworthiness Design of Vehicle by Using Multiobjective Robust Optimization.” Structural and Multidisciplinary Optimization 44 (1): 99–110. doi: 10.1007/s00158-010-0601-z
   Web of Science ®Google Scholar
• Torstenfelt, B., and A. Klarbring. 2007. “Conceptual Optimal Design of Modular Car Product Families Using Simultaneous Size, Shape and Topology Optimization.” Finite Elements in Analysis and Design 43 (14): 1050–1061. doi: 10.1016/j.finel.2007.06.005
   Web of Science ®Google Scholar
• Volz, K., and F. Duddeck. 2012. “A New Topology Optimization Approach for Crashworthiness of Passenger Vehicles Based on Physically Defined Equivalent Static Loads.” Article presented at the International Crashworthiness Conference, Milano, July 18–20.
   Google Scholar
• Wierzbicki, T., and W. Abramowicz. 1983. “On the Crushing Mechanics of Thin-Walled Structures.” Journal of Applied Mechanics 50: 727–734. doi: 10.1115/1.3167137
   Web of Science ®Google Scholar
• Witowski, K., A. Erhart, P. Schumacher, and H. Müllerschön. 2012. “Topology Optimization for Crash.” In 12th International LS-DYNA Users Conference, 1–8. Detroit, MI: DYNAmore.
   Google Scholar
• Witowski, K., H. Müllerschön, A. Erhart, and P. Schumacher. 2014. “Topology and Topometry Optimization of Crash Applications with the Equivalent Static Load Method.” 13th International LS-DYNA Users Conference, 1–11.
   Google Scholar
• Xu, S., Y. Cai, and G. Cheng. 2010. “Volume Preserving Nonlinear Density Filter Based on Heaviside Functions.” Structural and Multidisciplinary Optimization 41 (4): 495–505. doi: 10.1007/s00158-009-0452-7
   Web of Science ®Google Scholar