A hybrid cellular automaton–bi-directional evolutionary optimization algorithm for topological optimization of crashworthiness

References

• Akin, J. E., and J. Arjona-Baez. 2001. “Enhancing Structural Topology Optimization.” Engineering Computations 18 (3-4): 663–675. doi: 10.1108/02644400110387640
   Web of Science ®Google Scholar
• Allaire, G., F. Jouve, and A. M. Toader. 2004. “Structural Optimization Using Sensitivity Analysis and a Level-Set Method.” Journal of Computational Physics 194 (1): 363–393. doi: 10.1016/j.jcp.2003.09.032
   Web of Science ®Google Scholar
• Bendsøe, M. P. 2000. “Topology Design of Structures, Materials and Mechanisms – Status and Perspectives.” In System Modelling and Optimization, edited by M. J. D. Powell and S. Scholtes, 1–17. Boston, MA: Springer.
   Google Scholar
• Bendsøe, M. P., and N. Kikuchi. 1988. “Generating Optimal Topologies in Structural Design Using a Homogenization Method.” Computer Methods in Applied Mechanics and Engineering 71: 197–224. doi: 10.1016/0045-7825(88)90086-2
   Web of Science ®Google Scholar
• Bendsøe, M. P., and O. Sigmund. 1999. “Material Interpolation Schemes in Topology Optimization.” Archive of Applied Mechanics (Ingenieur Archiv) 69: 635–654. doi: 10.1007/s004190050248
   Web of Science ®Google Scholar
• Bennage, W. A., and K. A. Dhingra. 1995. “Optimization of Truss Topology Using Tabu Search.” International Journal for Numerical Methods in Engineering 38: 4035–4052. doi: 10.1002/nme.1620382308
   Web of Science ®Google Scholar
• Bochenek, B., and K. TajsZielinska. 2012. “Novel Local Rules of Cellular Automata Applied to Topology and Size Optimization.” Engineering Optimization 44 (1): 23–35. doi: 10.1080/0305215X.2011.561843
   Web of Science ®Google Scholar
• Bulman, S., J. Sienz, and E. Hinto. 2001. “Comparisons Between Algorithms for Structural Topology Optimization Using a Series of Benchmark Studies.” Computers and Structures 79 (12): 1203–1218. doi: 10.1016/S0045-7949(01)00012-8
   Web of Science ®Google Scholar
• Fang, J. G., Y. K. Gao, G. Y. Sun, Y. T. Zhang, and Q. Li. 2014. “Parametric Analysis and Multiobjective Optimization for Functionally Graded Foam-Filled Thin-Wall Tube Under Lateral Impact.” Computational Materials Science 90: 265–275. doi: 10.1016/j.commatsci.2014.03.044
   Web of Science ®Google Scholar
• Fang, J. G., G. Y. Sun, N. Qiu, N. H. Kim, and Q. Li. 2017a. “On Design Optimization for Structural Crashworthiness and its State of the Art.” Structural and Multidisciplinary Optimization 55: 1091–1119. doi: 10.1007/s00158-016-1579-y
   Web of Science ®Google Scholar
• Fang, J. G., G. Y. Sun, N. Qiu, G. P. Steven, and Q. Li. 2017b. “Topology Optimization of Multicell Tubes Under Out-of-Plane Crushing Using a Modified Artificial Bee Colony Algorithm.” Journal of Mechanical Design 139: 071403-1. doi: 10.1115/1.4036561
   Web of Science ®Google Scholar
• Forsberg, J., and L. Nilsson. 2006. “Evaluation of Response Surface Methodologies Used in Crashworthiness Optimization.” International Journal of Impact Engineering 32: 759–777. doi: 10.1016/j.ijimpeng.2005.01.007
   Web of Science ®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
• Guo, X., W. Zhang, and J. Zhang. 2016. “Explicit Structural Topology Optimization Based on Moving Morphable Components (MMC) with Curved Skeletons.” Computer Methods in Applied Mechanics and Engineering 310: 711–748. doi: 10.1016/j.cma.2016.07.018
   Web of Science ®Google Scholar
• Haftka, R. T., D. Villanueva, and A. Chaudhuri. 2016. “Parallel Surrogate-Assisted Global Optimization with Expensive Functions – A Survey.” Structural and Multidisciplinary Optimization 54: 3–13. doi: 10.1007/s00158-016-1432-3
   Web of Science ®Google Scholar
• He, G., X. Huang, H. Wang, and G. Li. 2016. “Topology Optimization of Periodic Structures Using BESO Based on Unstructured Design Points.” Structural and Multidisciplinary Optimization 53 (2): 271–275. doi: 10.1007/s00158-015-1342-9
   Web of Science ®Google Scholar
• Hou, S. H., Q. Li, S. Y. Long, X. J. Yang, and W. Li. 2009. “Crashworthiness Design for Foam Filled Thin-Wall Structures.” Materials and Design 30: 2024–2032. doi: 10.1016/j.matdes.2008.08.044
   Web of Science ®Google Scholar
• Huang, X., and Y. M. Xie. 2007. “Convergent and Mesh-Independent Solutions for the Bi-directional Evolutionary Structural Optimization Method.” Finite Elements in Analysis and Design 43: 1039–1049. doi: 10.1016/j.finel.2007.06.006
   Web of Science ®Google Scholar
• Huang, X., Y. M. Xie, and G. Lu. 2007. “Topology Optimization of Energy-Absorbing Structures.” International Journal of Crashworthiness 12 (6): 663–675. doi: 10.1080/13588260701497862
   Web of Science ®Google Scholar
• Jin, R., W. Chen, and T. W. Simpson. 2001. “Comparative Studies of Metamodelling Techniques Under Multiple Modelling Criteria.” Structural and Multidisciplinary Optimization 23: 1–13. doi: 10.1007/s00158-001-0160-4
   Web of Science ®Google Scholar
• Jog, C. S. 2002. “Topology Design of Structures Using a Dual Algorithm and a Constraint on the Perimeter.” International Journal for Numerical Methods in Engineering 54: 1007–1019. doi: 10.1002/nme.457
   Web of Science ®Google Scholar
• Kane, C., and M. Schoenauer. 1996. “Topological Optimum Design Using Genetic Algorithms.” Control and Cybernetics 25 (5): 1059–1088.
   Google Scholar
• Kantar, E., R. T. Erdem, and Ö. Anil. 2011. “Nonlinear Finite Element Analysis of Impact Behavior of Concrete Beam.” Mathematical and Computational Applications 16 (1): 183–193. doi: 10.3390/mca16010183
   Google Scholar
• Kato, J., H. Hoshiba, S. Takase, K. Terada, and T. Kyoya. 2015. “Analytical Sensitivity in Topology Optimization for Elastoplastic Composites.” Structural and Multidisciplinary Optimization 52: 507–526. doi: 10.1007/s00158-015-1246-8
   Web of Science ®Google Scholar
• Kim, D. M., I. M. Kim, S. Choi, G. W. Jang, and Y. Y. Kim. 2016. “Topology Optimization of Thin-Walled Box Beam Structures Based on the Higher-Order Beam Theory.” International Journal for Numerical Methods in Engineering 106 (7): 576–590. doi: 10.1002/nme.5143
   Web of Science ®Google Scholar
• Kita, E., and T. Toyoda. 2000. “Structural Design Using Cellular Automaton.” Structural and Multidisciplinary Optimization 19 (1): 64–73. doi: 10.1007/s001580050086
   Web of Science ®Google Scholar
• Li, Q., G. P. Steven, and Y. M. Xie. 2001. “A Simple Checkerboard Suppression Algorithm for Evolutionary Structural Optimization.” Structural and Multidisciplinary Optimization 22: 230–239. doi: 10.1007/s001580100140
   Web of Science ®Google Scholar
• Li, G. Y., Z. S. Zhang, G. Y. Sun, X. D. Huang, and Q. Li. 2015. “Comparison of Functionally-Graded Structures Under Multiple Loading Angles.” Thin-Walled Structures 94: 334–347. doi: 10.1016/j.tws.2015.04.030
   Web of Science ®Google Scholar
• Li, G. Y., Z. S. Zhang, G. Y. Sun, F. X. Xu, and X. D. Huang. 2014. “Crushing Analysis and Multi-objective Optimization for Functionally Graded Foam-Filled Tubes Under Multiple Load Cases.” International Journal of Mechanical Sciences 89: 439–452. doi: 10.1016/j.ijmecsci.2014.10.001
   Web of Science ®Google Scholar
• Liu, J., and G. L. Wen. 2017. “Continuum Topology Optimization Considering Uncertainties in Load Locations Based on the Cloud Model.” Engineering Optimization 14: 1–20.
   Google Scholar
• Maute, K., and D. M. Frangopol. 2003. “Reliability-Based Design of MEMS Mechanisms by Topology Optimization.” Computers & Structures 81: 813–824. doi: 10.1016/S0045-7949(03)00008-7
   Web of Science ®Google Scholar
• Meng, F., S. Li, H. Lin, B. Jia, and X. Huang. 2016. “Topology Optimization of Photonic Structures for All-Angle Negative Refraction.” Finite Elements in Analysis and Design 117-118: 46–56. doi: 10.1016/j.finel.2016.04.005
   Web of Science ®Google Scholar
• Missoum, S., Z. Gürdal, and S. Setoodeh. 2005. “Study of a New Local Update Scheme for Cellular Automaton in Structural Design.” Structural and Multidisciplinary Optimization 29 (2): 103–112. doi: 10.1007/s00158-004-0464-2
   Web of Science ®Google Scholar
• Niyazi, T., and F. O. Sonmez. 2014. “Optimal Shape Design of Thin-Walled Tubes Under High-Velocity Axial Impact Loads.” Thin-Walled Structures 84: 302–312. doi: 10.1016/j.tws.2014.07.003
   Web of Science ®Google Scholar
• Patel, N. M. 2007. “Crashworthiness Design Using Topology Optimization.” Ph.D. thesis, University of Notre Dame, South Bend, IN.
   Google Scholar
• Patel, N. M., B. Kang, and J. E. Renaud. 2006. “Topology Synthesis of Structures Under Impact Loading Using a Hybrid Cellular Automaton Algorithm.” Paper presented at the 11th AIAA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, Portsmouth, VA, September 6–8.
   Google Scholar
• Patel, N. M., B. Kang, J. E. Renaud, and A. Tovar. 2009. “Crashworthiness Design Using Topology Optimization.” Journal of Mechanical Design 131: 1–12.
   Web of Science ®Google Scholar
• Patel, N. M., D. Tillotson, and J. E. Renaud. 2008. “Comparative Study of Topology Optimization Techniques.” AIAA Journal 46 (8): 1963–1975. doi: 10.2514/1.31053
   Web of Science ®Google Scholar
• Pedersen, C. B. W. 2004. “Crashworthiness Design of Transient Frame Structures Using Topology Optimization.” Computer Methods in Applied Mechanics and Engineering 193: 653–678. doi: 10.1016/j.cma.2003.11.001
   Web of Science ®Google Scholar
• Qiu, N., Y. Gao, J. Fang, Z. Feng, G. Sun, and Q. Li. 2016. “Theoretical Prediction and Optimization of Multi-cell Hexagonal Tubes Under Axial Crashing.” Thin-Walled Structures 102: 111–121. doi: 10.1016/j.tws.2016.01.023
   Web of Science ®Google Scholar
• Qiu, N., Y. M. Gao, J. G. Fang, G. Y. Sun, and N. H. Kim. 2018. “Topological Design of Multi-cell Hexagonal Tubes Under Axial and Lateral Loading Cases Using a Modified Particle Swarm Algorithm.” Applied Mathematical Modelling 53: 567–583. doi: 10.1016/j.apm.2017.08.017
   Web of Science ®Google Scholar
• Querin, O. M., V. Young, G. P. Steven, and Y. M. Xie. 2000. “Computational Efficiency and Validation of Bi-directional Evolutionary Structural Optimisation.” Computer Methods in Applied Mechanics and Engineering 189: 559–573. doi: 10.1016/S0045-7825(99)00309-6
   Web of Science ®Google Scholar
• Rozvany, G. I. N. 2001. “Aims, Scope, Methods, History and Unified Terminology of Computer-Aided Topology Optimization in Structural Mechanics.” Structural and Multidisciplinary Optimization 21 (2): 90–108. doi: 10.1007/s001580050174
   Web of Science ®Google Scholar
• Shi, L., R. J. Yang, and P. Zhu. 2012. “A Method for Selecting Surrogate Models in Crashworthiness Optimization.” Structural and Multidisciplinary Optimization 46 (2): 159–170. doi: 10.1007/s00158-012-0760-1
   Web of Science ®Google Scholar
• Sigmund, O. 2001. “A 99 Line Topology Optimization Code Written in MATLAB.” Structural and Multidisciplinary Optimization 21 (2): 120–127. doi: 10.1007/s001580050176
   Web of Science ®Google Scholar
• Sun, G. Y., T. Pang, J. G. Fang, G. Y. Li, and Q. Li. 2017. “Parameterization of Criss-Cross Configurations for Multiobjective Crashworthiness Optimization.” International Journal of Mechanical Sciences 124-125: 147–157. doi: 10.1016/j.ijmecsci.2017.02.027
   Web of Science ®Google Scholar
• Sun, G. Y., F. X. Xu, G. Y. Li, and Q. Li. 2014. “Crashing Analysis and Multiobjective Optimization for Thin-Walled Structures with Functionally Graded Thickness.” International Journal of Impact Engineering 64: 62–74. doi: 10.1016/j.ijimpeng.2013.10.004
   Web of Science ®Google Scholar
• Sun, G. Y., H. L. Zhang, J. G. Fang, G. Y. Li, and Q. Li. 2017. “Multi-objective and Multi-case Reliability-Based Design Optimization for Tailor Rolled Blank (TRB) Structures.” Structural and Multidisciplinary Optimization 55: 1899–1916. doi: 10.1007/s00158-016-1592-1
   Web of Science ®Google Scholar
• Tong, L. Y., and Q. T. Luo. 2017. “A Novel Algorithm Using an Orthotropic Material Model for Topology Optimization.” Engineering Optimization 49 (9): 1523–1540. doi: 10.1080/0305215X.2016.1257213
   Web of Science ®Google Scholar
• Tovar, A. 2004. “Bone Remodeling as a Hybrid Cellular Automaton Optimization Process.” Ph.D. Thesis. University of Notre Dame, South Bend, IN.
   Google Scholar
• Tovar, A., G. L. Niebur, M. Sen, and J. E. Renaud. 2006. “Topology Optimization Using a Hybrid Cellular Automaton Method with Local Control Rules.” Journal of Mechanical Design 1286: 1205–1216. doi: 10.1115/1.2336251
   Web of Science ®Google Scholar
• Wang, H., G. Y. Li, and E. Li. 2010. “Time-Based Metamodeling Technique for Vehicle Crashworthiness Optimization.” Computer Methods in Applied Mechanics and Engineering 199: 2497–2509. doi: 10.1016/j.cma.2010.04.002
   Web of Science ®Google Scholar
• Wang, H., E. Li, and G. Y. Li. 2011. “Probability-Based Least Square Support Vector Regression Metamodeling Technique for Crashworthiness Optimization Problems.” Computational Mechanics 47: 251–263. doi: 10.1007/s00466-010-0532-y
   Web of Science ®Google Scholar
• Wang, S. Y., and K. Tai. 2004. “Graph Representation for Structural Topology Optimization Using Genetic Algorithms.” Computers and Structures 82: 1609–1622. doi: 10.1016/j.compstruc.2004.05.005
   Web of Science ®Google Scholar
• Wolfram, S. 2002. A New Kind of Science. Champaign, IL: Wolfram Media.
   Google Scholar
• Wu, S. Z., G. Zheng, G. Y. Sun, Q. Liu, G. Y. Li, and Q. Li. 2016. “On Design of Multi-cell Thin-Wall Structures for Crashworthiness.” International Journal of Impact Engineering 88: 102–117. doi: 10.1016/j.ijimpeng.2015.09.003
   Web of Science ®Google Scholar
• Yang, X. Y., Y. M. Xie, G. T. Liu, and P. J. Clarkson. 2003. “Perimeter Control of the Bidirectional Evolutionary Optimization Method.” Structural and Multidisciplinary Optimization 24: 430–440.
   Web of Science ®Google Scholar
• Yang, X. Y., Y. M. Xie, G. P. Steven, and Q. M. Querin. 1999. “Bidirectional Evolutionary Method for Stiffness Optimization.” AIAA Journal 37: 1483–1488. doi: 10.2514/2.626
   Web of Science ®Google Scholar
• Yin, H. F., G. L. Wen, Z. B. Liu, and Q. X. Qing. 2014. “Crashworthiness Optimization Design for Foam-Filled Multi-cell Thin-Walled Structures.” Thin-Walled Structures 75: 8–17. doi: 10.1016/j.tws.2013.10.022
   Web of Science ®Google Scholar
• Yin, H. F., Y. Y. Xiao, G. L. Wen, and Q. X. Qing. 2015. “Multiobjective Optimization for Foam-Filled Multi-cell Thin-Walled Structures Under Lateral Impact.” Thin-Walled Structures 94: 1–12. doi: 10.1016/j.tws.2015.03.031
   Web of Science ®Google Scholar
• Zhang, X., G. Cheng, and H. Zhang. 2006. “Theoretical Prediction and Numerical Simulation of Multi-cell Square Thin-Walled Structures.” Thin-Walled Structures 44 (11): 1185–1191. doi: 10.1016/j.tws.2006.09.002
   Web of Science ®Google Scholar
• Zhang, X., and H. Zhang. 2013. “Energy Absorption of Multi-cell Stub Columns Under Axial Compression.” Thin-Walled Structures 68 (10): 156–163. doi: 10.1016/j.tws.2013.03.014
   Web of Science ®Google Scholar
• Zhu, B. L., X. M. Zhang, S. Fatikow, and N. F. Wang. 2015. “Bi-directional Evolutionary Level Set Method for Topology Optimization.” Engineering Optimization 47 (3): 390–406. doi: 10.1080/0305215X.2014.892596
   Web of Science ®Google Scholar