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Research Papers: Design Automation

Topology Optimization of Multicell Tubes Under Out-of-Plane Crushing Using a Modified Artificial Bee Colony Algorithm

[+] Author and Article Information
Jianguang Fang

School of Aerospace, Mechanical
and Mechatronic Engineering,
The University of Sydney,
Sydney NSW 2006, Australia;
School of Civil and Environmental Engineering,
University of Technology Sydney,
Sydney NSW 2007, Australia
e-mail: fangjg87@gmail.com

Guangyong Sun

School of Aerospace, Mechanical
and Mechatronic Engineering,
The University of Sydney,
Sydney NSW 2006, Australia
e-mail: sgy800@126.com

Na Qiu

School of Automotive Studies,
Tongji University,
Shanghai 201804, China

Grant P. Steven

School of Aerospace, Mechanical
and Mechatronic Engineering,
The University of Sydney,
Sydney NSW 2006, Australia
e-mail: grant.steven@sydney.edu.au

Qing Li

School of Aerospace, Mechanical
and Mechatronic Engineering,
The University of Sydney,
Sydney NSW 2006, Australia
e-mail: qing.li@sydney.edu.au

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received February 9, 2016; final manuscript received March 10, 2017; published online May 18, 2017. Assoc. Editor: James K. Guest.

J. Mech. Des 139(7), 071403 (May 18, 2017) (16 pages) Paper No: MD-16-1115; doi: 10.1115/1.4036561 History: Received February 09, 2016; Revised March 10, 2017

Multicell tubal structures have generated increasing interest in engineering design for their excellent energy-absorbing characteristics when crushed through severe plastic deformation. To make more efficient use of the material, topology optimization was introduced to design multicell tubes under normal crushing. The design problem was formulated to maximize the energy absorption while constraining the structural mass. In this research, the presence or absence of inner walls were taken as design variables. To deal with such a highly nonlinear problem, a heuristic design methodology was proposed based on a modified artificial bee colony (ABC) algorithm, in which a constraint-driven mechanism was introduced to determine adjacent food sources for scout bees and neighborhood sources for employed and onlooker bees. The fitness function was customized according to the violation or the satisfaction of the constraints. This modified ABC algorithm was first verified by a square tube with seven design variables and then applied to four other examples with more design variables. The results demonstrated that the proposed heuristic algorithm is capable of handling the topology optimization of multicell tubes under out-of-plane crushing. They also confirmed that the optimized topological designs tend to allocate the material at the corners and around the outer walls. Moreover, the modified ABC algorithm was found to perform better than a genetic algorithm (GA) and traditional ABC in terms of best, worst, and average designs and the probability of obtaining the true optimal topological configuration.

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References

Alexander, J. M. , 1960, “ An Approximate Analysis of the Collapse of Thin Cylindrical Shells Under Axial Loading,” Q. J. Mech. Appl. Math., 13(1), pp. 10–15. [CrossRef]
Wierzbicki, T. , and Abramowicz, W. , 1983, “ On the Crushing Mechanics of Thin-Walled Structures,” ASME J. Appl. Mech., 50(4A), pp. 727–734. [CrossRef]
Abramowicz, W. , and Jones, N. , 1984, “ Dynamic Axial Crushing of Square Tubes,” Int. J. Impact Eng., 2(2), pp. 179–208. [CrossRef]
Abramowicz, W. , and Jones, N. , 1986, “ Dynamic Progressive Buckling of Circular and Square Tubes,” Int. J. Impact Eng., 4(4), pp. 243–270. [CrossRef]
Meng, Q. , Al-Hassani, S. T. S. , and Soden, P. D. , 1983, “ Axial Crushing of Square Tubes,” Int. J. Mech. Sci., 25(9–10), pp. 747–773. [CrossRef]
Andrews, K. R. F. , England, G. L. , and Ghani, E. , 1983, “ Classification of the Axial Collapse of Cylindrical Tubes Under Quasi-Static Loading,” Int. J. Mech. Sci., 25(9–10), pp. 687–696. [CrossRef]
Mamalis, A. G. , and Johnson, W. , 1983, “ The Quasi-Static Crumpling of Thin-Walled Circular Cylinders and Frusta Under Axial Compression,” Int. J. Mech. Sci., 25(9–10), pp. 713–732. [CrossRef]
Abramowicz, W. , and Wierzbicki, T. , 1989, “ Axial Crushing of Multicorner Sheet Metal Columns,” ASME J. Appl. Mech., 56(1), pp. 113–120. [CrossRef]
Kim, H.-S. , 2002, “ New Extruded Multi-Cell Aluminum Profile for Maximum Crash Energy Absorption and Weight Efficiency,” Thin-Walled Struct., 40(4), pp. 311–327. [CrossRef]
Tang, Z. , Liu, S. , and Zhang, Z. , 2013, “ Analysis of Energy Absorption Characteristics of Cylindrical Multi-Cell Columns,” Thin-Walled Struct., 62, pp. 75–84. [CrossRef]
Zhang, X. , and Zhang, H. , 2013, “ Energy Absorption of Multi-Cell Stub Columns Under Axial Compression,” Thin-Walled Struct., 68, pp. 156–163. [CrossRef]
Hou, S. J. , Li, Q. , Long, S. Y. , Yang, X. J. , and Li, W. , 2008, “ Multiobjective Optimization of Multi-Cell Sections for the Crashworthiness Design,” Int. J. Impact Eng., 35(11), pp. 1355–1367. [CrossRef]
Fang, J. , Gao, Y. , Sun, G. , Qiu, N. , and Li, Q. , 2015, “ On Design of Multi-Cell Tubes Under Axial and Oblique Impact Loads,” Thin-Walled Struct., 95, pp. 115–126. [CrossRef]
Qiu, N. , Gao, Y. , Fang, J. , Feng, Z. , Sun, G. , and Li, Q. , 2015, “ Crashworthiness Analysis and Design of Multi-Cell Hexagonal Columns Under Multiple Loading Cases,” Finite Elem. Anal. Des., 104, pp. 89–101. [CrossRef]
Fang, J. , Gao, Y. , Sun, G. , Zheng, G. , and Li, Q. , 2015, “ Dynamic Crashing Behavior of New Extrudable Multi-Cell Tubes With a Functionally Graded Thickness,” Int. J. Mech. Sci., 103, pp. 63–73. [CrossRef]
Davis, S. C. , Diegel, S. W. , and Boundy, R. G. , 2013, “ Transportation Energy Data Book,” Oak Ridge National Laboratory, Oak Ridge, TN.
Zhang, Y. , Zhu, P. , Chen, G. , and Lin, Z. , 2007, “ Study on Structural Lightweight Design of Automotive Front Side Rail Based on Response Surface Method,” ASME J. Mech. Des., 129(5), pp. 553–557. [CrossRef]
Mayer, R. R. , Kikuchi, N. , and Scott, R. A. , 1996, “ Application of Topological Optimization Techniques to Structural Crashworthiness,” Int. J. Numer. Methods Eng., 39(8), pp. 1383–1403. [CrossRef]
Pedersen, C. B. W. , 2003, “ Topology Optimization Design of Crushed 2D-Frames for Desired Energy Absorption History,” Struct. Multidiscip. Optim., 25(5), pp. 368–382. [CrossRef]
Soto, C. A. , 2004, “ Structural Topology Optimization for Crashworthiness,” Int. J. Crashworthiness, 9(3), pp. 277–283. [CrossRef]
Forsberg, J. , and Nilsson, L. , 2007, “ Topology Optimization in Crashworthiness Design,” Struct. Multidiscip. Optim., 33(1), pp. 1–12. [CrossRef]
Huang, X. , Xie, Y. M. , and Lu, G. , 2007, “ Topology Optimization of Energy-Absorbing Structures,” Int. J. Crashworthiness, 12(6), pp. 663–675. [CrossRef]
Patel, N. M. , Kang, B.-S. , Renaud, J. E. , and Tovar, A. , 2009, “ Crashworthiness Design Using Topology Optimization,” ASME J. Mech. Des., 131(6), p. 061013. [CrossRef]
Fang, J. , Sun, G. , Qiu, N. , Kim, N. H. , and Li, Q. , 2017, “ On Design Optimization for Structural Crashworthiness and Its State of the Art,” Struct. Multidiscip. Optim., 55(3), pp. 1091–1119. [CrossRef]
Karaboga, D. , and Basturk, B. , 2007, “ A Powerful and Efficient Algorithm for Numerical Function Optimization: Artificial Bee Colony (ABC) Algorithm,” J. Global Optim., 39(3), pp. 459–471. [CrossRef]
Karaboga, D. , and Basturk, B. , 2008, “ On the Performance of Artificial Bee Colony (ABC) Algorithm,” Appl. Soft Comput., 8(1), pp. 687–697. [CrossRef]
Fang, J. , Gao, Y. , Sun, G. , Xu, C. , Zhang, Y. , and Li, Q. , 2014, “ Optimization of Spot-Welded Joints Combined Artificial Bee Colony Algorithm With Sequential Kriging Optimization,” Adv. Mech. Eng., 6, p. 573694. [CrossRef]
Sun, G. , Li, G. , and Li, Q. , 2012, “ Variable Fidelity Design Based Surrogate and Artificial Bee Colony Algorithm for Sheet Metal Forming Process,” Finite Elem. Anal. Des., 59, pp. 76–90. [CrossRef]
Karaboga, D. , Gorkemli, B. , Ozturk, C. , and Karaboga, N. , 2014, “ A Comprehensive Survey: Artificial Bee Colony (ABC) Algorithm and Applications,” Artif. Intell. Rev., 42(1), pp. 21–57. [CrossRef]
Sonmez, M. , 2011, “ Discrete Optimum Design of Truss Structures Using Artificial Bee Colony Algorithm,” Struct. Multidiscip. Optim., 43(1), pp. 85–97. [CrossRef]
Duan, L. , Sun, G. , Cui, J. , Chen, T. , Cheng, A. , and Li, G. , 2016, “ Crashworthiness Design of Vehicle Structure With Tailor Rolled Blank,” Struct. Multidiscip. Optim., 53(2), pp. 321–338. [CrossRef]
Hallquist, J. O. , 2006, “ LS-DYNA Theory Manual,” Livermore Software Technology Corporation, Livermore, CA.
Belytschko, T. , Lin, J. I. , and Chen-Shyh, T. , 1984, “ Explicit Algorithms for the Nonlinear Dynamics of Shells,” Comput. Methods Appl. Mech. Eng., 42(2), pp. 225–251. [CrossRef]
Fang, J. , Gao, Y. , Sun, G. , Zhang, Y. , and Li, Q. , 2014, “ Parametric Analysis and Multiobjective Optimization for Functionally Graded Foam-Filled Thin-Wall Tube Under Lateral Impact,” Comput. Mater. Sci., 90, pp. 265–275. [CrossRef]
Santosa, S. P. , Wierzbicki, T. , Hanssen, A. G. , and Langseth, M. , 2000, “ Experimental and Numerical Studies of Foam-Filled Sections,” Int. J. Impact Eng., 24(5), pp. 509–534. [CrossRef]
Fenton, J. , and Hodkinson, R. , 2001, Lightweight Electric/Hybrid Vehicle Design, Butterworth/Heinemann, Oxford, UK.
Golberg, D. E. , 1989, Genetic Algorithms in Search, Optimization, and Machine Learning, Addison Wesley, Boston, MA.
Chandrasekaran, K. , Hemamalini, S. , Simon, S. P. , and Padhy, N. P. , 2012, “ Thermal Unit Commitment Using Binary/Real Coded Artificial Bee Colony Algorithm,” Electr. Power Syst. Res., 84(1), pp. 109–119. [CrossRef]
Wu, S. , Zheng, G. , Sun, G. , Liu, Q. , Li, G. , and Li, Q. , 2016, “ On Design of Multi-Cell Thin-Wall Structures for Crashworthiness,” Int. J. Impact Eng., 88, pp. 102–117. [CrossRef]
Karagiozova, D. , and Alves, M. , 2004, “ Transition From Progressive Buckling to Global Bending of Circular Shells Under Axial Impact—Part I: Experimental and Numerical Observations,” Int. J. Solids Struct., 41(5–6), pp. 1565–1580. [CrossRef]
Karagiozova, D. , and Alves, M.. , 2004, “ Transition From Progressive Buckling to Global Bending of Circular Shells Under Axial Impact—Part II: Theoretical Analysis,” Int. J. Solids Struct., 41(5–6), pp. 1581–1604. [CrossRef]
Abramowicz, W. , and Jones, N. , 1997, “ Transition From Initial Global Bending to Progressive Buckling of Tubes Loaded Statically and Dynamically,” Int. J. Impact Eng., 19(5–6), pp. 415–437. [CrossRef]

Figures

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Fig. 1

Finite element model of a multicell tube under out-of-plane loading

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Fig. 2

Initial configuration with seven design variables

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Fig. 3

Unconnected designs: (a) type A and (b) type B

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Fig. 4

Energy absorption versus mass fraction

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Fig. 5

Curves of fconsi: (a) the feasible and infeasible cases and (b) variation with respect to d1

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Fig. 6

Flowcharts of ABC based topology optimization for multicell tubes: (a) general procedures and (b) procedures for fitness evaluation

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Fig. 7

History of the objective function for the first example with different mass constraints

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Fig. 8

Comparison of impact force versus displacement curves for the first example: (a) w = 20% and (b) w = 40%

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Fig. 9

Design variables of the second example

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Fig. 10

History of the objective function for the second example

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Fig. 11

Comparison of impact force versus displacement curves for the second example (case III)

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Fig. 12

History of energy absorption and number of FEA

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Fig. 13

Design variables of the third example

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Fig. 14

History of the objective function for the third example

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Fig. 15

Comparison of impact force versus displacement curves for the third example (case IV)

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Fig. 16

Design variables of the fourth example

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Fig. 17

History of the objective function for the fourth example

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Fig. 18

Comparison of impact force versus displacement curves for the fourth example: (a) case I and (b) case II

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Fig. 19

Design variables of the fifth example

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Fig. 20

History of the objective function for the fifth example

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Fig. 21

Comparison of impact force versus displacement curves for the fifth example (case III)

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