Design and optimization of corrugated multi-cell gradient structures based on machine learning

YAN Kaibo; ZHOU Peng; LU Sisi; WANG Junjie; FAN Zhiwei

doi:10.11883/bzycj-2025-0388

Volume 46 Issue 6

Jun. 2026

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YAN Kaibo, ZHOU Peng, LU Sisi, WANG Junjie, FAN Zhiwei. Design and optimization of corrugated multi-cell gradient structures based on machine learning[J]. Explosion And Shock Waves, 2026, 46(6): 061442. doi: 10.11883/bzycj-2025-0388

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YAN Kaibo, ZHOU Peng, LU Sisi, WANG Junjie, FAN Zhiwei. Design and optimization of corrugated multi-cell gradient structures based on machine learning[J]. Explosion And Shock Waves, 2026, 46(6): 061442. doi: 10.11883/bzycj-2025-0388

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Design and optimization of corrugated multi-cell gradient structures based on machine learning

doi: 10.11883/bzycj-2025-0388

YAN Kaibo^{1, 2
,},
ZHOU Peng¹,
LU Sisi^{1, 2
,
,},
WANG Junjie¹,
FAN Zhiwei¹

1.
School of Mechatronics & Vehicle Engineering, Chongqing Jiaotong University, Chongqing 400074, China
2.
Chongqing Jialing Special Equipment Co., Ltd., Chongqing 400032, China

Received Date: 2025-12-02
Rev Recd Date: 2026-03-09

Available Online: 2026-03-19

Publish Date: 2026-06-05

Abstract

Abstract

To address the collision protection requirements in fields such as aeronautics and space, traffic transportation, and civil construction, a novel design method for the corrugated multi-cell gradient hexagonal tube (CMGHT) was proposed. The sinusoidal corrugated ribs were introduced into a conventional hexagonal tube, integrated with the functional gradient design concept to improve the energy absorption performance of the structure. First, the finite element model of the structure was established and numerical simulation analysis was conducted. Results indicate that under the same wall thickness condition, the key energy absorption indicators of CMGHT outperform existing structures significantly. Compared with the hexagonal tube (HT), the energy absorption (E_a), specific energy absorption (E_sa), mean crushing force ($ \overline{F} $), and crushing force efficiency (η) are improved by 390%, 76%, 395%, and 46%, respectively; Compared with the multi-cell hexagonal tube (MHT), the aforementioned indicators are increased by 121%, 58%, 121%, and 97%, respectively; Relative to a corrugated multi-cell hexagonal tube (CMHT), the enhancements are 7%, 7%, 8%, and 33% respectively, while the initial peak crushing force (F_max) is decreased by 18%. These results fully demonstrate its superior energy absorption performance. Subsequently, the geometric parameters of the ribs and outer tube were selected as design variables. A total of 540 sample sets were generated via full factorial experimental design, and a support vector machine (SVM) surrogate model was constructed. Combined with the crested porcupine optimization (CPO) algorithm, model optimization was completed to achieve the accurate prediction of the crashworthiness indicators for CMGHT. Finally, the multi-objective coati optimization algorithm (MOCOA) was adopted for multi-objective optimization to obtain the optimal combination of characteristic parameters. The optimization results show that compared with the CMGHT basic model without parameter optimization (the parameters are initially set based on the common range of engineering: rib thickness of 1 mm, rib amplitude of 3 mm, outer tube gradient thickness of 0.5 mm-1 mm-1.5 mm, outer tube length of 33.3 mm), the E_sa of the optimized structure is increased by 22%, the η is increased by 53%, and the $ \overline{F} $ is increased by 270%, which further verifies the effectiveness of the design method.
- multi-cell gradient structures,
- finite element simulation,
- machine learning,
- multi-objective optimization

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References(38)

References

[1]	朱擎, 李述涛, 陈叶青, 等. 细长薄壁弹冲击下高强钢-混凝土复合结构的厚度极限计算模型 [J]. 爆炸与冲击, 2026. DOI: 10.11883/bzycj-2025-0023. ZHU Q, LI S T, CHEN Y Q, et al. Calculation model for the thickness limit of high-strength steel-concrete composite structures under the impact of slender thin-walled projectiles [J]. Explosion and Shock Waves, 2026. DOI: 10.11883/bzycj-2025-0023.
[2]	LIU W Y, LIN Z Q, WANG N L, et al. Dynamic performances of thin-walled tubes with star-shaped cross section under axial impact [J]. Thin-Walled Structures, 2016, 100: 25–37. DOI: 10.1016/j.tws.2015.11.016.
[3]	RONG Y, LIU J X, LUO W, et al. Effects of geometric configurations of corrugated cores on the local impact and planar compression of sandwich panels [J]. Composites Part B: Engineering, 2018, 152: 324–335. DOI: 10.1016/j.compositesb.2018.08.130.
[4]	TIWARI G, IQBAL M A, GUPTA P K. Energy absorption characteristics of thin aluminium plate against hemispherical nosed projectile impact [J]. Thin-Walled Structures, 2018, 126: 246–257. DOI: 10.1016/j.tws.2017.04.014.
[5]	YAHAYA M A, RUAN D, LU G, et al. Response of aluminium honeycomb sandwich panels subjected to foam projectile impact-an experimental study [J]. International Journal of Impact Engineering, 2015, 75: 100–109. DOI: 10.1016/j.ijimpeng.2014.07.019.
[6]	MOHAMMADI H, AHMAD Z, PETRŮ M, et al. An insight from nature: honeycomb pattern in advanced structural design for impact energy absorption [J]. Journal of Materials Research and Technology, 2023, 22: 2862–2887. DOI: 10.1016/j.jmrt.2022.12.063.
[7]	XIANG Y F, YU T X, YANG L M. Comparative analysis of energy absorption capacity of polygonal tubes, multi-cell tubes and honeycombs by utilizing key performance indicators [J]. Materials & Design, 2016, 89: 689–696. DOI: 10.1016/j.matdes.2015.10.004.
[8]	TANG Z L, LIU S T, ZHANG Z H. Analysis of energy absorption characteristics of cylindrical multi-cell columns [J]. Thin-Walled Structures, 2013, 62: 75–84. DOI: 10.1016/j.tws.2012.05.019.
[9]	KHANCHEHZAR P, NIKNEJAD A, AMIRHOSSEINI S G. Influences of different internal stiffeners on energy absorption behavior of square sections during the flattening process [J]. Thin-Walled Structures, 2016, 107: 462–472. DOI: 10.1016/j.tws.2016.07.006.
[10]	JIN M Z, HOU X H, YIN G S, et al. Improving the crashworthiness of bio-inspired multi-cell thin-walled tubes under axial loading: experimental, numerical, and theoretical studies [J]. Thin-Walled Structures, 2022, 177: 109415. DOI: 10.1016/j.tws.2022.109415.
[11]	DENG X L, LIU W Y, JIN L. On the crashworthiness analysis and design of a lateral corrugated tube with a sinusoidal cross-section [J]. International Journal of Mechanical Sciences, 2018, 141: 330–340. DOI: 10.1016/j.ijmecsci.2018.03.001.
[12]	LI Z X, YAO S G, MA W, et al. Energy-absorption characteristics of a circumferentially corrugated square tube with a cosine profile [J]. Thin-Walled Structures, 2019, 135: 385–399. DOI: 10.1016/j.tws.2018.11.028.
[13]	BAYKASOGLU C, CETIN M T. Energy absorption of circular aluminium tubes with functionally graded thickness under axial impact loading [J]. International Journal of Crashworthiness, 2015, 20(1): 95–106. DOI: 10.1080/13588265.2014.982269.
[14]	XU F, TIAN X, LI G. Experimental study on crashworthiness of functionally graded thickness thin-walled tubular structures [J]. Experimental Mechanics, 2015, 55(7): 1339–1352. DOI: 10.1007/s11340-015-9994-3.
[15]	XU F X. Enhancing material efficiency of energy absorbers through graded thickness structures [J]. Thin-Walled Structures, 2015, 97: 250–265. DOI: 10.1016/j.tws.2015.09.020.
[16]	朱创, 丁喆, 黄垲轩. 基于智能优化算法的梯度点阵结构承载性能优化设计 [J]. 力学学报, 2025, 57(11): 2733–2745. DOI: 10.6052/0459-1879-25-256. ZHU C, DING Z, HUANG K X. Optimization design of load-bearing performance for graded lattice structures based on intelligent optimization algorithms [J]. Chinese Journal of Theoretical and Applied Mechanics, 2025, 57(11): 2733–2745. DOI: 10.6052/0459-1879-25-256.
[17]	WANG C, KOH J M, YU T T, et al. Material and shape optimization of bi-directional functionally graded plates by GIGA and an improved multi-objective particle swarm optimization algorithm [J]. Computer Methods in Applied Mechanics and Engineering, 2020, 366: 113017. DOI: 10.1016/j.cma.2020.113017.
[18]	MIAO F X, JIN Y. Crashworthiness analysis and structural optimization of thin-walled circular tubes with porous arrays [J]. Structures, 2024, 70: 107811. DOI: 10.1016/j.istruc.2024.107811.
[19]	LI P F, XIAO J M. Crashworthiness design and multi-objective optimization of bionic thin-walled hybrid tube structures [J]. Computer Modeling in Engineering & Sciences, 2024, 139(1): 999–1016. DOI: 10.32604/cmes.2023.044059.
[20]	YIN H F, XIAO Y Y, WEN G L, et al. Crushing analysis and multi-objective optimization design for bionic thin-walled structure [J]. Materials & Design, 2015, 87: 825–834. DOI: 10.1016/j.matdes.2015.08.095.
[21]	ZHANG Z Y, FENG C, ZHAO L B, et al. Crashworthiness analysis and optimization design of special-shaped thin-walled tubes by experiments and numerical simulation [J]. Thin-Walled Structures, 2024, 205: 112240. DOI: 10.1016/j.tws.2024.112240.
[22]	HA N S, LU G X. Thin-walled corrugated structures: a review of crashworthiness designs and energy absorption characteristics [J]. Thin-Walled Structures, 2020, 157: 106995. DOI: 10.1016/j.tws.2020.106995.
[23]	ZHANG X, ZHANG H. Energy absorption of multi-cell stub columns under axial compression [J]. Thin-Walled Structures, 2013, 68: 156–163. DOI: 10.1016/j.tws.2013.03.014.
[24]	FU J, LIU Q, LIUFU K M, et al. Design of bionic-bamboo thin-walled structures for energy absorption [J]. Thin-Walled Structures, 2019, 135: 400–413. DOI: 10.1016/j.tws.2018.10.003.
[25]	ABRAMOWICZ W. The effective crushing distance in axially compressed thin-walled metal columns [J]. International Journal of Impact Engineering, 1983, 1(3): 309–317. DOI: 10.1016/0734-743X(83)90025-8.
[26]	李昊霖, 陈洪胜, 柴斐, 等. 带网格内筋铝合金壳体热旋压组织与性能 [J]. 航空学报, 2026, 47(3): 431981. DOI: 10.7527/S1000-6893.2025.31981. LI H L, CHEN H S, CHAI F, et al. Microstructure and performance of hot spinning of aluminum alloy shell with internal grid reinforcement [J]. Acta Aeronautica et Astronautica Sinica, 2026, 47(3): 431981. DOI: 10.7527/S1000-6893.2025.31981.
[27]	YANG W D, LOU Z Z, JI B. A multi-factor analysis model of quantitative investment based on GA and SVM [C]//Proceedings of 2nd International Conference on Image, Vision and Computing (ICIVC). Chengdu: IEEE, 2017: 1152–1155. DOI: 10.1109/ICIVC.2017.7984734.
[28]	KAREEM F Q, ABDULAZEEZ A M. Ultrasound medical images classification based on deep learning algorithms: a review [J]. Fusion: Practice and Applications, 2021, 3(1): 29–42. DOI: 10.54216/FPA.030102.
[29]	TAO P Y, SUN Z, SUN Z X. An improved intrusion detection algorithm based on GA and SVM [J]. IEEE Access, 2018, 6: 13624–13631. DOI: 10.1109/ACCESS.2018.2810198.
[30]	ZHANG D K, HAN Y, WANG C L, et al. Time series prediction of tunnel surrounding rock deformation using CPO-CLA integrated model [J]. Journal of Rock Mechanics and Geotechnical Engineering, 2025, 17(12): 7915–7930. DOI: 10.1016/j.jrmge.2025.03.050.
[31]	ZHENG M, LI T, SUN L P, et al. An automatic sampling ratio detection method based on genetic algorithm for imbalanced data classification [J]. Knowledge-Based Systems, 2021, 216: 106800. DOI: 10.1016/j.knosys.2021.106800.
[32]	ZHANG D R, MA G, DENG Z R, et al. A self-adaptive gradient-based particle swarm optimization algorithm with dynamic population topology [J]. Applied Soft Computing, 2022, 130: 109660. DOI: 10.1016/j.asoc.2022.109660.
[33]	DAS S C, KHAN M A A, SHAIKH A A, et al. Interval valued inventory model with different payment strategies for green products under interval valued Grey Wolf optimizer algorithm fitness function [J]. Egyptian Informatics Journal, 2024, 28: 100561. DOI: 10.1016/j.eij.2024.100561.
[34]	TAN H L, HE Z C, LI E, et al. Crashworthiness design and multi-objective optimization of a novel auxetic hierarchical honeycomb crash box [J]. Structural and Multidisciplinary Optimization, 2021, 64(4): 2009–2024. DOI: 10.1007/s00158-021-02961-9.
[35]	范升阳, 栗建桥. 薄壁椭球壳在冲击载荷作用下的动态变形模型 [J]. 爆炸与冲击, 2025, 45(8): 083301. DOI: 10.11883/bzycj-2024-0062. FAN S Y, LI J Q. Dynamic deformation model of thin-walled ellipsoidal shells under impact loading [J]. Explosion and Shock Waves, 2025, 45(8): 083301. DOI: 10.11883/bzycj-2024-0062.
[36]	刘苗苗, 张玉莹, 郭景峰, 等. 融合多策略改进的自适应狮群优化算法 [J]. 北京邮电大学学报, 2024, 47(1): 85–93. DOI: 10.13190/j.jbupt.2022-276. LIU M M, ZHANG Y Y, GUO J F, et al. Improved adaptive lion swarm optimization algorithm based on multi-strategy [J]. Journal of Beijing University of Posts and Telecommunications, 2024, 47(1): 85–93. DOI: 10.13190/j.jbupt.2022-276.
[37]	DEHGHANI M, MONTAZERI Z, TROJOVSKÁ E, et al. Coati optimization algorithm: a new bio-inspired metaheuristic algorithm for solving optimization problems [J]. Knowledge-Based Systems, 2023, 259: 110011. DOI: 10.1016/j.knosys.2022.110011.
[38]	DEB K, PRATAP A, AGARWAL S, et al. A fast and elitist multiobjective genetic algorithm: NSGA-II [J]. IEEE Transactions on Evolutionary Computation, 2002, 6(2): 182–197. DOI: 10.1109/4235.996017.