Structural and Multidisciplinary Optimization

, Volume 59, Issue 5, pp 1789–1812 | Cite as

Parametric modeling and multiobjective crashworthiness design optimization of a new front longitudinal beam

  • Libin Duan
  • Haobin JiangEmail author
  • Guoqing Geng
  • Xuerong Zhang
  • Zhanjiang Li
Industrial Application


The front longitudinal beam (FLB) is the most important energy-absorbing and crashing force–transmitting structure of a vehicle under front-impact collision. For better weight reduction and crashworthiness of the FLB, a new structure, variable rolled blank–variable cross-sectional shape FLB (VRB-VCS FLB), is proposed. It has both the continuous variation of thickness and variable cross-sectional shape in space. As the thickness distribution and cross-sectional shape change continuously, the proposed structure evolves into three distinct forms, i.e., the uniform-thickness FLB, variable rolled blank FLB, and variable cross-sectional shape FLB. However, literature on parametric modeling and crashworthiness design optimization of the VRB-VCS FLB is very limited. This paper proposes a parametric modeling method of VRB-VCS FLB with manufacturing constraints. Multiobjective crashworthiness design optimization is performed to explore the lightweightness and crashworthiness performance of the VRB-VCS FLB. Firstly, thickness distribution and cross-sectional shape parameters are defined. Secondly, local parametric subsystem front-impact model is established to balance accuracy and efficiency. Thirdly, a multiobjective optimization model of VRB-VCS FLB is constructed. Finally, a fully automated design of experiment platform is established to improve the data collection efficiency, and epsilon-support vector regression technique and non-dominated sorting genetic algorithm II are utilized to search the Pareto optimal frontier. The numerical results show that the lightweightness and crashworthiness of the VRB-VCS FLB are significantly improved when compared with the uniform-thickness FLB.


Parametric modeling Multiobjective crashworthiness optimization Front longitudinal beam (FLB) Variable rolled blank (VRB) Variable cross-sectional shape (VCS) 



Constant-thickness zone


Front longitudinal beam


FLB inner plate


FLB outer plate


Multiobjective optimization


Non-dominated sorting genetic algorithm II


Optimal Latin hypercube sampling


Peak crushing force


Specific energy absorption


Thickness transition zone


Uniform-thickness FLB

UT FLB-inner

Uniform-thickness FLB inner plate


Variable cross-sectional shape


Variable cross-sectional shape FLB


Variable rolled blank


Variable rolled blank FLB


Variable rolled blank–variable cross-sectional shape FLB


VRB-VCS FLB inner plate


Epsilon-support vector regression


Funding information

The authors would like to thank the support of National Natural Science Foundation of China (Grant No. 51805221) and Research Project funded by China Postdoctoral Science Foundation (No. 2018M640460). The authors also wish to thank Jiangsu Planned Projects for Postdoctoral Research Fund (NO. 2018K018C). This work was supported by the high-performance computing platform of Jiangsu University.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Libin Duan
    • 1
  • Haobin Jiang
    • 1
    Email author
  • Guoqing Geng
    • 1
  • Xuerong Zhang
    • 1
  • Zhanjiang Li
    • 2
  1. 1.School of Automotive and Traffic EngineeringJiangsu UniversityZhenjiangChina
  2. 2.Nanjing Yueboo Power System Co., Ltd.NanjingChina

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