Gauge sensitivity analysis and optimization of the modular automotive body with different loadings

  • Yu Liu
  • Zijian LiuEmail author
  • Haolong Zhong
  • Huan Qin
  • Cheng Lv
Industrial Application


The structural optimization method based on sensitivity analysis is an effective way to reduce the mass of automotive body structure. In this paper, an effective structural optimization method is proposed to facilitate the lightweight design of modular automotive body, where gauge sensitivity analysis values are used to determine the optimized direction to increase or decrease the thickness of each beam element in the body model. An object-oriented MATLAB toolbox constructed in our previous study is adopted as a black box for the structural analysis and optimization of the body-in-white (BIW) model, in which the beam element sensitivity values of BIW structure under different loading conditions are fast calculated by the method of reverberation ray matrix (MRRM) and the finite difference method (FDM). Then, the optimized direction of each beam element is identified, and a structural optimization model is formulated and solved by the genetic algorithm (GA). In order to verify the effectiveness of this method, a simplified modular automotive body model is constructed to implement the performance indexes comparison between the initial body model and optimized body model. The analysis results show that this method is feasible and effective for the optimal design of modular automotive body structure.


Gauge sensitivity analysis Modular automotive body Structural optimization Method of reverberation ray matrix Finite difference method Genetic algorithm 



This research is supported by the National Natural Science Foundation of China (no. 51475152).


  1. Al-Zaher A, Elmaraghy W (2014) Design method of under-body platform automotive framing systems. Proc CIRP 17:380–385CrossRefGoogle Scholar
  2. Apostol V, Santos JLT, Paiva M (2002) Sensitivity analysis and optimization of truss/beam components of arbitrary cross-section II. Shear stresses. Comput Struct 80(5):391–401CrossRefGoogle Scholar
  3. Besharati SR, Dabbagh V, Amini H et al (2016) Multi-objective selection and structural optimization of the gantry in a gantry machine tool for improving static, dynamic, and weight and cost performance. Concurr Eng 24(1):83–93CrossRefGoogle Scholar
  4. Cetin OL, Saitou K (2004) Decomposition-based assembly synthesis for structural modularity. J Mech Des 126:234–243. CrossRefGoogle Scholar
  5. Chen W, Zuo WJ (2014) Component sensitivity analysis of conceptual vehicle body for lightweight design under static and dynamic stiffness demands. Int J Veh Des 66(2):107–123CrossRefGoogle Scholar
  6. Cheng GD, Liu YW (1987) A new computational scheme for sensitivity analysis. Eng Optim 12(3):219–234CrossRefGoogle Scholar
  7. Doke P, Fard M, Jazar R (2012) Vehicle concept modeling: a new technology for structures weight reduction. Proc Eng 49:287–293CrossRefGoogle Scholar
  8. Donders S, Takahashi Y, Hadjit R et al (2009) A reduced beam and joint concept modeling approach to optimize global vehicle body dynamics. Finite Elem Anal Des 45(6–7):439–455CrossRefGoogle Scholar
  9. Fellini R, Kokkolaras M, Michelena N et al (2004) A sensitivity-based commonality strategy for family products of mild variation, with application to automotive body structures. Struct Multidiscip Optim 27(1–2):89–96CrossRefGoogle Scholar
  10. Hou WB, Zhang HZ, Chi RF, Hu P (2009) Development of an intelligent CAE system for auto-body concept design. Int J Automot Technol 10(2):175–180CrossRefGoogle Scholar
  11. Howard SM, Pao YH (1998) Analysis and experiments on stress waves in planar trusses. J Eng Mech 124(8):884–891CrossRefGoogle Scholar
  12. Liu YC, Glass G (2011) Effects of wall thickness and geometric shape on thin-walled parts structural performance. Thin-Walled Struct 49(1):223–231CrossRefGoogle Scholar
  13. Liu Y, Liu ZJ, Qin H et al (2018) An efficient structural optimization approach for the modular automotive body conceptual design. Struct Multidiscip Optim 58(3):1275–1289CrossRefGoogle Scholar
  14. Martensson P, Zenkert D, Akermo M (2015) Integral versus differential design for high-volume manufacturing of composite structures. J Compos Mater 49(23):2897–2908CrossRefGoogle Scholar
  15. Miao F, Sun G, Zhu P (2016) Developed reverberation-ray matrix analysis on transient responses of laminated composite frame based on the first-order shear deformation theory. Compos Struct 143:255–271CrossRefGoogle Scholar
  16. Mihaylova P, Baldanzini N, Pratellesi A, Pierini M (2012) Beam bounding box – a novel approach for beam concept modeling and optimization handling. Finite Elem Anal Des 60(9):13–24CrossRefGoogle Scholar
  17. Mohan R, Venkatesan H, Mahadevan S (2016) New methodology for light weight solutions to improve BIW structural performance using bulk head optimization. J Mech Sci Technol 30(8):3533–3537CrossRefGoogle Scholar
  18. Mundo D, Hadjit R, Donders S et al (2009) Simplified modelling of joints and beam-like structures for BIW optimization in a concept phase of the vehicle design process. Finite Elem Anal Des 45(6–7):456–462CrossRefGoogle Scholar
  19. Munster M, Schaffer M, Kopp G et al (2016) New approach for a comprehensive method for urban vehicle concepts with electric powertrain and their necessary vehicle structures. Transp Res Proc 14:3686–3695CrossRefGoogle Scholar
  20. Pao YH, Sun G (2003) Dynamic bending strains in planar trusses with pinned or rigid joints. J Eng Mech 129(3):324–332CrossRefGoogle Scholar
  21. Pao YH, Keh DC, Howard SM (1999) Dynamic response and wave propagation in plane trusses and frames. AIAA J 37(5):594–603CrossRefGoogle Scholar
  22. Park D, Jeong SH, Chang WK et al (2016) Material arrangement optimization for weight minimization of an automotive body in white using a bi-level design strategy. Proc Inst Mech Eng Part D J Autom Eng, Part D: Journal of Automobile Engineering 230(3):395–405CrossRefGoogle Scholar
  23. Qin H, Liu ZJ, Liu Y, Zhong HL (2017) An object-oriented MATLAB toolbox for automotive body conceptual design using distributed parallel optimization. Adv Eng Softw 106:19–32CrossRefGoogle Scholar
  24. Qin H, Guo Y, Liu ZJ et al (2018) Shape optimization of automotive body frame using an improved genetic algorithm optimizer. Adv Eng Softw 121:235–249CrossRefGoogle Scholar
  25. Sergeyev O, Mroz Z (2000) Sensitivity analysis and optimal design of 3D frame structures for stress and frequency constraints. Comput Struct 75(2):167–185CrossRefGoogle Scholar
  26. Shao D, Hu S, Wang Q et al (2017) Free vibration of refined higher-order shear deformation composite laminated beams with general boundary conditions. Compos Part B 108:75–90CrossRefGoogle Scholar
  27. Tang D, Yao XL, Wu GX, Peng Y (2017) Free and forced vibration analysis of multi-stepped circular cylindrical shells with arbitrary boundary conditions by the method of reverberation-ray matrix. Thin-Walled Struct 116:154–168CrossRefGoogle Scholar
  28. Torstenfelt B, Klarbring A (2006) Structural optimization of modular product families with application to car space frame structures. Struct Multidiscip Optim 32(2):133–140CrossRefGoogle Scholar
  29. Torstenfelt B, Klarbring A (2007) Conceptual optimal design of modular car product families using simultaneous size, shape and topology optimization. Finite Elem Anal Des 43(14):1050–1061MathSciNetCrossRefGoogle Scholar
  30. Wang CQ, Wang DF, Zhang S (2016) Design and application of lightweight multi-objective collaborative optimization for a parametric body-in-white structure. Proc Inst Mech Eng Part D J Autom Eng 230(2):273–288CrossRefGoogle Scholar
  31. Xia Y, Hao H (2000) Measurement selection for vibration-based structural damage identification. J Sound Vib 236(1):89–104CrossRefGoogle Scholar
  32. Xia L, Zhang L, Xia Q, Shi TL (2018) Stress-based topology optimization using bi-directional evolutionary structural optimization method. Comput Methods Appl Mech Eng 333:356–370MathSciNetCrossRefGoogle Scholar
  33. Yoshimura M, Nishiwaki S, Izui K (2005) A multiple cross-sectional shape optimization method for automotive body frames. J Mech Des 127(1):49–57CrossRefGoogle Scholar
  34. Zhang SY (2013) Improving vehicle body stiffness with reinforcements at optimal locations based upon local gauge sensitivity. Int J Mech Appl 3(4):81–87. Google Scholar
  35. Zhang SY, Jr GP (2009) A study of the effect of elastic instability on stiffness-based gauge sensitivity indices for vehicle body structure assessment. Thin-Walled Struct 47(12):1590–1596CrossRefGoogle Scholar
  36. Zhang SY, Jr GP (2011) Gauge sensitivity indices and application for assessing vehicle body structural stiffness. Int J Veh Des 57(1):1–16CrossRefGoogle Scholar
  37. Zhang LM, Wu XG, Zhu HP et al (2017) Performing global uncertainty and sensitivity analysis from given data in tunnel construction. J Comput Civ Eng 31(6).
  38. Zuo WJ (2013) An object-oriented graphics interface design and optimization software for cross-sectional shape of automobile body. Adv Eng Softw 64:1–10CrossRefGoogle Scholar
  39. Zuo WJ (2015) Bi-level optimization for the cross-sectional shape of a thin-walled car body frame with static stiffness and dynamic frequency stiffness constraints. Proc Inst Mech Eng Part D J Autom Eng 229(8):1046–1059CrossRefGoogle Scholar
  40. Zuo WJ, Bai JT (2016) Cross-sectional shape design and optimization of automotive body with stamping constraints. Int J Automot Technol 17(6):1003–1011CrossRefGoogle Scholar
  41. Zuo J, Yao WX, Xia TX (2016) A sensitivity-based coordination method for optimization of product families. Eng Optim 48(7):1145–1163MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Yu Liu
    • 1
  • Zijian Liu
    • 1
    Email author
  • Haolong Zhong
    • 1
  • Huan Qin
    • 1
  • Cheng Lv
    • 2
  1. 1.State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, College of Mechanical and Vehicle EngineeringHunan UniversityChangshaChina
  2. 2.The School of Robot Engineering and Mechanical-Electrical EngineeringChongqing University of Arts and SciencesChongqingChina

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