Skip to main content
Log in

Variable Cross-Section Rectangular Beam and Sensitivity Analysis for Lightweight Design of Bus Frame

  • Published:
International Journal of Automotive Technology Aims and scope Submit manuscript

Abstract

Timoshenko beam element of variable cross-section rectangular tube is developed and applied in the lightweight design of bus frame in this paper. Firstly, the finite element formulations of variable cross-section beam (VCB) are derived under the loadsteps of axial deformation, torsional deformation and bending deformation. Secondly, bending deformation experiment and its detailed shell finite element model (FEM) simulation of variable cross-section rectangular tube were conducted; and the proposed VCB, detailed shell FEM and experimental results can be highly consistent. Thirdly, VCBs are used to substitute for parts of the uniform ones in a bus frame. An innovatively lightweight bus frame is obtained and all the performance responses are improved simultaneously. Finally, rollover analysis further shows the advantage of variable cross-section bus frame in crashworthiness design.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Arbabi, F. and Li, F. (1991). Buckling of variable crosssection columns: Integral-equation approach. J. Structural Engineering 117, 8, 2426–2441.

    Article  Google Scholar 

  • Bai, J., Li, Y. and Zuo, W. (2017). Cross-sectional shape optimisation for thin-walled beam crashworthiness with stamping constraints using genetic algorithm. Int. J. Vehicle Design 73, 1–3, 76−95.

    Article  Google Scholar 

  • Balesdent, M. and Chriette, A. (2012). A survey of multidisciplinary design optimization methods in launch vehicle design. Structural and Multidisciplinary Optimization 45, 5, 619–642.

    Article  MathSciNet  MATH  Google Scholar 

  • Chen, W. and Zuo, W. (2014). Component sensitivity analysis of conceptual vehicle body for lightweight design under static and dynamic stiffness demands. Int. J. Vehicle Design 66, 2, 107–123.

    Article  Google Scholar 

  • Choi, I. S., Jang, G. W., Choi, S., Shin, D. and Kim, Y. Y. (2016). Higher order analysis of thin-walled beams with axially varying quadrilateral cross sections. Computers & Structures, 179, 127–139.

    Article  Google Scholar 

  • Eisenberger, M. (1990). Exact static and dynamic stiffness matrices for general variable cross section members. AIAA Journal 28, 6, 1105–1109.

    Article  MATH  Google Scholar 

  • Eisenberger, M. (1991). Buckling loads for variable crosssection members with variable axial forces. Int. J. Solids and Structures 27, 2, 135–143.

    Article  Google Scholar 

  • Eisenberger, M. (1995). Dynamic stiffness matrix for variable cross-section Timoshenko beams. Communications in Numerical Methods in Engineering 11, 6, 507–513.

    Article  MATH  Google Scholar 

  • Gaines, J. and Volterra, E. (1966). Transverse vibrations of cantilever bars of variable cross section. J. Acoustical Society of America 39, 4, 674–679.

    Article  Google Scholar 

  • Kim, H. and Jang, G. W. (2017). Higher-order thin-walled beam analysis for axially varying generally shaped cross sections with straight cross-section edges. Computers & Structures, 189, 83–100.

    Article  Google Scholar 

  • Kim, J. H. and Kim, Y. Y. (1999). Analysis of thin-walled closed beams with general quadrilateral cross sections. J. Applied Mechanics 66, 4, 904–912.

    Article  Google Scholar 

  • Kim, J. H. and Kim, Y. Y. (2000). One-dimensional analysis of thin-walled closed beams having general cross-sections. Int. J. Numerical Methods in Engineering 49, 5, 653–668.

    Article  MATH  Google Scholar 

  • Lyu, N., Lee, B. and Saitou, K. (2006). Optimal subassembly partitioning of space frame structures for in-process dimensional adjustability and stiffness. J. Mechanical Design 128, 3, 527–535.

    Article  Google Scholar 

  • Lyu, N. and Saitou, K. (2005). Topology optimization of multicomponent beam structure via decompositionbased assembly synthesis. J. Mechanical Design 127, 2, 170–183.

    Article  Google Scholar 

  • Mayyas, A., Shen, Q., Mayyas, A., Abdelhamid, M., Shan, D., Qattawi, A. and Omar, M. (2011). Using quality function deployment and analytical hierarchy process for material selection of body-in-white. Materials & Design 32, 5, 2771–2782.

    Article  Google Scholar 

  • Ronagh, H., Bradford, M. and Attard, M. (2000a). Nonlinear analysis of thin-walled members of variable cross-section. Part I: Theory. Computers & Structures 77, 3, 285–299.

    Google Scholar 

  • Ronagh, H., Bradford, M. and Attard, M. (2000b). Nonlinear analysis of thin-walled members of variable cross-section. Part II: Application. Computers & Structures 77, 3, 301–313.

    Google Scholar 

  • Takezawa, A., Nishiwaki, S., Izui, K. and Yoshimura, M. (2007). Structural optimization based on topology optimization techniques using frame elements considering cross-sectional properties. Structural and Multidisciplinary Optimization 34, 1, 41–60.

    Article  Google Scholar 

  • Thomas, H., Zhou, M. and Schramm, U. (2002). Issues of commercial optimization software development. Structural and Multidisciplinary Optimization 23, 2, 97–110.

    Article  Google Scholar 

  • Torstenfelt, B. and Klarbring, A. (2007). Conceptual optimal design of modular car product families using simultaneous size, shape and topology optimization. Finite Elements in Analysis and Design 43, 14, 1050–1061.

    Article  MathSciNet  Google Scholar 

  • Wang, H., Li, E., Li, G. and Zhong, Z. (2008a). Optimization of sheet metal forming processes by the use of space mapping based metamodeling method. Int. J. Advanced Manufacturing Technology 39, 7, 642–655.

    Google Scholar 

  • Wang, H., Li, G. and Zhong, Z. (2008b). Optimization of sheet metal forming processes by adaptive response surface based on intelligent sampling method. J. Materials Processing Technology 197, 1–3, 77−88.

    Article  Google Scholar 

  • Zou, M., Wei, C., Li, J., Xu, S. and Zhang, X. (2015). The energy absorption of bamboo under dynamic axial loading. Thin-Walled Structures, 95, 255–261.

    Article  Google Scholar 

  • Zou, M., Xu, S., Wei, C., Wang, H. and Liu, Z. (2016). A bionic method for the crashworthiness design of thinwalled structures inspired by bamboo. Thin-Walled Structures, 101, 222–230.

    Article  Google Scholar 

  • Zuo, W. (2013). An object-oriented graphics interface design and optimization software for cross-sectional shape of automobile body. Advances in Engineering Software, 64, 1–10.

    Article  Google Scholar 

  • Zuo, W. (2015). Bi-level optimization for the crosssectional shape of a thin-walled car body frame with static stiffness and dynamic frequency stiffness constraints. Proc. Institution of Mechanical Engineers, Part D: J. Automobile Engineering 229, 8, 1046–1059.

    Google Scholar 

  • Zuo, W. and Bai, J. (2016). Cross-sectional shape design and optimization of automotive body with stamping constraints. Int. J. Automotive Technology 17, 6, 1003–1011.

    Article  Google Scholar 

  • Zuo, W., Bai, J. and Li, B. (2014). A hybrid OC–GA approach for fast and global truss optimization with frequency constraints. Applied Soft Computing 14, Part C, 528−535.

    Google Scholar 

  • Zuo, W., Li, W., Xu, T., Xuan, S. and Na, J. (2012). A complete development process of finite element software for body-in-white structure with semi-rigid beams in.NET framework. Advances in Engineering Software 45, 1, 261–271.

    Article  Google Scholar 

  • Zuo, W. and Saitou, K. (2017). Multi-material topology optimization using ordered SIMP interpolation. Structural and Multidisciplinary Optimization 55, 2, 477–491.

    Article  MathSciNet  Google Scholar 

  • Zuo, W., Yu, J. and Saitou, K. (2016). Stress sensitivity analysis and optimization of automobile body frame consisting of rectangular tubes. Int. J. Automotive Technology 17, 5, 843–851.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Wenjie Zuo.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zuo, W., Fang, J., Zhong, M. et al. Variable Cross-Section Rectangular Beam and Sensitivity Analysis for Lightweight Design of Bus Frame. Int.J Automot. Technol. 19, 1033–1040 (2018). https://doi.org/10.1007/s12239-018-0100-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12239-018-0100-6

Key Words

Navigation