Abstract
This paper presents a multi-material topology optimisation (MMTO) process for the lightweight design of an electric bus roof structure including the self-weight. The usage of electric buses is increasing owing to environmental issues. However, it is challenging to design a lightweight structure, because the heavy battery pack mounted on the roof increases the deformation and reduces the safety. In a design including the self-weight, the appropriate distribution of multiple materials improves the performance more than that of a single material. The MMTO method has been applied to identify the optimal distribution of multiple materials. However, in the real-engineering problem, only a simple objective function such as compliance and a single constraint function such as the volume of material have been considered, whereas the mass reduction is the most important factor. In this paper, an MMTO process is proposed for the lightweight design of the bus roof structure to consider multiple displacement constraints including the self-weight. To control the complexity of the distribution of multiple materials for improving the manufacturability, the welding surface function is proposed. An optimisation process was constructed that can handle the complex finite-element model and multiple load cases, and it was validated according to the well-known compliance minimisation problem. Mass reduction was achieved via the lightweight optimisation, and the interfacial area between the different materials was reduced by employing the welding surface function.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aulig N, Nutwell E, Menzel S, Detwiler D (2018) Preference-based topology optimization for vehicle concept design with concurrent static and crash load cases. Struct Multidiscip Optim 57:251–266. https://doi.org/10.1007/s00158-017-1751-z
Bendsoe MP, Sigmund O (1999) Material interpolation schemes in topology optimization. Arch Appl Mech 69:635–654. https://doi.org/10.1007/s004190050248
Bendsoe MP, Sigmund O (2004) Topology optimization: theory, Methods and Applications. Springer, Berlin
Bruyneel M, Duysinx P (2005) Note on topology optimization of continuum structures including self-weight. Struct Multidiscip Optim 29:245–256. https://doi.org/10.1007/s00158-004-0484-y
Cavazzuti M, Baldini A, Bertocchi E, Costi D, Torricelli E, Moruzzi P (2011) High performance automotive chassis design: a topology optimization based approach. Struct Multidiscip Optim 44:45–56. https://doi.org/10.1007/s00158-010-0578-7
Cherukuri AK (2014) Potential weight saving in buses through multi material approach. Paper presented at the SAE 2014 commercial vehicle engineering congress. https://doi.org/10.4271/2014-01-2453
Chuang C-H, Chen S, Yang R-J, Vogiatzis P (2018) Topology optimization with additive manufacturing consideration for vehicle load path development. Int J Numer Methods Eng 113:1434–1445. https://doi.org/10.1002/nme.5549
Deaton JD, Grandhi RV (2014) A survey of structural and multidisciplinary continuum topology optimization: post 2000. Struct Multidiscip Optim 49:1–38. https://doi.org/10.1007/s00158-013-0956-z
Gao T, Zhang WH (2011) A mass constraint formulation for structural topology optimization with multiphase materials. Int J Numer Methods Eng 88:774–796. https://doi.org/10.1002/nme.3197
Gauchia A, Diaz V, Boada MJL, Boada BL (2010) Torsional stiffness and weight optimization of a real bus structure. Int J Automot Technol 11:41–47. https://doi.org/10.1007/s12239-010-0006-4
Ko HY, Shin KB, Jeon KW, Cho SH (2009) A study on the crashworthiness and rollover characteristics of low-floor bus made of sandwich composites. J Mech Sci Technol 23:2686–2693. https://doi.org/10.1007/s12206-009-0731-7
Kubo S, Yaji K, Yamada T, Izui K, Nishiwaki S (2017) A level set-based topology optimization method for optimal manifold designs with flow uniformity in plate-type microchannel reactors. Struct Multidiscip Optim 55:1311–1327. https://doi.org/10.1007/s00158-016-1577-0
Kumar A, Sharma S (2017) Development of methodology for full bus bodyoptimisation and strengthening by numerical simulation. In: Paper presented at the WCX™ 17: SAE world congress experience. https://doi.org/10.4271/2017-01-1341
Lan F, Chen J, Lin J (2004) Comparative analysis for bus side structures and lightweight optimization. Proceedings of the Institution of Mechanical Engineers Part D: Journal of Automobile Engineering 218:1067–1075. https://doi.org/10.1177/095440700421801001
Li C, Kim IY (2018a) Multi-material topology optimization for automotive design problems. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering 232:1950–1969. https://doi.org/10.1177/0954407017737901
Li DZ, Kim IY (2018b) Multi-material topology optimization for practical lightweight design. Struct Multidiscip Optim 58:1081–1094. https://doi.org/10.1007/s00158-018-1953-z
Lim S, Yamada T, Min S, Nishiwaki S (2011) Topology optimization of a magnetic actuator based on a level set and phase-field approach. IEEE Trans Magn 47:1318–1321. https://doi.org/10.1109/TMAG.2010.2097583
Liu JK, Ma YS (2018) A new multi-material level set topology optimization method with the length scale control capability. Comput Methods Appl Mech Eng 329:444–463. https://doi.org/10.1016/j.cma.2017.10.011
Liu J et al (2018) Current and future trends in topology optimization for additive manufacturing. Struct Multidiscip Optim 57:2457–2483. https://doi.org/10.1007/s00158-018-1994-3
Lu S, Ma H, Xin L, Zuo W (2018) Lightweight design of bus frames from multi-material topology optimization to cross-sectional size optimization. Eng Optim:1–17. https://doi.org/10.1080/0305215X.2018.1506770
Munk DJ (2019) A bidirectional evolutionary structural optimization algorithm for mass minimization with multiple structural constraints. Int J Numer Methods Eng 118:93–120. https://doi.org/10.1002/nme.6005
Sigmund O (2007) Morphology-based black and white filters for topology optimization. Struct Multidiscip Optim 33:401–424. https://doi.org/10.1007/s00158-006-0087-x
Stegmann J, Lund E (2005) Discrete material optimization of general composite shell structures. Int J Numer Methods Eng 62:2009–2027. https://doi.org/10.1002/nme.1259
Su RY, Gui LJ, Fan ZJ (2011) Multi-objective optimization for bus body with strength and rollover safety constraints based on surrogate models. Struct Multidiscip Optim 44:431–441. https://doi.org/10.1007/s00158-011-0627-x
Sun GY, Tan DD, Lv XJ, Yan XL, Li Q, Huang XD (2018) Multi-objective topology optimization of a vehicle door using multiple material tailor-welded blank (TWB) technology. Adv Eng Softw 124:1–9. https://doi.org/10.1016/j.advengsoft.2018.06.014
Wang MY, Wang XM (2004) “Color” level sets: a multi-phase method for structural topology optimization with multiple materials. Comput Methods Appl Mech Eng 193:469–496. https://doi.org/10.1016/j.cma.2003.10.008
Wang YQ, Luo Z, Kang Z, Zhang N (2015) A multi-material level set-based topology and shape optimization method. Comput Methods Appl Mech Eng 283:1570–1586. https://doi.org/10.1016/j.cma.2014.11.002
Xu H, Guan L, Chen X, Wang L (2013) Guide-weight method for topology optimization of continuum structures including body forces. Finite Elem Anal Des 75:38–49. https://doi.org/10.1016/j.finel.2013.07.002
Yamada T, Izui K, Nishiwaki S, Takezawa A (2010) A topology optimization method based on the level set method incorporating a fictitious interface energy. Comput Methods Appl Mech Eng 199:2876–2891. https://doi.org/10.1016/j.cma.2010.05.013
Yang RJ, Chahande AI (1995) Automotive applications of topology optimization. Structural Optimization 9:245–249. https://doi.org/10.1007/Bf01743977
Zhang W, Zhao L, Gao T (2017) CBS-based topology optimization including design-dependent body loads. Comput Methods Appl Mech Eng 322:1–22. https://doi.org/10.1016/j.cma.2017.04.021
Zhong W, Su RY, Gui LJ, Fan ZJ (2016) Multi-objective topology and sizing optimization of bus body frame. Struct Multidiscip Optim 54:701–714. https://doi.org/10.1007/s00158-016-1431-4
Zuo WJ, Saitou K (2017) Multi-material topology optimization using ordered SIMP interpolation. Struct Multidiscip Optim 55:477–491. https://doi.org/10.1007/s00158-016-1513-3
Zuo WJ, Fang JX, Zhong MH, Guo GK (2018) Variable cross-section rectangular beam and sensitivity analysis for lightweight design of bus frame. Int J Automot Technol 19:1033–1040. https://doi.org/10.1007/s12239-018-0100-6
Funding
This research was supported by Hyundai Motor Group through a project “Optimal topology design of lightweight multi-material automotive body structure”.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Additional information
Responsible Editor: Xu Guo
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Jung, Y., Lim, S., Kim, J. et al. Lightweight design of electric bus roof structure using multi-material topology optimisation. Struct Multidisc Optim 61, 1273–1285 (2020). https://doi.org/10.1007/s00158-019-02410-8
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00158-019-02410-8