In this paper, a complete optimization design verification process is proposed and a novel structure of connecting brackets is presented, solving the fatigue failure of chassis connecting brackets operating on harsh roads. First, an endurance road test and fatigue life analysis were applied to the truck equipped with the original brackets, verifying the fatigue damage of the structure. Based on the solid isotropic material with penalization method, a novel lightweight connecting bracket layout was obtained by using the method of moving asymptotes (MMA) for topology optimization under multiple working conditions with multiple performance constraints. Moreover, the derivatives of objective and constraint functions concerning design variables were applied for the MMA. Considering manufacturability and functionality, the improved model based on the topology optimization results was further optimized by size optimization. Finally, fatigue life analysis and an endurance road test were conducted using the optimal design. Compared with the original structure, the novel brackets showed better stiffness, strength and fatigue performance while reducing the total mass by 15.2%. The whole optimization and validation process can provide practical ideas and value for developing multi-performance suspensions in the pre-product development stage.
Citation: Furong Xie, Yunkai Gao, Ting Pan, De Gao, Lei Wang, Yanan Xu, Chi Wu. Novel lightweight connecting bracket design with multiple performance constraints based on optimization and verification process[J]. Electronic Research Archive, 2023, 31(4): 2019-2047. doi: 10.3934/era.2023104
In this paper, a complete optimization design verification process is proposed and a novel structure of connecting brackets is presented, solving the fatigue failure of chassis connecting brackets operating on harsh roads. First, an endurance road test and fatigue life analysis were applied to the truck equipped with the original brackets, verifying the fatigue damage of the structure. Based on the solid isotropic material with penalization method, a novel lightweight connecting bracket layout was obtained by using the method of moving asymptotes (MMA) for topology optimization under multiple working conditions with multiple performance constraints. Moreover, the derivatives of objective and constraint functions concerning design variables were applied for the MMA. Considering manufacturability and functionality, the improved model based on the topology optimization results was further optimized by size optimization. Finally, fatigue life analysis and an endurance road test were conducted using the optimal design. Compared with the original structure, the novel brackets showed better stiffness, strength and fatigue performance while reducing the total mass by 15.2%. The whole optimization and validation process can provide practical ideas and value for developing multi-performance suspensions in the pre-product development stage.
[1] | A. C. R. Teixeira, P. G. Machado, F. M. de Almeida Collaço, D. Mouette, Alternative fuel technologies emissions for road heavy-duty trucks: a review, Environ. Sci. Pollut. Res., 28 (2021), 20954−20969. https://doi.org/10.1007/s11356-021-13219-8 doi: 10.1007/s11356-021-13219-8 |
[2] | T. Kuczek, Application of manufacturing constraints to structural optimization of thin-walled structures, Eng. Optim., 48 (2016), 351−360. https://doi.org/10.1080/0305215X.2015.1017350 doi: 10.1080/0305215X.2015.1017350 |
[3] | K. T. Cheng, N. Olhoff, An investigation concerning optimal design of solid elastic plates, Int. J. Solids Struct., 17 (1981), 305−323. https://doi.org/10.1016/0020-7683(81)90065-2 doi: 10.1016/0020-7683(81)90065-2 |
[4] | M. P. Bendsoe, N. Kikuchi, Generating optimal topologies in structural design using a homogenization method, Comput. Methods Appl. Mech. Eng., 71 (1988), 197−224. https://doi.org/10.1016/0045-7825(88)90086-2 doi: 10.1016/0045-7825(88)90086-2 |
[5] | M. P. Bendsoe, O. Sigmund, Material interpolation schemes in topology optimization, Arch. Appl. Mech., 69 (1999), 635−654. https://doi.org/10.1007/s004190050248 doi: 10.1007/s004190050248 |
[6] | J. M. Martínez, A note on the theoretical convergence properties of the SIMP method, Struct. Multidiscip. Optim., 29 (2005), 319−323. https://doi.org/10.1007/s00158-004-0479-8 doi: 10.1007/s00158-004-0479-8 |
[7] | M. Stolpe, K. Svanberg, An alternative interpolation scheme for minimum compliance topology optimization, Struct. Multidiscip. Optim., 22 (2001), 116−124. https://doi.org/10.1007/s001580100129 doi: 10.1007/s001580100129 |
[8] | H. Zhang, X. H. Ren, Topology optimization of continuum structures based on SIMP, Adv. Mater. Res., Trans Tech Publications, Ltd., 255–260 (2011), 14–19. https://doi.org/10.4028/www.scientific.net/AMR.255-260.14 |
[9] | W. J. Zuo, J. T. Bai, J. F. Yu, Sensitivity reanalysis of static displacement using Taylor series expansion and combined approximate method, Struct. Multidiscip. Optim., 53 (2016), 953−959. https://doi.org/10.1007/s00158-015-1368-z doi: 10.1007/s00158-015-1368-z |
[10] | K. T. Zuo, L. P. Chen, Y. Q. Zhang, J. Yang, Manufacturing- and machining-based topology optimization, Int. J. Adv. Manuf. Technol., 27 (2006), 531−536. https://doi.org/10.1007/s00170-004-2210-8 doi: 10.1007/s00170-004-2210-8 |
[11] | X. J. Gao, L. J. Li, H. T. Ma, An adaptive continuation method for topology optimization of continuum structures considering buckling constraints, Int. J. Appl. Mech., 9 (2017). https://doi.org/10.1142/S1758825117500922 doi: 10.1142/S1758825117500922 |
[12] | S. Z. Xu, J. K. Liu, B. Zou, Q. H. Li, Y. S. Ma, Stress constrained multi-material topology optimization with the ordered SIMP method, Comput. Methods Appl. Mech. Eng., 373 (2021). https://doi.org/10.1016/j.cma.2020.113453 doi: 10.1016/j.cma.2020.113453 |
[13] | Y. F. Bai, M. Cong, Y. Y. Li, Structural topology optimization for a robot upper arm based on SIMP method, in 3rd IEEE/IFToMM/ASME International Conference on Reconfigurable Mechanisms and Robots (ReMAR), 2015. https://doi.org/10.1007/978-3-319-23327-7_62 |
[14] | B. Mohamodhosen, F. Gillon, A. Tounzi, L. Chevallier, J. Korecki, Topology optimisation of a 3D electromagnetic device using the SIMP density-based method, in 2016 IEEE Conference on Electromagnetic Field Computation (CEFC), IEEE, Miami, FL, 2016. https://doi.org/10.1109/CEFC.2016.7816001 |
[15] | G. L. Srinivas, S. P. Singh, A. Javed, Experimental evaluation of topologically optimized manipulator-link using PLC and HMI based control system, in 3rd International E-Conference on Frontiers in Mechanical Engineering and NanoTechnology (ICFMET), 2020. https://doi.org/10.1016/j.matpr.2020.08.023 |
[16] | Q. Liu, X. K. Ma, Y. Z. Lin, Z. J. Zong, Topology and sizing optimization of light-weight frame for energy-saving vehicle, in International Conference on Advanced Design and Manufacturing Engineering (ADME 2011), Trans Tech Publications Ltd., 2011. https://doi.org/10.4028/www.scientific.net/AMR.308-310.1220 |
[17] | B. Torstenfelt, A. Klarbring, Conceptual optimal design of modular car product families using simultaneous size, shape and topology optimization, Finite Elem. Anal. Des., 43 (2007), 1050−1061. https://doi.org/10.1016/j.finel.2007.06.005 doi: 10.1016/j.finel.2007.06.005 |
[18] | L. Wang, X. K. Chen, Q. H. Zhao, Muti-objective topology optimization of an electric vehicle's traction battery enclosure, in Applied Energy Symposium and Summit - Low Carbon Cities and Urban Energy Systems (CUE), 2015. https://doi.org/10.1016/j.egypro.2016.06.103 |
[19] | J. G. Cho, J. S. Koo, H. S. Jung, A lightweight design approach for an EMU carbody using a material selection method and size optimization, J. Mech. Sci. Technol., 30 (2016), 673−681. https://doi.org/10.1007/s12206-016-0123-8 doi: 10.1007/s12206-016-0123-8 |
[20] | S. B. Lu, H. G. Ma, W. J. Zuo, Lightweight design of bus frames from multi-material topology optimization to cross-sectional size optimization, Eng. Optim., 51 (2019), 961−977. https://doi.org/10.1080/0305215X.2018.1506770 doi: 10.1080/0305215X.2018.1506770 |
[21] | J. Bai, Y. Zhao, G. Meng, W. Zuo, Bridging topological results and thin-walled frame structures considering manufacturability, J. Mech. Des., 143 (2021). https://doi.org/10.1115/1.4050300 doi: 10.1115/1.4050300 |
[22] | H. Ma, J. Wang, Y. Lu, Y. Guo, Lightweight design of turnover frame of bridge detection vehicle using topology and thickness optimization, Struct. Multidiscip. Optim., 59 (2019), 1007−1019. https://doi.org/10.1007/s00158-018-2113-1 doi: 10.1007/s00158-018-2113-1 |
[23] | G. Y. Sun, D. D. Tan, X. J. Lv, X. L. Yan, Q. Li, X. D. Huang, Multi-objective topology optimization of a vehicle door using multiple material tailor-welded blank (TWB) technology, Adv. Eng. Software, 124 (2018), 1−9. https://doi.org/10.1016/j.advengsoft.2018.06.014 doi: 10.1016/j.advengsoft.2018.06.014 |
[24] | J. Zhang, L. Ning, Y. Hao, T. Sang, Topology optimization for crashworthiness and structural design of a battery electric vehicle, Int. J. Crashworthiness, 26 (2021), 651−660. https://doi.org/10.1080/13588265.2020.1766644 doi: 10.1080/13588265.2020.1766644 |
[25] | D. J. Munk, J. D. Miller, Topology optimization of aircraft components for increased sustainability, AIAAJ, 60 (2022), 445−460. https://doi.org/10.2514/1.J060259 doi: 10.2514/1.J060259 |
[26] | Y. L. Lee, M. E. Barkey, H. T. Kang, Metal Fatigue Analysis Handbook: Practical Problem-Solving Techniques for Computer-Aided Engineering, Burlington: Elsevier Butterworth-Heinemann, (2012), 1−580. https://doi.org/10.1016/C2010-0-66376-0 |
[27] | C. H. Wang, M. W. Brown, Life prediction techniques for variable amplitude multiaxial fatigue−Part 2: comparison with experimental results, J. Eng. Mater. Technol., 118 (1996), 371−374. https://doi.org/10.1115/1.2806822 doi: 10.1115/1.2806822 |
[28] | S. H. Jeong, J. W. Lee, G. H. Yoon, D. H. Choi, Topology optimization considering the fatigue constraint of variable amplitude load based on the equivalent static load approach, Appl. Math. Model., 56 (2018), 626−647. https://doi.org/10.1016/j.apm.2017.12.017 doi: 10.1016/j.apm.2017.12.017 |
[29] | R. T. Haftka, Z. Gürdal, M. P. Kamat, Elements of structural optimization, Kluwer Academic Publishers, 1991. https://doi.org/10.1007/978-94-015-7862-2 |
[30] | D. L. Shu, Mechanical Property of Engineering Material, Beijing, China: China Machine Press, 2007. Available from: https://ss.zhizhen.com/detail_38502727e7500f26a296ae892b789bcc44b4f281d9485a991921b0a3ea25510134114c969f2eae5c13747adaf1f08d1c325955064941cd542e24c1535a7f8b4287df4e09375dba6c27789fd2eaaf69be. |
[31] | A. Li, C. S. Liu, Lightweight design of a crane frame under stress and stiffness constraints using super-element technique, Adv. Mech. Eng., 9 (2017), 15. https://doi.org/10.1177/1687814017716621 doi: 10.1177/1687814017716621 |
[32] | O. Sigmund, J. Petersson, Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima, Struct. Optim., 16 (1998), 68−75. https://doi.org/10.1007/BF01214002 doi: 10.1007/BF01214002 |
[33] | K. Svanberg, The method of moving asymptotes—a new method for structural optimization, Int. J. Numer. Methods Eng., 24 (1987), 359−373. https://doi.org/10.1002/nme.1620240207 doi: 10.1002/nme.1620240207 |
[34] | Z. Hu, S. Sun, O. Vambol, K. Tan, Topology optimization of laminated composite structures under harmonic force excitations, J. Compos. Mater., 56 (2022), 409−420. https://doi.org/10.1177/00219983211052605 doi: 10.1177/00219983211052605 |
[35] | Q. Q. Liang, Y. M. Xie, G. P. Steven, Optimal topology selection of continuum structures with displacement constraints, Comput. Struct., 77 (2000), 635−644. https://doi.org/10.1016/S0045-7949(00)00018-3 doi: 10.1016/S0045-7949(00)00018-3 |
[36] | X. J. Yang, J. Zheng, S. Y. Long, Topology optimization of continuum structures with displacement constraints based on meshless method, Int. J. Mech. Mater. Des., 13 (2017), 311−320. https://doi.org/10.1007/s10999-016-9337-2 doi: 10.1007/s10999-016-9337-2 |
[37] | M. Bruggi, On an alternative approach to stress constraints relaxation in topology optimization, Struct. Multidiscip. Optim., 36 (2008), 125−141. https://doi.org/10.1007/s00158-007-0203-6 doi: 10.1007/s00158-007-0203-6 |
[38] | C. Le, J. Norato, T. Bruns, C. Ha, D. Tortorelli, Stress-based topology optimization for continua, Struct. Multidiscip. Optim., 41 (2010), 605−620. https://doi.org/10.1007/s00158-009-0440-y doi: 10.1007/s00158-009-0440-y |
[39] | S. H. Jeong, S. H. Park, D. H. Choi, G. H. Yoon, Topology optimization considering static failure theories for ductile and brittle materials, Comput. Struct., 110 (2012), 116−132. https://doi.org/10.1016/j.compstruc.2012.07.007 doi: 10.1016/j.compstruc.2012.07.007 |
[40] | X. J. Peng, Fatigue Estimation based on Stress RMS under Stochastic Excitation, in 2nd International Conference on Advanced Electronic Materials, Computers and Materials Engineering (AEMCME), 2019. https://doi.org/10.1088/1757-899X/563/4/042058 |