Topology Optimization Approaches and Its Application and Prospect in Transportation Engineering

doi:10.3901/JME.2024.04.369

Abstract

Abstract: As an advanced structural optimization approach, the essence of topology optimization is to obtain the structural topology configurations with the best performance by seeking the optimal distribution of materials in the design domain under given load and boundary conditions. In recent years, with the continuous development of optimization algorithms and computer science, structural optimization technology has a wide application prospect in aerospace, automobile, ship and other transportation engineering. Based on the theoretical research level, topology optimization approaches and characteristics of discrete and continuous structures are discussed.Then by considering the specific applications of topology optimization in aerospace, automobile, ship and other transportation engineering, the shortcomings of structural topology optimization and the challenges faced by their popularization are pointed out. At the same time, the present situation and development trend of topology optimization industrial software development and application from home and abroad are discussed. At present, the main problem faced by topology optimization is that in the iterative process of large-scale transportation engineering structure optimization, multiple finite element analysis is required which increases the complexity of calculation space and time. By considering the situation, the new discipline direction represented by isogeometric analysis and machine learning to improve the deficiency of topology optimization design is introduced, so as to shorten the design cycle of transportation equipment. and A preliminary discussion on the research trend in the future is also given.

Key words: topology optimization, transportation engineering, structure design, mechanical properties

CLC Number:

TG156

GAO Qiang, WANG Jian, ZHANG Yan, ZHENG Xuyang, LÜ Hao, YIN Guodong. Topology Optimization Approaches and Its Application and Prospect in Transportation Engineering[J]. Journal of Mechanical Engineering, 2024, 60(4): 369-390.

References

[1] 周唯儒.拓扑优化方法在口腔种植体周围松质骨结构模拟中的应用[D].长春:吉林大学,2015.ZHOU Weiru. The application of topology optimization method in the simulation of cancellous bone structure around dental implant[D]. Changchun:Jilin University,2015.
[2] 李诚良,丁亚林,刘磊.大口径反射镜水平集拓扑优化设计[J].红外与激光工程,2018,47(9):303-309.LI Chengliang,DING Yalin,LIU Lei. Level set topology optimization design of large-aperture mirror[J]. Infrared and Laser Engineering,2018,47(9):303-309.
[3] 孙东磊,韩学山,张波.计及电网拓扑优化的电压支撑决策模型[J].电力自动化设备,2015,35(11):137-142,151.SUN Donglei, HAN Xueshan, ZHANG Bo.Voltage-support decision-making model considering power network topology optimization[J]. Electric Power Automation Equipment,2015,35(11):137-142,151.
[4] 胡启国,周松.考虑刚柔耦合的工业机器人多目标可靠性拓扑优化[J].计算机集成制造系统,2020,26(3):623-631.HU Qiguo, ZHOU Song. Multi-objective reliability topology optimization analysis of rigid-flexible coupling industrial robots[J]. Computer Integrated Manufacturing Systems,2020,26(3):623-631.
[5] 陈洪芳,韩梦蕊,孙若水,等.激光追踪系统机械结构拓扑优化轻量化方法[J].哈尔滨工程大学学报,2022,43(2):282-289.CHEN Hongfang,HAN Mengrui,SUN Ruoshui,et al.Methods for topology optimization of lightweight mechanical structures in laser tracking systems[J]. Journal of Harbin Engineering University,2022,43(2):282-289.
[6] MICHELL A G M. LVIII. The limits of economy of material in frame-structures[J]. Philosophical Magazine,1904,8(47):589-597.
[7] OLBERMANN H. Michell truss type theories as aΓ-limit of optimal design in linear elasticity[J]. Advances in Calculus of Variations,2020,15(3):305-322.
[8] GAO Jie,WANG Lin,LUO Zhen,et al. IgaTop:An implementation of topology optimization for structures using IGA in MATLAB[J]. Structural and Multidisciplinary Optimization,2020,8(47):589-597.
[9] HEGEMIER G A,PRAGER W. On Michell trusses[J].International Journal of Mechanical Sciences,1969,11(2):209-215.
[10] DORN W,GOMORY R,GREENBERG H. Automatic design of optimal structures[J]. Design Mechaniuque,1964,3(1):25-52.
[11] DOBBS M W,FELTON L P. Optimization of truss geometry[J]. Journal of Structural Division Proceedings of the American Society of Civil Engineers,1969,95(10):2105-2118.
[12] ZHOU M,ROZVANY G. The COC algorithm,Part II:Topological, geometrical and generalized shape optimization[J]. Computer Methods in Applied Mechanics and Engineering,2015,89(1-3):309-336.
[13] XU G,DAI N. Michell truss design for lightweight gear bodies[J]. Mathematical Biosciences and Engineering:MBE,2021,18(2):1653-1669.
[14] 李栋泓.非平稳随机地震下桁架结构形状与拓扑优化[D].广州:华南理工大学,2016.LI Donghong. Shape and topology optimization of truss structures with non-stationary stochastic seismic excitation[D]. Guangzhou:South China University of Technology,2016.
[15] 刘晓峰,阎军,程耿东.采用自动分组遗传算法的频率约束下桁架拓扑优化[J].计算力学学报,2011,28(1):1-7.LIU Xiaofeng,YAN Jun,CHENG Gengdong. Topology optimization of skeletal structures with frequency constraints based on automatic grouping genetic algorithm[J]. Chinese Journal of Computational Mechanics,2011,28(1):1-7.
[16] 王琦,饶碧波,王源博,等.基于分段遗传算法的桁架拓扑优化设计[J].中国机械工程,2013,24(6):755-760.WANG Qi,RAO Bibo,WANG Yuanbo,et al. Topological optimization design for truss structures using the paragraphing ga[J]. China Mechanical Engineering,2013,24(6):755-760.
[17] 张卓群,李宏男.基于蚁群算法的桁架结构布局离散变量优化方法[J].计算力学学报,2013,30(3):336-342.ZHANG Zhuoqun,LI Hongnan. The method of truss structure layout discrete variable optimization based on ant colony optimization[J]. China Mechanical Engineering,2013,30(3):336-342.
[18] 郝群茹,潘帅.基于禁忌搜索算法的物流系统车辆路径优化[J].科学技术与工程,2019,19(34):401-407.HAO Qunru,PAN Shuai. Vehicle routing optimization of logistics system based on tabu search algorithm[J].Science Technology and Engineering,2019,19(34):401-407.
[19] 武岳,胡庆杰,李清朋.基于改进萤火虫算法的杆系结构拓扑优化[J].建筑结构学报,2016,37(6):46-52.WU Yue, HU Qingjie, LI Qingpeng. Topology optimization for truss structures based on improved firefly algorithm[J]. Journal of Building Structures,2016,37(6):46-52.
[20] 朱朝艳,刘斌,李艺,等.离散变量桁架结构拓扑优化的杂交算法[J].东北大学学报,2004(8):800-803.ZHU Chaoyan,LIU Bin,LI Yi,et al. A hybrid algorithm for topology optimization of truss structures with discrete variables[J]. Journal of Northeastern University,2004(8):800-803.
[21] 张卓群.基于蚁群算法的输电塔结构离散变量优化设计[D].大连:大连理工大学,2014.ZHANG Zhuoqun. The transmission tower structure discrete variable optimal design base on ant colony optimization[D]. Dalian:Dalian University of Technology,2014.
[22] 胡庆杰.基于改进萤火虫算法的杆系结构拓扑优化[D].哈尔滨:哈尔滨工业大学,2015.HU Qingjie. Topology optimization analysis for framed structures based on the improved firefly algorithm[D].Harbin:Harbin Institute of Technology,2015.
[23] ROSSOW M P,TAYLOR J E. A finite element method for the optimal design of variable thickness sheets[J].AIAA Journal,2012,11(11):1566-1569.
[24] CHENG K T,OLHOFF N. An investigation concerning optimal design of solid elastic plates[J]. International Journal of Solids and Structures,1981,17(3):305-323.
[25] BENDSØE M P, KIKUCHI N. Generating optimal topologies in structural design using a homogenization method[J]. Computer Methods in Applied Mechanics and Engineering,1988,71(2):197-224.
[26] MLEJNEK H P. An engineer's approach to optimal material distribution and shape finding[J]. Computer Methods in Applied Mechanics & Engineering,1993,106(1-2):1-26.
[27] BENDSØE M P. Optimal shape design as a material distribution problem[J]. Structural Optimization,1989,1(4):193-202.
[28] ROZVANY G. I. N,ZHOU M,BIRKER T. Generalized shape optimization without homogenization[J]. Structural & Multidisciplinary Optimization,1992,4(3-4):250-252.
[29] STOLPE M, SVANBERG K. On the trajectories of penalization methods for topology optimization[J].Structural and Multidisciplinary Optimization,2001,21(2):128-139.
[30] LIU K,TOVAR A. An efficient 3D topology optimization code written in Matlab[J]. Structural & Multidisciplinary Optimization,2014,50:1175-1196.
[31] 张志飞,徐伟,徐中明,等.抑制拓扑优化中灰度单元的双重SIMP方法[J].农业机械学报,2015,46(11):405-410.ZHANG Zhifei, XU Wei, XU Zhongming, et al.Double-SIMP method for gray-scale elements suppression in topology optimization[J]. Transactions of the Chinese Society for Agricultural Machinery, 2015, 46(11):405-410.
[32] XIE Y M,STEVEN G P. A simple evolutionary procedure for structural optimization[J]. Computers & Structures,1993,49(5):885-896.
[33] 唐腾飞,高隆隆,廖利辉,等.自适应渐进结构优化法的调节阀结构研究[J].北京理工大学学报,2020,40(5):466-470.TANG Tengfei,GAO Longlong,LIAO Lihui,et al.Design of control valve structure with adaptive evolutionary structural optimization method[J].Transactions of Beijing Institute of Technology,2020,40(5):466-470.
[34] 罗晓瑜,王春生,姚书奎,等.基于双向渐进结构优化法的钢桥系统失效模式识别[J].中国公路学报,2017,30(3):31-39.LUO Xiaoyu,WANG Chunsheng,YAO Shukui,et al.Identification of system failure modes of steel bridges based on bi-directional evolutionary structural optimization[J]. China Journal of Highway and Transport,2017,30(3):31-39.
[35] 程自然,颜健,彭佑多.基于渐进结构优化法的碟式聚光器轻量化研究[J].太阳能学报,2020,41(4):99-106.CHENG Ziran,YAN Jian,PENG Youduo. Lightweight design of solar dish concentrator based on evolutionary structure method[J]. Acta Energiae Solaris Sinica,2020,41(4):99-106.
[36] QUERIN O M,STEVEN G P,XIE Y M. Evolutionary structural optimisation (ESO) using a bidirectional algorithm[J]. Engineering Computations:Int. J. for Computer-Aided Engineering,1998,15(8):1031-1048.
[37] HUANG Xiaodong,XIE Yimin. A further review of ESO type methods for topology optimization[J]. Structural & Multidisciplinary Optimization,2010,41:671-683.
[38] XIA Liang, XIA Qi, HUANG Xiaodong, et al.Bi-directional evolutionary structural optimization on advanced structures and materials:A comprehensive review[J]. Archives of Computational Methods in Engineering,2018,25(2):437-478.
[39] 何健,何猛,夏凉,等.基于双向渐进结构优化法的柔性机构设计[J].机械工程学报,2021,57(19):39-47.HE Jian,HE Meng,XIA Liang,et al. Design of compliant actuation mechanisms by evolutionary structural optimization method[J]. Journal of Mechanical Engineering,2021,57(19):39-47.
[40] 王选,刘宏亮,龙凯,等.基于改进的双向渐进结构优化法的应力约束拓扑优化[J].力学学报,2018,50(2):385-94.WANG Xuan, LIU Hongliang, LONG Kai, et al.Stress-constrained topology optimization based on improved bi-directional evolutionary optimization method[J]. Chinese Journal of Theoretical and Applied Mechanics,2018,50(2):385-394.
[41] 才琪,冯若强.基于改进双向渐进结构优化法的桁架结构拓扑优化[J].建筑结构学报,2022,43(4):68-76.CAI Qi,FENG Ruoqiang. Topology optimization of truss structure based on improved bi-directional evolutionary structural optimization method[J]. Journal of Building Structures,2022,43(4):68-76.
[42] MEI Yulin,WANG Xiaoming. A level set method for structural topology optimization[J]. Computer Methods in Applied Mechanics & Engineering,2004,35(7):415-441.
[43] OSHER S,FEDKIW R. Level set methods and dynamic implicit surfaces[M]. New York:Springer,2002.
[44] LUO Zhen,WANG M Y,WANG Shengyin,et al. A level set-based parameterization method for structural shape and topology optimization[J]. International Journal for Numerical Methods in Engineering,2008,76(1):1-26.
[45] ALLAIRE G,JOUVE F,TOADER A M. Structural optimization using sensitivity analysis and a level-set method[J]. Journal of Computational Physics,2003,194(1):363-393.
[46] WEI Peng,LI Zuyu,LI Xueping,et al. An 88-line MATLAB code for the parameterized level set method based topology optimization using radial basis functions[J]. Structural and Multidisciplinary Optimization,2018,58(2):831-849.
[47] SETHIAN J A,WIEGMANN A. Structural boundary design via level set and immersed interface methods[J].Journal of Computational Physics,2000,163(2):489-528.
[48] XU Guo,ZHANG Weisheng,ZHONG Wenliang. Doing topology optimization explicitly and geometrically-A new moving morphable components based framework[J].Journal of Applied Mechanics,2014,81(8):081009.
[49] ZHANG Weisheng,YUAN Jieyuan,ZHANG Jian,et al.A new topology optimization approach based on moving morphable components (MMC) and the ersatz material model[J]. Structural & Multidisciplinary Optimization,2016,53(6):1243-1260.
[50] ZHANG Weisheng,CHEN Jishun,ZHU Xuefeng,et al.Explicit three-dimensional topology optimization via moving morphable void (MMV) approach[J]. Computer Methods in Applied Mechanics & Engineering,2017,322:590-614.
[51] WEI Peng,MA Haitao,WANG M Y. The stiffness spreading method for layout optimization of truss structures[J]. Structural and Multidisciplinary Optimization,2014,49(4):667-682.
[52] HOANG V N,JIANG G W. Topology optimization using moving morphable bars for versatile thickness control[J].Computer Methods in Applied Mechanics & Engineering,2017,317:153-173.
[53] NORATO J A,BENDSE M P,HABER R B,et al. A topological derivative method for topology optimization[J]. Structural and Multidisciplinary Optimization,2007,33(4):375-386.
[54] 张军峰,廖靖宇,刘恩海.基于SIMP-MMC结构尺寸精确控制拓扑优化方法[J].机械强度,2022,44(1):102-110.ZHANG Junfeng,LIAO Jingyu,LIU Enhai. Topology optimization method based on SIMP-MMC for structure size precise control[J]. Journal of Mechanical Strength,2022,44(1):102-110.
[55] BURGER M,STAINKO R. Phase-field relaxation of topology optimization with local stress constraints[J].Siam Journal on Control & Optimization,2006,45(4):1447-1466.
[56] ZHANG Xiaopeng,TAKEZAWA A,KANG Zhan. A phase-field based robust topology optimization method for phononic crystals design considering uncertain diffuse regions[J]. Computational Materials Science,2019,160:159-172.
[57] TAKEZAWA A,NISHIWAKI S,KITAMURA M. Shape and topology optimization based on the phase field method and sensitivity analysis[J]. Journal of Computational Physics,2010,229(7):2697-2718.
[58] GAIN A L,PAULINO G H. Phase-field based topology optimization with polygonal elements:A finite volume approach for the evolution equation[J]. Structural & Multidisciplinary Optimization,2012,46(3):327-342.
[59] SOKOLOWSKI J, ZOCHOWSKI A. Topological derivative in shape optimization[J]. Siam Journal on Control and Optimization,1999,37(4):1251-1272.
[60] YERA R,FORZANI L,MÉNDEZ C G,et al. A topology optimization algorithm based on topological derivative and level-set function for designing phononic crystals[J].Engineering Computations,2022,39(1):354-379.
[61] ESCHENAUER H A,KOBELEV V V,SCHUMACHER A. Bubble method for topology and shape optimization of structures[J]. Structural and Multidisciplinary Optimization,1994,8(1):42-51.
[62] XIAO Qi,SHI Tielin,XIA Liang. Stable hole nucleation in level set based topology optimization by using the material removal scheme of BESO[J]. Computer Methods in Applied Mechanics and Engineering,2019,343:438-452.
[63] NOVOTNY A A, LOPES C G, SANTOS R B.Topological derivative-based topology optimization of structures subject to self-weight loading[J]. Structural and Multidisciplinary Optimization,2021,63(4):1853-1861.
[64] CARVALHO F S,RUSCHEINSKY D,GIUSTI S M,et al. Topological derivative-based topology optimization of plate structures under bending effects[J]. Structural and Multidisciplinary Optimization,2020,63(28):1-14.
[65] CAI Shouyu,ZHANG Weihong. An adaptive bubble method for structural shape and topology optimization[J].Computer Methods in Applied Mechanics and Engineering,2020,360:112778.
[66] HUGHES T, COTTRELL J A, BAZILEVS Y.Isogeometric analysis:CAD,finite elements,NURBS,exact geometry and mesh refinement[J]. Computer Methods in Applied Mechanics & Engineering,2005,194(39-41):4135-4195.
[67] SEO Y D,KIM H J,YOUN S K. Isogeometric topology optimization using trimmed spline surfaces[J]. Computer Methods in Applied Mechanics and Engineering,2010,199(49-52):3270-3296.
[68] WANG Z P,POH L H,DIRRENBERGER J,et al.Isogeometric shape optimization of smoothed petal auxetic structures via computational periodic homogenization[J]. Computer Methods in Applied Mechanics & Engineering,2017,323(15):250-271.
[69] WANG Yingjun,WANG Zhenpei,XIA Zhaohui,et al.Structural design optimization using isogeometric analysis:A comprehensive review[J]. Computer Modeling in Engineering & Sciences,2018,117(3):455-507.
[70] 刘宏亮,杨迪雄.基于IGA-SIMP法的连续体结构应力约束拓扑优化[J].计算力学学报,2018,35(2):144-151.LIU Hongliang, YANG Dixiong. IGA-SIMP method based stress-constrained topology optimization of continuous structures[J]. Chinese Journal of Computational Mechanics,2018,35(2):144-151.
[71] YANG Dixiong,LIU Hongliang,ZHANG Weisheng,et al. Stress-constrained topology optimization based on maximum stress measures[J]. Computers & Structures,2018,198:23-39.
[72] LIEU Q X,LEE J. Multiresolution topology optimization using isogeometric analysis[J]. International Journal for Numerical Methods in Engineering,2017,112(13):2025-2047.
[73] LIEU Q X,LEE J. A multi-resolution approach for multi-material topology optimization based on isogeometric analysis[J]. Computer Methods in Applied Mechanics & Engineering,2017,323:272-302.
[74] WANG Y,XU H,PASINI D. Multiscale isogeometric topology optimization for lattice materials[J]. Computer Methods in Applied Mechanics & Engineering,2017,316:568-585.
[75] 王选,祝雪峰,胡平,等.基于NURBS插值的三维渐进结构优化方法[J].计算力学学报,2016,33(4):536-542.WANG Xuan, ZHU Xuefeng, HU Ping, et al.Bi-directional evolutionary method using NURBS interpolation for optimal design of 3D continuum structures[J]. Chinese Journal of Computational Mechanics,2016,33(4):536-42.
[76] 王选,胡平,祝雪峰,等.考虑结构自重的基于NURBS插值的3D拓扑描述函数法[J].力学学报,2016,48(6):1437-1445.WANG Xuan,HU Ping,ZHU Xuefeng,et al. Topology description function approach using NURBS interpolation for 3D structures with self-weight loads[J]. Chinese Journal of Theoretical and Applied Mechanics,2016,48(6):1437-1445.
[77] WANG Y, BENSON D J. Isogeometric analysis for parameterized LSM-based structural topology optimization[J]. Computational Mechanics,2016,57(1):19-35.
[78] WANG Yinjun,BENSON D J. Geometrically constrained isogeometric parameterized level-set based topology optimization via trimmed elements[J]. Frontiers of Mechanical Engineering,2016,11(4):328-343.
[79] GHASEMI H,PARK H S,RABCZUK T. A level-set based IGA formulation for topology optimization of flexoelectric materials[J]. Computer Methods in Applied Mechanics and Engineering,2017,313:239-258.
[80] JAHANGIRY H A,TAVAKKOLI S M. An isogeometrical approach to structural level set topology optimization[J].Computer Methods in Applied Mechanics and Engineering,2017,319:240-257.
[81] HOU Wenbin,GAI Yundong,ZHU Xuefeng,et al.Explicit isogeometric topology optimization using moving morphable components[J]. Computer Methods in Applied Mechanics and Engineering,2017,326(1):694-712.
[82] 刘宏亮,祝雪峰,杨迪雄.基于等几何分析的结构优化设计研究进展[J].固体力学学报,2018,39(3):248-267.LIU Hongliang,ZHU Xuefeng,YANG Dixiong. Research advances in isogeometric analysis-based optimum design of structure[J]. Chinese Journal of Solid Mechanics,2018,39(3):248-267.
[83] SALEHI H, BURGUEÑO R. Emerging artificial intelligence methods in structural engineering[J].Engineering Structures,2018,171:170-189.
[84] YU Y,HUR T,JUNG J,et al. Deep learning for determining a near-optimal topological design without any iteration[J]. Structural and Multidisciplinary Optimization,2019,59(3):787-799.
[85] SOSNOVIK I, OSELEDETS I. Neural networks for topology optimization[J]. Russian Journal of Numerical Analysis and Mathematical Modelling,2019,34(4):215-223.
[86] BANGA S,GEHANI H,BHILARE S,et al. 3D Topology optimization using convolutional neural networks[J].arXiv,2018,39(3):20.
[87] XUE Liang,LIU Jie,WEN Guilin,et al. Efficient,high-resolution topology optimization method based on convolutional neural networks[J]. Frontiers of Mechanical Engineering,2021,16:80-96.
[88] DENG Changyu, WANG Yizhou, QIN Can, et al.Self-directed online machine learning for topology optimization[J]. Nature Communications,2022,13(1):388.
[89] RAWAT S, SHEN M H. A novel topology design approach using an integrated deep learning network architecture[EB/OL].[2018-08-03]. https://arxiv.dosf.top/pdf/1808.02334.
[90] SHARPE C,SEEPERSAD C C. Topology design with conditional generative adversarial networks[C]//ASME2019 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference,2019.
[91] NIE Zhangguo,LIN Tong,JIANG Haoliang,et al.TopologyGAN:Topology optimization using generative adversarial networks based on physical fields over the initial domain[J]. Journal of Mechanical Design,2021,143(3):031715.
[92] 王英奇.基于拓扑优化和深度学习的新型结构生成方法研究[D].开封:河南大学,2022.WANG Yingqi. Research on generation method of innovative structures based on topology optimization and deep learning[D]. Kaifeng:Henan University,2022.
[93] 王龙轩,杜文风,张帆,等.四分叉铸钢节点拓扑优化及3D打印制造[J].建筑结构学报,2021,42(6):37-49.WANG Longxuan,DU Wenfeng,ZHANG Fan,et al.Topology optimization and 3D printing of three-branch joints in treelike structures[J]. Journal of Building Structures,2021,42(6):37-49.
[94] FUJII D,CHEN B C,KIKUCHI N. Composite material design of two-dimensional structures using the homogenization design method[J]. International Journal for Numerical Methods in Engineering,2001,50(9):2031-2051.
[95] 张卫红,徐仕杰,朱继宏.循环对称结构的多尺度拓扑优化方法[J].计算力学学报,2021,38(4):512-522.ZHANG Weihong,XU Shijie,ZHU Jihong. Multi-scale topology optimization method for cyclic symmetric structures[J]. Chinese Journal of Computational Mechanics,2021,38(4):512-522.
[96] LIU Ling, YAN Jun, CHENG Gengdong. Optimum structure with homogeneous optimum truss-like material[J]. Computers & Structures,2008,86(13-14):1417-1425.
[97] YAN X,HUANG X,ZHA Y M,et al. Concurrent topology optimization of structures and their composite microstructures[J]. Computers & Structures,2014,133:103-110.
[98] WANG Y,WANG M Y,CHEN F. Structure-material integrated design by level sets[J]. Structural and Multidisciplinary Optimization,2016,54(5):1145-1156.
[99] 牛斌.基于结构和材料一体化的多尺度动力优化设计[D].大连:大连理工大学,2010.NIU Bin. Multi-scale dynamic design optimization based on integrated design of structure and material[D].Dalian:Dalian University of Technology,2020.
[100] 熊海林.复合材料结构多尺度一体化优化设计[D].武汉:华中科技大学,2016.XIONG Hailin. Multi-scale integrated topology optimization design of composite structures[D]. Wuhan:Huazhong University of Science & Technology,2016.
[101] 段尊义.纤维增强复合材料框架结构拓扑与纤维铺角一体化优化设计[D].大连:大连理工大学,2016.DUAN Zunyi. Integrated optimization design of structural topology and laying angle of fiber reinforced composite frame[D]. Dalian:Dalian University of Technology,2016.
[102] RODRIGUES H,GUEDES J M,BENDSØE M P.Hierarchical optimization of material and structure[J].Structural and Multidisciplinary Optimization,2002,24(1):1-10.
[103] COELHO P G,FERNANDES P R,GUEDES J M,et al.A hierarchical model for concurrent material and topology optimisation of three-dimensional structures[J].Structural and Multidisciplinary Optimization,2008,35(2):107-115.
[104] SIVAPURAM R, DUNNING P D, KIM H A.Simultaneous material and structural optimization by multiscale topology[J]. Structural and Multidisciplinary Optimization,2016,54(5):1267-1281.
[105] LI Hao,LUO Zhen,GAO Liang,et al. Topology optimization for concurrent design of structures with multi-patch microstructures by level sets[J]. Computer Methods in Applied Mechanics and Engineering,2018,331:536-561.
[106] ZHANG Yan,XIAO Mi,LI Hao,et al. Multiscale concurrent topology optimization for cellular structures with multiple microstructures based on ordered SIMP interpolation[J]. Computational Materials Science,2018,155:74-91.
[107] ZHANG Yan,XIAO Mi,LI Hao,et al. Concurrent topology optimization for cellular structures with nonuniform microstructures based on the kriging metamodel[J]. Structural and Multidisciplinary Optimization,2018:1-27.
[108] 高杰.基于参数化水平集的结构/材料多尺度拓扑优化设计研究[D].武汉:华中科技大学,2019.GAO Jie. Research on topology optimization for multiscale design of structure-material based on parametric level set[D]. Wuhan:Huazhong University of Science and Technology,2019.
[109] GU Xiaojun, YANG Kaike, WU Manqiao, et al.Integrated optimization design of smart morphing wing for accurate shape control[J]. Chinese Journal of Aeronautics,2021,34(1):135-147.
[110] GASPARI A D. Multi-objective optimization for the aero-structural design of adaptive compliant wing devices[J]. Appl. Sci.-Basel,2020,10(18):29.
[111] DUNNING P D,STANFORD B K,KIM H A. Coupled aerostructural topology optimization using a level set method for 3D aircraft wings[J]. Structural and Multidisciplinary Optimization,2015,51(5):1-20.
[112] 邱福生,赵红娟,戴良景,等.考虑气动-结构耦合的机翼三维结构拓扑优化方法[J].科学技术与工程,2019,19(22):350-355.QIU Fusheng,ZHAO Hongjuan,DAI Liangjing,et al.Topology optimization of three-dimensional structure for aerodynamic-structure coupling problem of wing[J].Science Technology and Engineering,2019,19(22):350-355.
[113] FEI Chengwei,LIU Haotian,ZHU Zhengzheng,et al.Whole-process design and experimental validation of landing gear lower drag stay with global/local linked driven optimization strategy[J]. Chinese Journal of Aeronautics,2021,34(2):318-328.
[114] 赵知辛,王琨,汪杰,等.飞机起落架的动力学分析与拓扑优化研究[J].机械设计与制造,2021(10):81-85.ZHAO Zhixin,WANG Kun,WANG Jie,et al. Dynamic analysis and topology optimization of aircraft landing gear[J]. Machinery Design & Manufacture,2021(10):81-85.
[115] 徐浩然,贺福强,李赟,等.飞机起落架的拓扑与自由曲面形状优化[J].组合机床与自动化加工技术,2021(4):134-138.XU Haoran,HE Fuqiang,LI Yun,et al. Topology and free-form surface shape optimization of aircraft landing gear[J]. Modular Machine Tool & Automatic Manufacturing Technique,2021(4):134-138.
[116] TAN Luyang,LI Lin,GU Song,et al. Multi-objective topology optimization to reduce vibration of micro-satellite primary supporting structure[J]. Journal of Vibroengineering,2017,19(2):831-843.
[117] 张肖,胡梦遥,顾亦磊,等.卫星载荷安装平台结构轻量优化与仿真分析[J].计算机仿真,2021,38(10):101-105.ZHANG Xiao, HU Mengyao, GU Yilei, et al.Lightweight optimization and simulation analysis of satellite load installation platform structure[J]. Computer Simulation,2021,38(10):101-105.
[118] 王瑞显,冯振伟,马灵犀,等.小卫星一体化星敏支架拓扑优化[J].南京航空航天大学学报,2021,53(S1):67-70.WANG Ruixian,FENG Zhenwei,MA Lingxi,et al.Topology optimization of sensor brackets for small satellites[J]. Journal of Nanjing University of Aeronautics & Astronautics,2021,53(S1):67-70.
[119] 徐皓.基于遗传算法的拓扑优化理论及在微小卫星设计中的应用[D].长沙:国防科技大学,2017.XU Hao. Topology optimization theory based on genetic algorithm and its application in micro satellite design[D].Changsha:National University of Defense Technology,2017.
[120] 李佳霖,赵剑,孙直,等.基于移动可变形组件法(MMC)的运载火箭传力机架结构的轻量化设计[J].力学学报,2022,54(1):244-251.LI Jialin,ZHAO Jian,SUN Zhi,et al. Lightweight design of transmission frame structures for launch vehicles based on moving morphable components (MMC) approach[J]. Chinese Journal of Theoretical and Applied Mechanics,2022,54(1):244-251.
[121] 毕祥军,陈炳全,吴浩,等.运载火箭线式捆绑分离装置的设计、分析与优化[J].机械工程学报,2019,55(14):60-68.BI Xiangjun,CHEN Bingquan,WU Hao,et al. Design,analysis and optimization of linear bundled separation device for launch vehicle[J]. Journal of Mechanical Engineering,2019,55(14):60-68.
[122] BALDZHIEV R S,ALEKSEYEV A A,AZAROV A V.Topology optimization of the lattice payload adapter for carrier rocket[J]. IOP Conference Series:Materials Science and Engineering,2019,683:012061.
[123] DUAN Libin,XIAO Ningcong,HU Zhaohui,et al. An efficient lightweight design strategy for body-in-white based on implicit parameterization technique[J].Structural and Multidisciplinary Optimization,2017,55(5):1927-1943.
[124] 郭立新,周宏扬.车架结构二次拓扑优化设计与性能分析[J].东北大学学报,2017,38(7):998-1001,1011.GUO Lixin, ZHOU Hongyang. Quatric topology optimization design and performance analysis of vehicle chassis structures[J]. Journal of Northeastern University,2017,38(7):998-1001,1011.
[125] 王登峰,毛爱华,牛妍妍,等.基于拓扑优化的纯电动大客车车身骨架轻量化多目标优化设计[J].中国公路学报,2017,30(2):136-143.WANG Dengfeng,MAO Aihua,NIU Yanyan,et al.Lightweight multi-objective optimization design for body frame of pure electric large bus based on topology optimization[J]. China Journal of Highway and Transport,2017,30(2):136-143.
[126] 郭建宇,陈建业,陈鹏,等.应急监测拖车车身骨架结构分析与轻量化研究[J].现代制造工程,2020(9):53-61.GUO Jianyu,CHEN Jianye,CHEN Peng,et al. Structure analysis and lightweight research of trailer body framework for emergency monitoring[J]. Modern Manufacturing Engineering,2020(9):53-61.
[127] TUNCER G,MANSOURI D,SENDUR P. The effect of spotwelds and structural adhesives on static and dynamic characteristics of vehicle body design[J]. Proc. Inst.Mech. Eng. Part D-J Automob. Eng.,2021,235(12):3207-3219.
[128] LONG Haiqiang,HU Yumei,JIN Xiaoqing,et al. An optimization procedure for spot-welded structures based on SIMP method[J]. Computational Materials Science,2016,117:602-607.
[129] 陈勇敢,毕传兴,张永斌,等.拓扑优化在某SRV白车身焊点缩减中的应用[J].汽车工程,2011,33(8):733-737.CHEN Yonggan,BI Chuanxing,ZHANG Yongbin,et al. Application of topology optimization to a SRV BIW aiming at welding spot reduction[J]. Automotive Engineering,2011,33(8):733-737.
[130] 吕毅宁,吕振华.车身结构中焊点布置的分区拓扑优化设计方法研究[J].计算力学学报,2010,27(4):648-654.LÜ Yining, LÜ Zhenhua. Multi-domain synthetic topology optimization method for automotive body spot weld layout design[J]. Chinese Journal of Computational Mechanics,2010,27(4):648-654.
[131] KIM J,KIM J J,JANG I G. Integrated topology and shape optimization of the five-spoke steel wheel to improve the natural frequency[J]. Structural and Multidisciplinary Optimization,2022,65(3):78.
[132] ZHANG Yue,SHAN Yingchun,LIU Xiandong,et al. An integrated multi-objective topology optimization method for automobile wheels made of lightweight materials[J].Structural and Multidisciplinary Optimization,2021,64(3):1585-1605.
[133] CHU D, BAI W, HE Y, et al. Research on lightweight technology of new carbon fiber wheel hub structure[C]//IOP Conference Series:Earth and Environmental Science. IOP Publishing,2021,632(5):052071.
[134] WANG Dengfeng, ZHANG Shuai, XU Wenchao.Multi-objective optimization design of wheel based on the performance of 13ånd 90°impact tests[J].International Journal of Crashworthiness,2019,24(3):336-361.
[135] JANG I G,SUNG Y H,YOO E J,et al. Pattern design of a non-pneumatic tyre for stiffness using topology optimization[J]. Engineering Optimization,2021,24(3):336-361.
[136] GARBATOV Y, HUANG Y C. Multi-objective reliability-based design of ship structures subjected to fatigue damage and compressive collapse[J]. Journal of Offshore Mechanics and Arctic Engineering,2020,142(5):051701.
[137] JIA Dejun,LI Fanchun,ZHANG Chong,et al. Design and simulation analysis of trimaran bulkhead based on topological optimization[J]. Ocean Engineering,2019,191:106304.
[138] MA M, HUGHES O, MCNATT T. Ultimate limit state based ship structural design using multi-objective discrete particle swarm optimization[C]//International Conference on Offshore Mechanics and Arctic Engineering. American Society of Mechanical Engineers,2015,56499:V003T02A084.
[139] 朱俊侠,吴嘉蒙,刘亚冲,等.复杂船体结构拓扑优化中最小稳定拓扑板厚的快速确定方法[J].中国舰船研究,2021,16(6):159-165.ZHU Junxia,WU Jiameng,LIU Yachong,et al. Rapid determination method of minimum stable topological plate thickness in topology optimization of complex hull structures[J]. Chinese Journal of Ship Research,2021,16(6):159-165.
[140] 纪博凯.基于CRH动车组高速列车车体结构拓扑优化设计研究[D].自贡:四川轻化工大学,2019.JI Bokai. Research on topology optimization design of high-speed train body based on CRH RMU[D]. Zigong:Sichuan University of Science & Engineering,2019.
[141] 邱正成,邱广宇,陈秉智.基于子模型的车体断面拓扑优化设计[J].大连交通大学学报,2022,43(4):50-54,95.QIU Zhengcheng, QIU Guangyu, CHEN Bingzhi.Topology optimization design of car body section based on sub-model[J]. Journal of Dalian Jiaotong University,2022,43(4):50-54,95.
[142] 谢素超,杜炫锦,马闻.铁道车辆底架前端承载式吸能结构设计及优化[J].中南大学学报(自然科学版),2022,53(5):1760-1769.XIE Suchao, DU Xuanjin, MA Wen. Design and optimization of bearing type energy absorbing structure at the front end of railway vehicle underframe[J]. Journal of Central South University (Science and Technology),2022,53(5):1760-1769.
[143] 朱瑶瑶.地铁车辆车体结构分析与轻量化研究[D].大连:大连交通大学,2020.ZHU Yaoyao. Research on the structure analysis and lightweight of metro vehicle car body[D]. Dalian:Dalian Jiaotong University,2020.
[144] 刘新武,孙丽萍,王玉艳,等.地铁不锈钢车体侧墙焊点拓扑优化[J].焊接技术,2018,47(8):98-101.LIU Xinwu,SUN Liping,WANG Yuyan,et al. Topology optimization of welding spot on side wall of stainless steel car body in subway[J]. Welding Technology,2018,47(8):98-101.
[145] 林鹏,于洋洋,田洪雷,等.面向不锈钢地铁整车结构的显式拓扑优化设计[J].固体力学学报,2022,43(1):111-120.LIN Peng,YU Yangyang,TIAN Honglei,et al. Explicit topology optimization design of stainless steel metro carbody[J]. Chinese Journal of Solid Mechanic,2022,43(1):111-120.