点阵结构设计制造与疲劳性能研究进展

doi:10.3901/JME.2025.03.347

摘要/Abstract

摘要： 轻量化设计是航空航天、汽车、医疗等行业的重要需求，在降低能耗、提高性能等方面具有显著优势，增材制造技术通过逐层添加材料可以实现复杂结构的制造，点阵结构与增材制造技术相结合已成为高性能轻量化结构设计与制造的新思路。然而，增材制造点阵结构在服役过程中往往会受到循环载荷，发生疲劳破坏，结构轻量化与抗疲劳的协同仍是制约新一代航空航天等结构研发的难题。介绍了轻量化设计与制造方法，总结了点阵结构设计与制造技术，综述增材制造点阵结构疲劳性能研究进展，指出设计/制造一体化是增材制造点阵结构抗疲劳的可行路线。

关键词: 轻量化, 疲劳, 点阵结构, 拓扑优化, 增材制造, 微缺陷

Abstract: Lightweight design is exceptionally needed in sectors including aerospace, automobile, and medical care because of its superiority in reducing energy consumption and enhancing performance of structures. Additive manufacturing can build complex structures by adding materials layer by layer. Today, the integration of lattice structure and additive manufacturing has shed new light on the design and manufacturing of high-performance lightweight structures. However, the lattice structure based on additive manufacturing is often subjected to cyclic loading in service and thus exposed to fatigue damage. The coordination between lightness and anti-fatigue property has yet been achieved in research and development of structures employed in the new generation of aerospace industry. In this review, an introduction of the methods utilized in design and manufacturing of lightweight structures is presented, and a summary of techniques in on the subject is given. After that, a review of the research on fatigue properties of additive-manufactured lattice structures is offered, and it is figured out that the integration of design and manufacturing is feasible to ensure the anti-fatigue property of these structures.

Key words: lightweight, fatigue, lattice structure, topology optimization, additive manufacturing, microdefect

中图分类号:

高壮, 刘雨欣, 朱明亮, 轩福贞. 点阵结构设计制造与疲劳性能研究进展[J]. 机械工程学报, 2025, 61(3): 347-375.

GAO Zhuang, LIU Yuxin, ZHU Mingliang, XUAN Fuzhen. Research Progress on Design, Manufacturing and Fatigue Properties of Lattice Structures[J]. Journal of Mechanical Engineering, 2025, 61(3): 347-375.

参考文献

[1] XIAO S，CHEN C，XIA Q，et al. Lightweight，strong，moldable wood via cell wall engineering as a sustain-able structural material[J]. Science，2021，374(6566):465-71.
[2] WEGST U G K，BAI H，SAIZ E，et al. Bioinspired structural materials[J]. Nature Materials，2015，14(1):23-36.
[3] TRAN M，GABERT L，HOOD S，et al. A lightweight robotic leg prosthesis replicating the biomechanics of the knee，ankle，and toe joint[J]. Science Robotics，2022，7(72):eabo3996.
[4] 王军武，刘旭贺，王飞超，等. 航空航天用高性能超轻镁锂合金[J]. 军民两用技术与产品，2013，(6):21-24.WANG Junwu，LIU Xuhe，WANG Feichao，et al. High Per-formance ultralight magnesium-lithium alloy for aer-ospace applications[J]. Dual-use Technology and Products，2013，(6):21-24.
[5] MARINO M，SABATINI R. Advanced lightweight aircraft design configurations for green operations [C]//Proceedings of the Practical Responses to Climate Change 2014(PRCC 2014). Barton:Engineers Australia，2014:1-9.
[6] ORDOUKHANIAN E，MADNI A M. Blended wing body architecting and design:Current status and fu-ture prospects[J]. Procedia Computer Science，2014，28:619-625.
[7] 范子杰，桂良进，苏瑞意. 汽车轻量化技术的研究与进展[J]. 汽车安全与节能学报，2014，5(1):1-16.FAN Zijie，GUI Liangjin，SU Ruiyi. Research and progress of automotive lightweight technology[J]. Journal of Automotive Safety and Energy Efficiency，2014，5(1):1-16.
[8] ASKARI M，HUTCHINS D A，THOMAS P J，et al. Additive manufacturing of metamaterials:A review[J]. Additive Manufacturing，2020，36:101562.
[9] 轩福贞，朱明亮，王国彪. 结构疲劳百年研究的回顾与展望[J]. 机械工程学报，2021，57(6):26-51.XUAN Fuzhen，ZHU Mingliang，WANG Guobiao. Review and pro-spect of 100-year research on structural fatigue[J]. Journal of Mechanical Engineering，2021，57(6):26-51.
[10] 郝琪，张继伟. 车门结构优化设计的灵敏度分析研究[J]. 汽车技术，2010(5):40-44.HAO Qi，ZHANG Jiwei. Sensitivity analysis of door structure optimization design[J]. Automotive Technology，2010(5):40-44.
[11] RAIS-ROHANI M，SOLANKI K，ACAR E，et al. Shape and sizing optimisation of automotive structures with deterministic and probabilistic design constraints[J]. International Journal of Vehicle Design，2010，54:309-338.
[12] 严君. 基于OptiStruct碳纤维复合材料薄壁结构优化设计研究[D]. 太原:中北大学，2012.YAN Jun. Optimization design of carbon fiber compo-site thin-walled structure based on optistruct[D]. Taiyuan:North University of China，2012.
[13] 李芳，凌道盛. 工程结构优化设计发展综述[J]. 工程设计学报(机械·设备和仪器的开发技术)，2002(5):229-235.LI Fang，LING Daosheng. Review on the development of engineering structure optimization design[J]. Journal of Engineering Design (Development Technology of Machinery，Equipment and Instruments)，2002(5):229-235.
[14] SHIMODA M，TSUJI J. Shape optimization for weight reduction of automotive shell structures subject to a strength constraint:2007-01-3720[R]. New York:SAE Technical Papers，2017.
[15] CEVIK M C，KANPOLAT E，REBBERT M. Shape optimization of a single cylinder engine crankshaft:2011-01-1077[R]. New York:SAE Technical Papers，2011.
[16] MICHELL A G M. The limits of economy of materials in frame structures[J]. Philosophical Magazine，1904，8(47):589-597.
[17] DORN W C. Automatic design of optimal structures[J]. Journal de Mecanique，1964，(3):25-52.
[18] 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.
[19] BENDSØE M P. Optimal shape design as a material distribution problem[J]. Structural Optimization，1989，1(4):193-202.
[20] 李光霁，刘新玲. 汽车轻量化技术的研究现状综述[J].材料科学与工艺，2020，28(5):47-61.LI Guangji，LIU Xinling. Review of research status of automotive lightweight technology[J]. Materials Science and Technology，2020，28(5):47-61.
[21] XIE Y M，STEVEN G P. A simple evolutionary procedure for structural optimization[J]. Computers & Structures，1993，49(5):885-896.
[22] OSHER S，SETHIAN J A. Fronts propagating with curvature-dependent speed:Algorithms based on Hamilton-Jacobi formulations[J]. Journal of Computational Physics，1988，79(1):12-49.
[23] 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.
[24] WANG M Y，WANG X，GUO D. A level set method for structural topology optimization[J]. Computer Methods in Applied Mechanics and Engineering，2003，192(1):227-246.
[25] YUNKANG S，DEQING Y. A new method for structural topological optimization based on the concept of independent continuous variables and smooth model[J]. Acta Mechanica Sinica，1998，14(2):179-185.
[26] 杨德庆，刘正兴，隋允康. 连续体结构拓扑优化设计的ICM方法[J]. 上海交通大学学报，1999(6):98-100.YANG Deqing，LIU Zhengxing，SUI Yunkang. ICM method for topology optimization design of continuum structures[J]. Journal of Shanghai Jiao Tong University，1999(6):98-100.
[27] ZHANG W，CHEN J，ZHU X，et al. Explicit three dimensional topology optimization via Moving Morphable Void (MMV) approach[J]. Computer Methods in Applied Mechanics and Engineering，2017，322:590-614.
[28] GUO X，ZHANG W，ZHONG W. Doing topology optimization explicitly and geometrically-A new moving morphable components based framework[J]. Journal of Applied Mechanics，2014，81(8):081009.
[29] SHI G，GUAN C，QUAN D，et al. An aerospace bracket designed by thermo-elastic topology optimization and manufactured by additive manufacturing[J]. Chinese Journal of Aeronautics，2020，33(4):1252-1259.
[30] 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(S01):67-70.WANG Ruixian，FENG Zhenwei，MA Lingxi，et al. Topology optimization of integrated satellite-sensitive scaffold for small satellites[J]. Journal of Nanjing University of Aeronautics and Astronautics，2021，53(S01):67-70.
[31] 吴云峰，曹文利，史淑娟，等. 面向增材制造和拓扑优化的火箭管路支架设计制造研究[J]. 热加工工艺，2023，52(11):109-13，17.WU Yunfeng，CAO Wenli，SHI Shujuan，et al. Research on design and manufacture of rocket pipeline support for additive manufacturing and topology optimization[J]. Hot Working Technology，2023，52(11):109-13，17.
[32] LI H，LIU R，WANG H，et al. Ant-inspired bionic design method for the support structure of the Fengyun-3 satellite payload infilled with lattice structure[J]. Materials，2023，16(2):736.
[33] GU D，SHI X，POPRAWE R，et al. Material-structure-performance integrated laser-metal additive manufacturing[J]. Science，2021，372(6545):eabg1487.
[34] 顾冬冬，张红梅，陈洪宇，等. 航空航天高性能金属材料构件激光增材制造[J]. 中国激光，2020，47(5):32-55.GU Dongdong，ZHANG Hongmei，CHEN Hongyu，et al. Laser additive manufacturing of aerospace high-performance metal components[J]. Chinese Journal of Lasers，2020，47(5):32-55.
[35] GU H，SHTERENLIKHT A，PAVIER M. Brittle fracture of three-dimensional lattice structure[J]. Engineering Fracture Mechanics，2019，219:106598.
[36] CHOUGRANI L，PERNOT J P，VERON P，et al. Parts internal structure definition using non-uniform patterned lattice optimization for mass reduction in additive manufacturing[J]. Engineering with Computers，2019，35(1):277-289.
[37] ZHOU H，CAO X，LI C，et al. Design of self-supporting lattices for additive manufacturing[J]. Journal of the Mechanics and Physics of Solids，2021，148:104298.
[38] 雷鹏福. 点阵结构的航空构件轻量化设计及优化技术研究[D]. 南京:南京航空航天大学，2020.LEI Pengfu. Research on lightweight design and opti-mization technology of aeronautical components with lattice structure[D]. Nanjing:Nanjing University of Aeronautics and Astronautics，2020.
[39] SCHAEDLER T A，CARTER W B. Architected cellular materials[J]. Annual Review of Materials Re-search，2016，46(1):187-210.
[40] PLOCHER J，PANESAR A. Review on design and structural optimisation in additive manufacturing:Towards next-generation lightweight structures[J]. Materials & Design，2019，183:108164.
[41] KOCAŃDA A，SADŁOWSKA H. Automotive com-ponent development by means of hydroforming[J]. Archives of Civil and Mechanical Engineering，2008，8(3):55-72.
[42] GIBSON L J，ASHBY M F. Cellular solids:Structure and properties[M]. Cambridge:Cambridge University Press，1997.
[43] 方岱宁. 轻质点阵材料力学与多功能设计[M]. 北京:科学出版社，2009.FANG Daining. Mechanics and multi-function design of lightweight lattice materials[M]. Beijing:Science Press，2009.
[44] GIBSON L J. The hierarchical structure and mechanics of plant materials[J]. Journal of the Royal Society Interface，2012，9(76):2749-2766.
[45] LAUNEY M E，BUEHLER M J，RITCHIE R O. On the mechanistic origins of toughness in bone[J]. Annual Review of Materials Research，2010，40(1):25-53.
[46] 荷马，王焕生. 荷马史诗·奥德赛[M]. 北京:人民文学出版社，1997.HOMER，WANG Huansheng. Homer's Odyssey[M]. Beijing:The People's Literature Publishing House，1997.
[47] 荷马，罗念生，王焕生. 荷马史诗·伊利亚特[M]. 上海:上海人民出版社，2016.HOMER，LUO Niansheng，WANG Huansheng. Homer's Epic Poem Iliad[M]. Shanghai:Shanghai People's Publishing House，2016
[48] SCHAEDLER T A，JACOBSEN A J，CARTER W B. Toward lighter，stiffer materials[J]. Science，2013，341(6151):1181-1182.
[49] EMMELMANN C，SANDER P，KRANZ J，et al. Laser additive manufacturing and bionics:Redefining lightweight design[J]. Physics Procedia，2011，12:364-368.
[50] YU Z，XIN R，XU Z，et al. Shock-resistant and energy-absorbing properties of bionic niti lattice structure manufactured by SLM[J]. Journal of Bionic Engineering，2022，19(6):1684-1698.
[51] WANG Y，WANG L，MA Z-D，et al. A negative Pois-son's ratio suspension jounce bumper[J]. Materials & Design，2016，103:90-99.
[52] ASHBY M F，EVANS A，FLECK N A，et al. Metal foams:A design guide[J]. Applied Mechanics Reviews，2002，23(6):119-121.
[53] DU PLESSIS A，RAZAVI N，BENEDETTI M，et al. Properties and applications of additively manufactured metallic cellular materials:A review[J]. Progress in Materials Science，2022，125:100918.
[54] MAXWELL J C，XL V. On reciprocal figures and dia-grams of forces[J]. The London，Edinburgh，and Dublin Philosophical Magazine and Journal of Science，1864，27(182):250-261.
[55] DESHPANDE V S ，ASHBY M F ，FLECK N A. Foam topology:Bending versus stretching dominated architectures[J]. Acta Materialia，2001，49(6):1035-1040.
[56] DESHPANDE V S，FLECK N A，ASHBY M F. Effective properties of the octet-truss lattice material[J]. Journal of the Mechanics & Physics of Solids，2001，49(8):1747-1769.
[57] MARTIN L，MACIEJ M，HUGH W，et al. Inconel 625 lattice structures manufactured by selective laser melting (SLM):Mechanical properties，deformation and failure modes[J]. Materials & Design，2018，157:179-199.
[58] ASHBY M F. The properties of foams and lattices[J]. Philos Trans A Math Phys Eng Sci，2006，364(1838):15-30.
[59] LI S J，XU Q S，WANG Z，et al. Influence of cell shape on mechanical properties of Ti-6Al-4V mesh-es fabricated by electron beam melting method[J]. Acta Biomaterialia，2014，10(10):4537-4547.
[60] 曾元辉. 面向增材制造的功能梯度TPMS点阵结构设计及力学性能研究[D]. 重庆:重庆大学，2022.ZENG Yuanhui. Design and mechanical properties of functional gradient tpms lattice for additive manu-facturing[D]. Chongqing:Chongqing University，2022.
[61] HAN L，CHE S. An overview of materials with triply periodic minimal surfaces and related geometry:From biological structures to self-assembled systems[J]. Advanced Materials，2018，30(17):1705708.
[62] SCHWARZ H A，SCHWARZ H. Bestimmung einer speciellen minimalfläche[J]. Gesammelte Mathe-matische Abhandlungen:Erster Band，1890:6-91.
[63] 王俣. 基于TPMS的骨支架优化设计[D]. 大连:大连理工大学，2022.WANG M. Optimal design of bone scaffold based on TPMS[D]. Dalian:Dalian University of Technology，2022.
[64] SCHOEN A H. Infinite periodic minimal surfaces without self-intersections[M]. Washington:National Aeronautics and Space Administration，1970.
[65] BHATE D，PENICK C A，FERRY L A，et al. Classifi-cation and selection of cellular materials in mechan-ical design:Engineering and biomimetic approaches[J]. Designs，2019，3(1):19-21.
[66] TORQUATO S，DONEV A. Minimal surfaces and multifunctionality[J]. Proceedings of The Royal Society A，2004，460(2047):1849-1856.
[67] LI G Y，ZHI B. Bioinspired heat exchangers based on triply periodic minimal surfaces for supercritical CO₂ cycles[J]. Applied Thermal Engineering:Design，Processes，Equipment，Economics，2020，179:115686.
[68] MASKERY I，STURM L，AREMU A O，et al. Insights into the mechanical properties of several triply periodic minimal surface lattice structures made by polymer additive manufacturing[J]. Polymer，2018，152:62-71.
[69] LEE D-W，KHAN K A，ABU AL-RUB R K. Stiffness and yield strength of architectured foams based on the schwarz primitive triply periodic minimal surface[J]. International Journal of Plasticity，2017，95:1-20.
[70] BERGER J B，WADLEY H N G，MCMEEKING R M. Mechanical metamaterials at the theoretical limit of isotropic elastic stiffness[J]. Nature，2017，543(7646):533-537.
[71] BONATTI C，MOHR D. Mechanical performance of additively-manufactured anisotropic and isotropic smooth shell-lattice materials:Simulations & experiments[J]. Journal of the Mechanics and Physics of Solids，2019，122:1-26.
[72] HAN S C，LEE J W，KANG K. A new type of low density material:Shellular[J]. Advanced Mate-rials，2015，27(37):5506-5511.
[73] TANCOGNE-DEJEAN T，DIAMANTOPOULOU M，GORJI M B，et al. 3D plate-lattices:An emerging class of low-density metamaterial exhibiting opti-mal isotropic stiffness[J]. Advanced Materials，2018，30(45):1803334.
[74] CHEN L-Y，LIANG S-X，LIU Y，et al. Additive manufacturing of metallic lattice structures:Unconstrained design，accurate fabrication，fascinated performances，and challenges[J]. Materials Science and Engineering:R:Reports，2021，146:100648.
[75] ZHANG L，SONG B，FU J J，et al. Topology-optimized lattice structures with simultaneously high stiffness and light weight fabricated by selective laser melting:Design，manufacturing and characterization[J]. Journal of manufacturing processes，2020，56:1166-1177.
[76] XIAO Z，YANG Y，XIAO R，et al. Evaluation of topology-optimized lattice structures manufactured via selective laser melting[J]. Materials & Design，2018，143(APR.):27-37.
[77] DU Y，LI H，LUO Z，et al. Topological design optimization of lattice structures to maximize shear stiff-ness[J]. Advances in Engineering Software，2017，112:211-21.
[78] VINCENT J F V，BOGATYREVA O A，BOGATYREV N R，et al. Biomimetics:Its practice and theory[J]. Journal of The Royal Society Inter-face，2006，3(9):471-82.
[79] HU K，LIN K，GU D，et al. Mechanical properties and deformation behavior under compressive loading of selective laser melting processed bio-inspired sandwich structures[J]. Materials Science and Engineering，2019，762:138089.
[80] YAN D，CHANG J，ZHANG H，et al. Soft three-dimensional network materials with rational bio-mimetic designs[J]. Nature Communications，2020，11(1):1180.
[81] HAO P，DU J. Energy absorption characteristics of bio-inspired honeycomb column thinwalled structure under impact loading[J]. Journal of the Mechanical Behavior of Biomedical Materials，2018，79:301-8.
[82] 张冬云，刘智远，胡松涛，等. 基于激光选区熔化的点阵结构设计、性能及应用研究进展[J]. 航空制造技术，2023，66(10):36-49.ZHANG Dongyun，LIU Zhiyuan，HU Songtao，et al. Research progress of lattice structure design，performance and application based on laser selective melting[J]. Aeronautical Manufacturing Technology，2023，66(10):36-49.
[83] ZHANG L，FEIH S，DAYNES S，et al. Energy absorption characteristics of metallic triply periodic minimal surface sheet structures under compressive loading[J]. Additive Manufacturing，2018，23:505-515.
[84] MASKERY I，ABOULKHAIR N T，AREMU A O，et al. Compressive failure modes and energy absorption in additively manufactured double gyroid lattices[J]. Additive Manufacturing，2017，16:24-29.
[85] PANESAR A，ABDI M，HICKMAN D，et al. Strategies for functionally graded lattice structures derived using topology optimisation for additive manufacturing[J]. Additive Manufacturing，2018，19:81-94.
[86] 金鑫. 面向激光增材制造的变密度多胞结构优化设计与建模研究[D]. 长沙:国防科技大学，2018.JIN Xin. Optimal design and modeling of variable density multi-cell structures for laser additive manufacturing[D]. Changsha:National University of Defense Technology，2018.
[87] DU PLESSIS A，YADROITSAVA I，YADROITSEV I，et al. Numerical comparison of lattice unit cell designs for medical implants by additive manufacturing[J]. Virtual and Physical Prototyping，2018，13(4):266-281.
[88] MASKERY I，HUSSEY A，PANESAR A，et al. An investigation into reinforced and functionally graded lattice structures[J]. Journal of Cellular Plastics，2017，53:151-165.
[89] BAI L，GONG C，CHEN X，et al. Mechanical properties and energy absorption capabilities of functionally graded lattice structures:Experiments and simulations[J]. International Journal of Mechanical Sciences，2020，182:105735.
[90] LIU F，MAO Z，ZHANG P，et al. Functionally graded porous scaffolds in multiple patterns:New design method，physical and mechanical properties[J]. Materials & Design，2018，160:849-60.
[91] LI S，ZHAO S，HOU W，et al. Functionally graded Ti-6Al-4V meshes with high strength and energy absorption[J]. Advanced Engineering Materials，2016，18(1):34-38.
[92] MASKERY I，AREMU A O，PARRY L，et al. Effective design and simulation of surface-based lattice structures featuring volume fraction and cell type grading[J]. Materials & Design，2018，155:220-232.
[93] ZHANG J，SONG B，YANG L，et al. Microstructure evolution and mechanical properties of TiB/Ti6Al4V gradient-material lattice structure fabricated by laser powder bed fusion[J]. Composites Part B Engineering，2020，202:108417.
[94] 赵芳垒，敬石开，刘晨燕. 基于局部相对密度映射的变密度多孔结构设计方法[J]. 机械工程学报，2018，54(19):121-128.ZHAO Fanglei，JING Shikai，LIU Chenyan. Variable density porous structure design method based on local relative density mapping[J]. Journal of Mechanical Engineering，2018，54(19):121-128.
[95] 易长炎，柏龙，陈晓红，等. 金属三维点阵结构拓扑构型研究及应用现状综述[J]. 功能材料，2017，48(10):10055-10065.YI Changyan，BAI Long，CHEN Xiaohong，et al. A review on the research and application of topological configurations of metal three-dimensional lattice structures[J]. Journal of Functional Materials，2017，48(10):10055-10065.
[96] 顾冬冬，张红梅，陈洪宇，等. 航空航天高性能金属材料构件激光增材制造[J]. 中国激光，2020，47(5):32-55.GU Dongdong，ZHANG Hongmei，CHEN Hongyu，et al. Laser additive manufacturing of high performance metal material components for aerospace[J]. Chinese Journal of Lasers，2020，47(5):32-55.
[97] SONG G H，JING S K，ZHAO F L，et al. Design optimization of irregular cellular structure for additive manufacturing[J]. Chinese Journal of Mechanical Engineering，2017，30(5):1184-1192.
[98] TAO W. Design of lattice structure for additive manufacturing[C]//2016 International Symposium on Flexible Automation (ISFA). Cleveland:IEEE，2016:325-332.
[99] DAL FABBRO P，ROSSO S，CERUTI A，et al. Analysis of a preliminary design approach for conformal lattice structures[J]. Applied Sciences，2021，11(23):11449.
[100] 汪志鹏. 基于等效模型的点阵结构仿真技术研究[D]. 南京:南京航空航天大学，2020.WANG Zhipeng. Research on simulation technology of lattice structure based on equivalent model[D]. Nanjing:Nanjing University of Aeronautics and Astronautics，2020.
[101] SAMOILENKO M，SEERS P，TERRIAULT P，et al. Design，manufacture and testing of porous materials with ordered and random porosity:Application to porous medium burners[J]. Applied Thermal Engineering，2019，158:113724.
[102] AREMU A，BRENNAN-CRADDOCK J P J，PANESAR A，et al. A voxel-based method of constructing and skinning conformal and functionally graded lattice structures suitable for additive manufacturing[J]. Additive Manufacturing，2017，13:1-13.
[103] HAO L. Design and additive manufacturing of cellular lattice structures[C]//The International Conference on Advanced Research in Virtual and Rapid Prototy (VRAP)，Leiria:Taylor & Francis Group，2011:249-254.
[104] 姚远，郭明. 模型体结构可控装配方法[J]. 计算机辅助设计与图形学学报，2014，26(10):1886-1893.YAO Yuan，GUO Ming. Controllable assembly method of model body structure[J]. Journal of Computer-Aided Design and Graphics，2014，26(10):1886-1893.
[105] HU J，LUO Y，LIU S. Two-scale concurrent topology optimization method of hierarchical structures with self-connected multiple lattice-material domains[J]. Composite Structures，2021，272:114224.
[106] WANG X，QIN R，CHEN B. Mechanical properties and energy absorption capability of a topology-optimized lattice structure manufactured via selective laser melting under axial and offset loading[J]. Proceedings of the Institution of Mechanical Engineers，Part C:Journal of Mechanical Engineering Science，2022，236:10221-10236.
[107] ZHANG P，TOMAN J，YU Y，et al. Efficient design-optimization of variable-density hexagonal cellular structure by additive manufacturing:Theory and validation[J]. Journal of Manufacturing Science and Engineering，2015，137(2):021004.
[108] SPEIRS M，VAN HOOREWEDER B，VAN HUMBEECK J，et al. Fatigue behaviour of NiTi shape memory alloy scaffolds produced by SLM，a unit cell design comparison[J]. Journal of the Mechanical Behavior of Biomedical Materials，2017，70:53-59.
[109] GORGULUARSLAN R M，GANDHI U N，MANDAPATI R，et al. Design and fabrication of periodic lattice-based cellular structures[J]. Computer-Aided Design and Applications，2016，13(1):50-62.
[110] 段晟昱，王潘丁，刘畅，等. 增材制造三维点阵结构设计、优化与性能表征方法研究进展[J]. 航空制造技术，2022，65(14):36-48，57.DUANG Shengyu，WANG Panding，LIU Chang，et al. Research progress of 3D lattice structure design，optimization and performance characterization methods for additive manufacturing[J]. Aeronautical Manufacturing Technology，2022，65(14):36-48，57.
[111] JAFFERSON J M，SHARMA H. Design of 3D printable airless tyres using NTopology[J]. Materials Today:Proceedings，2021，46:1147-1160.
[112] HELOU M，KARA S. Design，analysis and manufacturing of lattice structures:An overview[J]. International Journal of Computer Integrated Manufacturing，2018，31(3):243-261.
[113] LU T，ZHANG Q. Novel strengthening methods for ultralightweight sandwich structures with periodic lattice cores[J]. Science China Technological Sciences，2010，53(3):875-877.
[114] MUN J，YUN B-G，JU J，et al. Indirect additive manufacturing based casting of a periodic 3D cellular metal – Flow simulation of molten aluminum alloy[J]. Journal of Manufacturing Processes，2015，17:28-40.
[115] LI Q，CHEN E，BICE D R，et al. Mechanical proper-ties of cast Ti-6Al-2Sn-4Zr-2Mo lattice block structures[J]. Advanced Engineering Materials，2008，10:939-942.
[116] SENNEWALD C，KAINA S，WECK D，et al. Metal sandwiches and metal-matrix-composites based on 3D woven wire structures for hybrid lightweight construction[J]. Advanced Engineering Materials，2014，16(10):1234-1242.
[117] LEE M G，KANG K J. A cellular metal composed of straight wires[J]. Procedia Materials Science，2014，4:169-174.
[118] KHODA B，AHSAN A. A novel rapid manufacturing process for metal lattice structure[J]. 3D Print Addit Manuf，2021，8(2):111-125.
[119] QUEHEILLALT D T，WADLEY H N G. Titanium alloy lattice truss structures[J]. Materials & Design，2009，30(6):1966-1975.
[120] SCHAEDLER T A，JACOBSEN A J，TORRENTS A，et al. Ultralight metallic microlattices[J]. Science，2011，334(6058):962-965.
[121] N'JOCK M Y，CAMPOSILVAN E，GREMILLARD L，et al. Characterization of 100Cr6 lattice structures produced by robocasting[J]. Materials & Design，2017，121:345-354.
[122] JIANG S，SUN F，ZHANG X，et al. Interlocking orthogrid:An efficient way to construct lightweight lattice-core sandwich composite structure[J]. Composite Structures，2017，176:55-71.
[123] RIMOLI J J，TALAMINI B，WETZEL J J，et al. Wet-sand impulse loading of metallic plates and corrugated core sandwich panels[J]. International Journal of Impact Engineering，2011，38(10):837-848.
[124] PENG E，WEI X，GARBE U，et al. Robocasting of dense yttria-stabilized zirconia structures[J]. Journal of Materials Science，2017，53:247-273.
[125] WANG X-T，LI X-W，MA L. Interlocking assembled 3D auxetic cellular structures[J]. Materials & Design，2016，99:467-476.
[126] POLLACK J，SINGH A，et al. Towards space from Hilbert space:Finding lattice structure in finite-dimensional quantum systems[J]. Quantum Studies:Mathematics and Foundations，2019，6(2):181-200.
[127] VANEKER T，BERNARD A，MORONI G，et al. Design for additive manufacturing:Framework and methodology[J]. CIRP Annals，2020，69(2):578-599.
[128] 刘书田，李取浩，陈文炯，等. 拓扑优化与增材制造结合:一种设计与制造一体化方法[J]. 航空制造技术，2017(10):26-31.LIU Shutian，LI Quhao，CHEN Wenjiong，et al. Combination of topology optimization and additive manufacturing:An integrated design and manufacturing method[J]. Aeronautical Manufacturing Technology，2017(10):26-31.
[129] 刘伟，李能，周标，等. 复杂结构与高性能材料增材制造技术进展[J]. 机械工程学报，2019，55(20):128-151，159.LIU Wei，LI Neng，ZHOU Biao，et al. Advances in additive manufacturing technology of complex structures and high performance materials[J]. Journal of Mechanical Engineering，2019，55(20):128-151，159.
[130] GU D，SHI X，POPRAWE R，et al. Material- structure-performance integrated laser-metal additive manufacturing[J]. Science，2021，372(6545):eabg1487.
[131] 朱家威，潘威，黄士争，等. 高速高强熔融沉积成型技术研究进展[J]. 中国塑料，2023，37(8):118-126.ZHU Jiawei，PAN Wei，HUANG Shizheng，et al. Research progress of high speed and high strength fused deposition molding technology[J]. China Plastics，2023，37(8):118-126.
[132] ZIAEE M，CRANE N B. Binder jetting:A review of process，materials，and methods[J]. Additive Manufacturing，2019，28:781-801.
[133] BLAKEY-MILNER B，GRADL P，SNEDDEN G，et al. Metal additive manufacturing in aerospace:A review[J]. Materials & Design，2021，(12):110008.
[134] JIA D，FANCHUN L I，ZHANG Y. 3D-printing process design of lattice compressor impeller based on residual stress and deformation[J]. Scientific Reports，2020，10(1):600.
[135] BICI M，BRISCHETTO S，CAMPANA F，et al. Development of a multifunctional panel for aerospace use through SLM additive manufacturing[J]. Procedia CIRP，2018，67:215-220.