Strength and lifetime assessment and design for additive manufacturing structures in aero-engine: review and prospects
-
摘要:
介绍了增材制造技术在航空发动机中的应用现状,重点论述航空发动机中增材制造结构强度、寿命评估与设计等关键技术的研究进展。分别从增材制造缺陷的无损检测方法与等效准则、考虑缺陷影响的关重件强度与寿命预测方法,以及创新结构一体化设计技术等方面探讨了现有研究进展、存在不足,以及发展趋势。结果表明:航空发动机中增材制造结构强度、寿命评估处于起步阶段,大多针对增材制造材料及简单结构的单一失效模式,仍需在复合疲劳失效、“结构特征-广布缺陷-表面形貌”多因素耦合失效等方面开展研究,从而发展适用于航空发动机增材制造结构的数据驱动评估方法、损伤容限设计方法以及专用试验技术。
Abstract:The application status of additive manufacturing technology in aero-engine was introduced, and the key technologies of strength, lifetime assessment and design methods for additive manufacturing structures in aero-engine were emphatically reviewed. The shortcomings and development trends of existing research were discussed in terms of nondestructive detection methods and equivalence criteria for additive manufacturing defects, strength and lifetime prediction methods considering the effects of defects, and the integrated innovative structure design technology of aero-engine additive manufacturing structures, respectively. The results showed that strength and life assessment of additive manufacturing structures in aero-engine was at the initial stage. Most of them were geared for the additive manufacturing materials and simple structures under a single failure mode, making it necessary to conduct research on compound fatigue failure, multi-factor failure coupled of structural characteristics-widespread defects-surface morphology, so as to develop data-driven evaluation methods, damage tolerance design methods and special test techniques for aero-engine additive manufacturing structures.
-
图 6 SLM成形AlSi10Mg铝合金试样内部的缺陷演化[42]
Figure 6. Defect evolution in AlSi10Mg aluminum alloy specimen formed by SLM
-
[1] 冀国锋,李俊励,杨进飞. 风扇/压气机增材制造技术的应用与发展趋势[J]. 航空动力,2020(2): 75-78.JI Guofeng,LI Junli,YANG Jinfei. Application and development trend of additive manufacturing technology for fan/compressor[J]. Aviation Power,2020(2): 75-78. (in Chinese) [2] 常坤,梁恩泉,张韧,等. 金属材料增材制造及其在民用航空领域的应用研究现状[J]. 材料导报,2021,35(3): 1-7. doi: 10.11896/cldb.19100153CHANG Kun,LIANG Enquan,ZHANG Ren,et al. Research status of additive manufacturing of metal materials and its application in civil aviation[J]. Material Guide,2021,35(3): 1-7. (in Chinese) doi: 10.11896/cldb.19100153 [3] 邵冬. 罗罗的智能发动机愿景分析[J]. 航空动力,2020(3): 27-30.SHAO Dong. Rolls-Royce’s vision analysis of intelligent engine[J]. Aviation power,2020(3): 27-30. (in Chinese) [4] 张小伟. 金属增材制造技术在航空发动机领域的应用[J]. 航空动力学报,2016,31(1): 10-16. doi: 10.13224/j.cnki.jasp.2016.01.002ZHANG Xiaowei. Application of metal additive manufacturing technology in aeroengine field[J]. Journal of Aerospace Power,2016,31(1): 10-16. (in Chinese) doi: 10.13224/j.cnki.jasp.2016.01.002 [5] 王强,孙跃. 增材制造技术在航空发动机中的应用[J]. 航空科学技术,2014,25(9): 6-10. doi: 10.3969/j.issn.1007-5453.2014.09.002WANG Qiang,SUN Yue. Application of additive manufacturing technology in aeroengine[J]. Aviation Science and Technology,2014,25(9): 6-10. (in Chinese) doi: 10.3969/j.issn.1007-5453.2014.09.002 [6] 汪文君,徐友良,吴雪蓓,等. 基于增材制造的微型涡喷发动机轻量化设计及试验[J]. 航空动力,2019(3): 20-22.WANG Wenjun,XU Youliang,WU Xuebei,et al. Lightweight design and test of micro turbojet engine based on additive manufacturing[J]. Aviation Power,2019(3): 20-22. (in Chinese) [7] Federal Aviation Administration. Guide for manufacturing and repairing formed turbine engine parts with powder bed melt additive: AC 33.15-4[S]. Washington DC: Federal Aviation Administration, 2018: 1-18. [8] European Aviation Safety Agency. Certification memorandum additive manufacturing: CM-S-008[S]. Cologne: European Aviation Safety Agency, 2021: 1-25. [9] SANAEI N,FATEMI A. Defects in additive manufactured metals and their effect on fatigue performance: A state-of-the-art review[J]. Progress in Materials Science,2021,117: 100724.1-100724.41. [10] SANAEI N,FATEMI A,PHAN N. Defect characteristics and analysis of their variability in metal L-PBF additive manufacturing[J]. Materials and Design,2019,182: 108091.1-108091.22. [11] PLESSIS A,YADROITSAVA I,YADROITSEV I. Effects of defects on mechanical properties in metal additive manufacturing: a review focusing on X-ray tomography insights[J]. Materials and Design,2020,187: 108385.1-108385.19. [12] ZERBST U,MADIA M,KLINGER C,et al. Defects as a root cause of fatigue failure of metallic components: Ⅰ basic aspects[J]. Engineering Failure Analysis,2019,97: 777-792. doi: 10.1016/j.engfailanal.2019.01.055 [13] BECKER T, KUMAR P, RAMAMURTY U. Fracture and fatigue in additively manufactured metals[J]. Acta Materialia, 2021, 219: 117240.1-11724041. [14] 吴正凯,张杰,吴圣川,等. 同步辐射X射线原位三维成像在金属增材制件缺陷评价中的应用[J]. 无损检测,2020,42(7): 46-50. doi: 10.11973/wsjc202007011WU Zhengkai,ZHANG Jie,WU Shengchuan,et al. Application of synchrotron radiation X-ray in situ three-dimensional imaging in defect evaluation of metal additive parts[J]. Nondestructive Testing,2020,42(7): 46-50. (in Chinese) doi: 10.11973/wsjc202007011 [15] HONARVAR F,VARVANI-FARAHANI A. A review of ultrasonic testing applications in additive manufacturing: defect evaluation, material characterization, and process control[J]. Ultrasonics,2020,108: 106227.1-106227.15. [16] 韩立恒,巩水利,锁红波,等. A-100钢电子束熔丝成形件超声相控阵检测应用初探[J]. 航空制造技术,2016(8): 66-70. doi: 10.16080/j.issn1671-833x.2016.08.066HAN Liheng,GONG Shuili,SUO Hongbo,et al. Preliminary study on ultrasonic phased array testing of A-100 steel electron beam fuse forming parts[J]. Aviation Manufacturing Technology,2016(8): 66-70. (in Chinese) doi: 10.16080/j.issn1671-833x.2016.08.066 [17] HANKS E, LIU D, PALAZOTTO A. Surface roughness of electron beam melting Ti-6Al-4V effect on ultrasonic testing[R]. AIAA 2016-1512, 2016. [18] RUDLIN J, CERNIGLIA D, SCAFID I, et al. Inspection of laser powder deposited layers[C]//Proceedings of 11th European Conference on Nondestructive Testing. Prague: European Federation for NDT, 2014: 1-10. [19] WALLER J, SAULSBERRY R, PARKER B, et al. Summary of NDE of additive manufacturing efforts in NASA [R]. NASA Report 20140009937, 2014. [20] 廉艳平, 王潘丁, 高杰, 等. 金属增材制造若干关键力学问题研究进展[J]. 力学进展, 2021, 51(3): 648-701.LIAN Yanping, WANG Panding, GAO Jie, et al. Research progress on some key mechanical problems of metal additive manufacturing[J]. Mechanical Progress, 2021, 51(3): 648-701. (in Chinese) [21] 吴圣川,吴正凯,胡雅楠,等. 同步辐射光源四维原位成像助力材料微结构损伤高分辨表征[J]. 机械工程材料,2020,44(6): 72-76. doi: 10.11973/jxgccl202006016WU Shengchuan,WU Zhengkai,HU Yanan,et al. High resolution characterization of microstructure damage in materials assisted by four-dimensional in-situ imaging with synchrotron radiation sources[J]. Mechanical Engineering Materials,2020,44(6): 72-76. (in Chinese) doi: 10.11973/jxgccl202006016 [22] MAIRE E,WITHERS P. Quantitative X-ray tomography[J]. International Materials Reviews,2014,59(1): 1-43. doi: 10.1179/1743280413Y.0000000023 [23] PLESSIS A,YADROITSAVA I,YADROITSEV I. X-Ray microcomputed tomography in additive manufacturing: a review of the current technology and applications[J]. 3D Printing and Additive Manufacturing,2018,5(3): 227-247. doi: 10.1089/3dp.2018.0060 [24] MURAKAMI Y,NEMAT-NASSER S. Growth and stability of interacting surface flaws of arbitrary shape[J]. Engineering Fracture Mechanics,1983,17(3): 193-210. doi: 10.1016/0013-7944(83)90027-9 [25] MURAKAMI Y. Additive manufacturing: effects of defects[M]. San Diego, US: Academic Press, 2019: 453-483.83. [26] EMANUELLI L,MOLINARI A,FACCHINI L,et al. Effect of heat treatment temperature and turning residual stresses on the plain and notch fatigue strength of Ti-6Al-4V additively manufactured via laser powder bed fusion[J]. International Journal of Fatigue,2022,162: 107009.1-107009.12. [27] XIE Cheng,WU Shengchuan,YU Yukuang,et al. Defect-correlated fatigue resistance of additively manufactured Al-Mg4.5Mn alloy with in situ micro-rolling[J]. Journal of Materials Processing Technology,2021,291: 117039.1-117039.13. [28] HU Yanan,WU Shengchuan,WU Zhengkai,et al. A new approach to correlate the defect population with the fatigue life of selective laser melted Ti-6Al-4V alloy[J]. International Journal of Fatigue,2020,136: 105584.1-105584.11. [29] LEUDERS S,VOLLMER M,BRENNE F,et al. Fatigue strength prediction for titanium alloy TiAl6V4 manufactured by selective laser melting[J]. Metallurgical and Materials Transactions A,2015,46(9): 3816-3823. doi: 10.1007/s11661-015-2864-x [30] LEUDERS S,LIENEKE T,LAMMERS S,et al. On the fatigue properties of metals manufactured by selective laser melting: the role of ductility[J]. Journal of Materials Research,2014,29(17): 1911-1919. doi: 10.1557/jmr.2014.157 [31] LEUDERS S,THONE M,RIEMER A,et al. On the mechanical behaviour of titanium alloy TiAl6V4 manufactured by selective laser melting: fatigue resistance and crack growth performance[J]. International Journal of Fatigue,2013,48: 300-307. doi: 10.1016/j.ijfatigue.2012.11.011 [32] NADOT Y,NADOT-MARTIN C,KAN W,et al. Predicting the fatigue life of an AlSi10Mg alloy manufactured via laser powder bed fusion by using data from computed tomography[J]. Additive Manufacturing,2020,32: 100899.1-100899.11. [33] WU Zhengkai,WU Shengchuan,BAO Jianguang,et al. The effect of defect population on the anisotropic fatigue resistance of AlSi10Mg alloy fabricated by laser powder bed fusion[J]. International Journal of Fatigue,2021,151: 106317.1-106317.14. [34] HU Dianyin,PAN Jinchao,MI Dong,et al. Prediction of anisotropic LCF behavior for SLM Ti-6Al-4V considering the spatial orientation of defects[J]. International Journal of Fatigue,2022,158: 106734.1-106734.12. [35] VINCENT M,NADOT-MARTIN C,NADOT Y,et al. Fatigue from defect under multiaxial loading: defect stress gradient (DSG) approach using ellipsoidal equivalent inclusion method[J]. International Journal of Fatigue,2014,59: 176-187. doi: 10.1016/j.ijfatigue.2013.08.027 [36] 战立鼎. 基于断层扫描成像的增材制造材料高周疲劳极限预测方法[D]. 北京: 北京航空航天大学, 2022.ZHAN Liding. High cycle fatigue limit prediction method for additive manufacturing materials based on tomography [D]. Beijing: Beihang University, 2022. (in Chinese) [37] YASIN A,SYLVAIN D,PAULINE D,et al. Compression behavior of lattice structures produced by selective laser melting: X-ray tomography based experimental and finite element approaches[J]. Acta Materialia,2018,159: 395-407. doi: 10.1016/j.actamat.2018.08.030 [38] WANG Panding,ZHOU Hao,ZHANG Limin,et al. In situ X-ray micro-computed tomography study of the damage evolution of prefabricated through-holes in SLM-Printed AlSi10Mg alloy under tension[J]. Journal of Alloys and Compounds,2020,821: 153576.1-153576.8. [39] 虞雨洭,吴正凯,吴圣川. 高分辨三维成像原位试验机研制进展及应用[J]. 中国材料进展,2021,40(2): 90-104. doi: 10.7502/j.issn.1674-3962.202007031YU Yuling,WU Zhengkai,WU Shengchuan. Development and application of high resolution 3D imaging in situ testing machine[J]. Material progress in China,2021,40(2): 90-104. (in Chinese) doi: 10.7502/j.issn.1674-3962.202007031 [40] BALE A,HABOUB A,MACDOWELL A,et al. Real-time quantitative imaging of failure events in materials under load at temperatures above 1 600 °C[J]. Nature Materials,2013,12(1): 40-46. doi: 10.1038/nmat3497 [41] DEZECOT S,BUFFIERE J,KOSTER A,at al. In situ 3D characterization of high temperature fatigue damage mechanisms in a cast aluminum alloy using synchrotron X-ray tomography[J]. Scripta Materialia,2016,113: 254-258. doi: 10.1016/j.scriptamat.2015.11.017 [42] BAO Jianguang,WU Shengchuan,WITHERS P,at al. Defect evolution during high temperature tension-tension fatigue of SLM AISi10Mg alloy by synchrotron tomography[J]. Materials Science and Engineering:A,2020,792: 139809.1-139809.13. [43] HU Dianyin,PAN Jinchao,MAO Jianxing,et al. Mechanical behavior prediction of additively manufactured components based on defect evolution observation by synchrotron radiation X-ray tomography[J]. Materials and Design,2021,198: 109353.1-109353.9. [44] WAN Hualiang,WANG Qizhi,JIA Chengxue,et al. Multi-scale damage mechanics method for fatigue life prediction of additive manufacture structures of Ti-6Al-4V[J]. Materials Science and Engineering A,2016,669: 269-278. doi: 10.1016/j.msea.2016.05.073 [45] GURSON A. Continuum theory of ductile rupture by void nucleation and growth: Part 1 yield criteria and flow rules for porous ductile media[J]. Journal of Engineering Materials and Technology1977, 99(1): 2-15. [46] TVERGAARD V,NEEDLEMAN A. Analysis of the cup-cone fracture in a round tensile bar[J]. Acta Metallurgica,1984,32(1): 157-169. doi: 10.1016/0001-6160(84)90213-X [47] YANG Xuan,LI Yazhi,JIANG Wei,et al. Ductile fracture prediction of additive manufactured Ti6Al4V alloy based on an extended GTN damage model[J]. Engineering Fracture Mechanics,2021,256: 107989.1-107989.12. [48] HORSTEMEYER M,GOKHALE A. A void-crack nucleation model for ductile metals[J]. International Journal of Solids and Structures,1999,36(33): 5029-5055. doi: 10.1016/S0020-7683(98)00239-X [49] POTIRNICHE G,HORSTEMEYER M,LING X. An internal state variable damage model in crystal plasticity[J]. Mechanics of Materials,2007,39(10): 941-952. doi: 10.1016/j.mechmat.2007.04.004 [50] YADOLLAHI A,SHAMSAEI N,HAMMI Y,et al. Quantification of tensile damage evolution in additive manufactured austenitic stainless steels[J]. Materials Science and Engineering A,2016,657: 399-405. doi: 10.1016/j.msea.2016.01.067 [51] 文长龙. 3D打印空心离心叶轮破裂转速测试试验报告[R]. 湖南 株洲: 中国航发湖南动力机械研究所, 2021.WEN Changlong. The test report on the fracture speed of 3D print hollow centrifugal impeller [R]. Zhuzhou Hunan: Hunan Aviation Powerplant Research Institute, Aero Engine Corporation of China, 2021. (in Chinese) [52] ROMANO S,BRANDAO A,GUMPINGER J,et al. Qualification of AM parts: extreme value statistics applied to tomographic measurements[J]. Materials and Design,2017,131: 32-48. doi: 10.1016/j.matdes.2017.05.091 [53] GÜNTHER J,KREWERTH D,LIPPMANN T,et al. Fatigue life of additively manufactured Ti–6Al–4V in the very high cycle fatigue regime[J]. International Journal of Fatigue,2017,94: 236-245. doi: 10.1016/j.ijfatigue.2016.05.018 [54] MOLAEI R,FATEMI A,SANAEI N,et al. Fatigue of additive manufactured Ti-6Al-4V Part Ⅱ: the relationship between microstructure, material cyclic properties, and component performance[J]. International Journal of Fatigue,2020,132,105363: 1-19. [55] LE V,PESSARD E,MOREL F,et al. Interpretation of the fatigue anisotropy of additively manufactured Ti-6Al-4V alloys via a fracture mechanics approach[J]. Engineering Fracture Mechanics,2019,214: 410-426. doi: 10.1016/j.engfracmech.2019.03.048 [56] LE V,PESSARD E,MOREL F,et al. Fatigue behaviour of additively manufactured Ti-6Al-4V alloy: the role of defects on scatter and statistical size effect[J]. International Journal of Fatigue,2020,140: 105811.1-105811.16. [57] BERETTA S,GARGOURIMOTLAGH M,FOLETTI S,et al. Fatigue strength assessment of as built AlSi10Mg manufactured by SLM with different build orientations[J]. International Journal of Fatigue,2020,139: 105737.1-105737.16. [58] TORRIES B,STERLING A J,SHAMSAEI N,et al. Utilization of a microstructure sensitive fatigue model for additively manufactured Ti-6Al-4V[J]. Rapid Prototyping Journal,2016,22(5): 817-825. doi: 10.1108/RPJ-11-2015-0168 [59] BISWAL R,ZHANG X,SHAMIR M,et al. Interrupted fatigue testing with periodic tomography to monitor porosity defects in wire arc additive manufactured Ti-6Al-4V[J]. Additive Manufacturing,2019,28: 517-527. doi: 10.1016/j.addma.2019.04.026 [60] XUE Yibin,BURTON C,HORSTEMEYER M,et al. Multistage fatigue modeling of cast A356-T6 and A380-F aluminum alloys[J]. Metallurgical and Materials Transactions B,2007,38(4): 601-606. doi: 10.1007/s11663-007-9062-1 [61] MCDOWELL D,GALL K,HORSTEMEYER M,et al. Microstructure-based fatigue modeling of cast A356-T6 alloy[J]. Engineering Fracture Mechanics,2003,70(1): 49-80. doi: 10.1016/S0013-7944(02)00021-8 [62] MCDOWELL D. Simulation-based strategies for microstructure-sensitive fatigue modeling[J]. Materials Science and Engineering:A,2007,468: 4-14. [63] XUE Yibin,MCDOWELL D,HORSTEMEYER M,et al. Microstructure-based multistage fatigue modeling of aluminum alloy 7075-T651[J]. Engineering Fracture Mechanics,2007,74(17): 2810-2823. doi: 10.1016/j.engfracmech.2006.12.031 [64] XUE Yibin,HORSTEMEYER M,MCDOWELL D,et al. Microstructure-based multistage fatigue modeling of a cast AE44 magnesium alloy[J]. International Journal of Fatigue,2007,29(4): 666-676. doi: 10.1016/j.ijfatigue.2006.07.005 [65] GUEST J,PRÉVOST J,BELYTSCHKO T. Achieving minimum length scale in topology optimization using nodal design variables and projection functions[J]. International Journal for Numerical Methods in Engineering,2004,61(2): 1-7. [66] GUEST J. Imposing maximum length scale in topology optimization[J]. Structural and Multidisciplinary Optimization,2009,37(5): 463-473. doi: 10.1007/s00158-008-0250-7 [67] BRACKETT D, ASHCROFT I, HAGUE R. Topology optimization for additive manufacturing[C]//Proceedings of 2011 International Solid Freeform Fabrication Symposium. Austin, US: AHS International, 2011: 1-8. [68] LIU Shutian,LI Quhao,CHEN Wwenjiong,et al. An identification method for enclosed voids restriction in manufacturability design for additive manufacturing structures[J]. Frontiers of Mechanical Engineering,2015,10(2): 126-137. doi: 10.1007/s11465-015-0340-3 [69] LI Quhao,CHEN Wenjiong,LIU Shutian,et al. Structural topology optimization considering connectivity constraint[J]. Structural and Multidisciplinary Optimization,2016,54(4): 971-984. doi: 10.1007/s00158-016-1459-5 [70] WANG Bo,WANG Guangming,SHI Yongxin,et al. Stress-constrained thermo-elastic topology optimization of axisymmetric disks considering temperature-dependent material properties[J]. Mechanics of Advanced Materials and Structures,2021,28: 2000080.1-2000080.9. [71] 韩永生, 徐斌, 赵磊. 基于应力的几何非线性结构拓扑优化[C]//中国力学大会论文集. 杭州: 中国力学大会, 2019, 1-9. [72] 赖斌皓. 基于OptiStruct的涡轮盘拓扑优化设计技术研究[D]. 长沙: 湖南大学, 2019.LAI Binhao. Research on topology optimization design technology of turbine disk based on Optistruct [D]. Changsha: Hunan University, 2019. (in Chinese) [73] 侯亮,柴象海,白国娟,等. 航空发动机短舱泄压门冲击载荷结构拓扑优化技术研究[J]. 航空科学技术,2022,33(1): 58-65. doi: 10.19452/j.issn1007-5453.2022.01.007HOU Liang,CHAI Xianghai,BAI Guojuan,et al. Research on topology optimization technology of impact load structure for pressure relief valve of aeroengine nacelle[J]. Aeronautical Science and technology,2022,33(1): 58-65. (in Chinese) doi: 10.19452/j.issn1007-5453.2022.01.007 [74] 张一雨,郑百林,吴一帆,等. 鸟撞工况下HCA动态拓扑优化整级叶片的数值模拟[J]. 推进技术,2019,40(2): 431-440. doi: 10.13675/j.cnki.tjjs.180058ZHANG Yiyu,ZHENG Bailin,WU Yifan,et al. Numerical simulation of HCA dynamic topology optimization integral stage blade under bird impact condition[J]. Propulsion Technology,2019,40(2): 431-440. (in Chinese) doi: 10.13675/j.cnki.tjjs.180058 [75] 黄协思. 疲劳约束下航空发动机涡轮盘结构优化设计[D]. 成都: 电子科技大学, 2020.HUANG Xiesi. Structural optimization design of aeroengine turbine disk under fatigue constraint [D]. Chengdu: University of Electronic Science and Technology of China, 2020. (in Chinese) [76] 邢广鹏,孙志刚,崔向敏,等. 多工况载荷下航空发动机支架拓扑优化设计[J]. 航空动力学报,2020,35(11): 2248-2262. doi: 10.13224/j.cnki.jasp.2020.11.002XING Guangpeng,SUN Zhigang,CUI Xiangmin,et al. Topology optimization design of aeroengine support under multi load conditions[J]. Journal of Aerospace Power,2020,35(11): 2248-2262. (in Chinese) doi: 10.13224/j.cnki.jasp.2020.11.002 [77] 邓小雷,盛泽枫,张江林,等. 基于不规则元胞的主轴温度-结构场耦合热拓扑优化设计方法[J]. 浙江大学学报(工学版),2020,54(1): 23-32. doi: 10.3785/j.issn.1008-973X.2020.01.003DENG Xiaolei,SHENG Zefeng,ZHANG Jianglin,et al. Optimization design method of spindle temperature structure field coupling thermal topology based on irregular cell[J]. Journal of Zhejiang University (Engineering Edition),2020,54(1): 23-32. (in Chinese) doi: 10.3785/j.issn.1008-973X.2020.01.003 [78] PICELLI R,RANJBARZADEH S,SIVAPURAM R,et al. Topology optimization of binary structures under design-dependent fluid-structure interaction loads[J]. Structural and Multidisciplinary Optimization,2020,62(4): 2101-2116. doi: 10.1007/s00158-020-02598-0 [79] YU Minghao,RUAN Shilun,GU Junfeng,et al. Three-dimensional topology optimization of thermal-fluid-structural problems for cooling system design[J]. Structural and Multidisciplinary Optimization,2020,62(6): 3347-3366. doi: 10.1007/s00158-020-02731-z [80] FEPPON F,ALLAIRE G,DAPOGNY C,et al. Topology optimization of thermal fluid–structure systems using body-fitted meshes and parallel computing[J]. Journal of Computational Physics,2020,417: 109574.1-109574.30. [81] 牟佳信,邢彬,郭梅,等. 考虑热、弹、流耦合的航空发动机齿轮箱壳体拓扑优化分析[J]. 机械传动,2022,46(2): 127-134. doi: 10.16578/j.issn.1004.2539.2022.02.021MU Jiaxin,XING Bin,GUO Mei,et al. Topology optimization analysis of aeroengine gearbox shell considering thermal, elastic and fluid coupling[J]. Mechanical Transmission,2022,46(2): 127-134. (in Chinese) doi: 10.16578/j.issn.1004.2539.2022.02.021 [82] KIM J,PAULINO G. Isoparametric graded finite elements for nonhomogeneous isotropic and orthotropic materials[J]. Journal of Apply Mechanics,2002,69(4): 502-514. doi: 10.1115/1.1467094 [83] RADMAN A,HUANG X,XIE Y. Topology optimization of functionally graded cellular materials[J]. Journal of Materials Science,2013,48(4): 1503-1510. doi: 10.1007/s10853-012-6905-1 [84] LIU Pai,LUO Yangjun,KANG Zhan. Multi-material topology optimization considering interface behavior via XFEM and level set method[J]. Computer Methods in Applied Mechanics and Engineering,2016,308: 113-133. doi: 10.1016/j.cma.2016.05.016 [85] 李雯竹. 基于功能梯度材料的涡轮盘拓扑优化方法研究[D]. 北京: 北京航空航天大学, 2022.LI Wenzhu. Study on topology optimization method of turbine disk based on functionally graded materials[D]. Beijing: Beihang University, 2022. (in Chinese) [86] YAN Jun,ZHANG Chenguang,HUO Sixu,et al. Experimental and numerical simulation of bird-strike performance of lattice-material-infilled curved plate[J]. Chinese Journal of Aeronautics,2021,34(8): 245-257. doi: 10.1016/j.cja.2020.09.026 [87] 张严. 超轻质多孔结构的多尺度拓扑优化方法研究[D]. 武汉: 华中科技大学, 2020.ZHANG Yan. Research on multi-scale topology optimization method for ultra light porous structures [D]. Wuhan: Huazhong University of Science and Technology, 2020. (in Chinese) [88] PHAM M,LIU C,TODD I,et al. Damage-tolerant architected materials inspired by crystal microstructure[J]. Nature,2019,565(7739): 305-311. doi: 10.1038/s41586-018-0850-3 [89] 米栋, 文长龙. 涡喷发动机转子部件轻量化设计及验证[R]. 湖南 株洲: 中国航发湖南动力机械研究所, 2022.MI Dong, WEN Changlong. Lightweight design and verification of turbojet engine rotor components[R]. Zhuzhou Hunan: Hunan Aviation Powerplant Research Institute, Aero Engine Corporation of China, 2022. (in Chinese)