Review on the analysis and control technology of curing residual stress in solid motor propellants

  • YU Bao-Shi ,
  • LEI Yong-Jun ,
  • SHEN Zhi-Bin ,
  • ZHANG Da-Peng
Expand

Received date: 2024-08-20

  Revised date: 2024-10-14

  Online published: 2024-10-15

Supported by

National Natural Science Foundation of China;National Natural Science Foundation of China;Independent Research and Cultivation Project for Young Talents of College of Aerospace Science and Engineering, National University of Defense Technology

Abstract

A certain residual stress will accumulate during the curing and cooling process of Solid Rocket Motor (SRM) grain, which will affect the structural integrity of the SRM. It is of great significance to analyze the Cure-induced Residual Stress (CRS) of the propellant grain and explore effective control methods for ensuring the reliability of space vehi-cles and the safety of weapons and equipment. In this paper, the research progress on the generation mechanism, release method, detection technique and inversion prediction of the CRS of propellant grain is reviewed. This paper summarizes the current status and shortcomings of the structural integrity research of SRM considering the CRS of propellant grain, and puts forward the development of its control methods and engineering applications based on the formation causes and release mechanism of the CRS. The analysis shows that the co-design method combining curing process control and structural configuration optimization can effectively control the CRS of the propellant grain, and establishing a standard test system is the key to validate the control method.

Cite this article

YU Bao-Shi , LEI Yong-Jun , SHEN Zhi-Bin , ZHANG Da-Peng . Review on the analysis and control technology of curing residual stress in solid motor propellants[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 0 : 0 -0 . DOI: 10.7527/S1000-6893.2024.31083

References

[1]Liu X Y, Xie X Y, Zhou D M, et al.Numerical analysis of curing residual stress and strain in NEPE propellant grain[J].Polymers, 2023, 15:1019-
[2]洪东, 鲍福廷, 郭颜红, 等.固化降温工艺对固体发动机药柱温度场和结构完整性的影响[J].固体火箭技术, 2023, 46(5):755-762
[3]HONG D, BAO F T, GUO Y H, et al.Influence of cooling process during on temperature field and structur-al integrity of SRM grain[J].Journal of Solid Rocket Technology, 2023, 46(5):755-762
[4]周东谟, 谢旭源, 王瑞民, 等.推进剂固化降温过程残余应力应变分析[J].含能材料, 2024, 32(2):193-203
[5]ZHOU D M, XIE X Y, WANG R M, et al.Residual stressstrain analysis of NEPE propellant under curing and cooling[J].Chinese Journal of Energetic Materials, 2024, 32(2):193-203
[6]侯晓, 张旭, 刘向阳, 等.固体火箭发动机药柱结构完整性研究进展[J].宇航学报, 2023, 44(4):566-579
[7]HOU X, ZHANG X, LIU X Y, et al.Research progress on structural integrity of solid rocket motor grain[J].Journal of Astronautics, 2023, 44(4):566-579
[8]WANG J X, QIANG H F, WANG Z J, et al.Strength criterion of HTPB composite solid propellant under ten-sion-shear loading at low temperature [J]. Propellants Explosives Pyrotechnics, 2022, 47, e202100267.
[9]周东谟, 王辉, 惠步青, 等.基于梯度有限元法的推进剂药柱结构完整性分析[J].固体火箭技术, 2023, 46(5):695-707
[10]ZHOU D M, WANG H, HUI B Q, et al.Structural in-tegrity analysis of HTPB propellant grain based on gra-dient finite element method[J].Journal of Solid Rocket Technology, 2023, 46(5):695-707
[11]LI Y Q, LI G C, KONG L Z, et al.Experimental meas-urement and molecular dynamics simulation analysis of thermal aging performance in composite solid propellants [J]. Polymer Degradation and Stability, 2024, 225: 110812.
[12]SEBASTIAN B, HANGIL Y, WEBBE T K, et al.Cure-induced residual stress buildup and distortions of CFRP laminates with stochastic thermo-chemical and viscoelas-tic models: Experimental verifications[J].Mechanics of Advanced Materials and Structures, 2022, 29(19):2740-2756
[13]LIU X D, GUAN Z D, WANG X D, et al.Study on cure-induced residual stresses and spring-in deformation of L-shaped composite laminates using a simplified con-stitutive model considering stress relaxation[J].Compo-site Structures, 2021, 272(15):114203-
[14]DANZI F, FANTERIA D, PANETTIERI E, et al.A numerical micro-mechanical study on damage induced by the curing process in carbon/epoxy unidirectional materi-al [J]. Composite Structures, 2019, 210: 755–766.
[15]薛景, 王晓洁, 王喜占, 等.碳纤维增强树脂基复合材料固化残余应力评估方法研究现状[J].固体火箭技术, 2023, 46(2):253-262
[16]XUE J, WANG X J, WANG X Z, et al.Research status of evaluation methods for curing residual stress of car-bon fiber reinforced resin matrix composites[J].Journal of Solid Rocket Technology, 2023, 46(2):253-262
[17]BEAUMONT P W R, SOUTIS C, HODZIE A.Struc-tural integrity and durability of advanced composites [M]. Elsevier, 2015:43-72.
[18]FAVRE J P.Residual thermal stresses in fiber reinforced composite materials-A review[J].Journal of the Me-chanical Behavior of Materials, 1988, 1(4):37-53
[19]CHEN A Y, BAEHR S, TURNER A, et al.Carbon-fiber reinforced polymer composites: A comparison of manu-facturing methods on mechanical properties[J].Interna-tional Journal of Lightweight Materials and Manufacture, 2021, 4(4):468-479
[20]TWIGG G, POURSARTIP A, Fernlund G.Tool–part interaction in composites processingPart I: experimental investigation and analytical model[J].Composites Part A: Applied Science and Manufacturing, 2004, 35(1):121-133
[21]PARLEVLIET P P, BERSEE H, BEUKERS A.Residual stresses in thermoplastic composites—A study of the lit-erature—Part I: Formation of residual stresses[J].Com-posites Part A: Applied Science and Manufacturing, 2006, 37(11):1847-1857
[22]刘世俭, 王艳茹.固体火箭发动机药柱固化收缩应力分析[C]∥全国固体火箭发动机设计技术学术交流会, 中国宇航学会, 2000, 325-329.
[23]LIU S Z, WANG Y R.Analysis of curing shrinkage stress of solid rocket motor [C]∥China Solid Rocket Motor Design Technology Academic Exchange Confer-ence, Chinese Society of Astronautics, 2000, 325-329. (in Chinese)
[24]郑启龙.叠氮类粘合剂环氧固化体系及其在火药中的应用研究[D]. 南京: 南京理工大学, 2019.
[25]ZHENG Q L.Curing system of azide binders with epoxides and its application in propellants [D]. Nanjing: Nanjing University of Science and Technology, 2019. (in Chinese)
[26]王瑞民.高能固体推进剂固化过程数值模拟研究[D]. 太原: 中北大学, 2024.
[27]WANG R M.Mumerical simulation of solidification process of high energy solid propellant [D]. Taiyuan: North University of China, 2024. (in Chinese)
[28]丁安心, 李书欣, 倪爱清, 等.热固性树脂基复合材料固化变形和残余应力数值模拟研究综述[J].复合材料学报, 2017, 34(3):471-485
[29]DING A X, LI S X, NI A Q, et al.A review of numerical simulation of cure-induced distortions and residual stresses in thermoset composites[J].Acta Materiae Compositae Sinica, 2017, 34(3):471-485
[30]乔巍, 姚卫星, 马铭泽, 等.复合材料残余应力和固化变形数值模拟及本构模型评价[J].材料导报, 2019, 33(24):4193-4198
[31]QIAO W, YAO W X, MA M Z, et al.Numerical simula-tion and constitutive models evaluation of residual stresses and process-induced deformations of composite structures[J].Materials Reports, 2019, 33(24):4193-4198
[32]李晔鑫, 职世君, 王虎干, 等.低温点火条件下发动机装药结构完整性分析及验证[J].航空兵器, 2021, 28(4):82-87
[33]LI Y X, ZHI S J, WANG H G, et al.Structural integrity analysis and experiment of motor grain under low tem-perature ignition[J].Aero Weaponry, 2021, 28(4):82-87
[34]张永侠, 贾小锋, 苏昌银.固体火箭发动机装药与总装工艺学[M]. 西安: 西北工业大学出版社, 2017.
[35]ZHANG Y X, JIA X F, SU C Y.Propellant loading and final assembly technology for solid rocket motor [M]. Xi' an: Northwestern Polytechnic University Press, 2017. (in Chinese)
[36]乌岳, 李卓, 鲁荣.固体推进剂花板浇注的数值模拟与实验研究[J].火炸药学报, 2018, 41(5):506-511
[37]WU Y, LI Z, LUO R.Numerical simulation and experi-mental study of flower plate pouring system for solid propellant[J].Chinese Journal of Explosives & Propel-lants, 2018, 41(5):506-511
[38]WU Y, LI Z, LU R.Simulation and visual tester verifica-tion of solid propellant slurry vacuum plate casting[J].Propellants, Explosives, Pyrotechnics, 2020, 45(6):871-879
[39]李大方.复合固体推进剂加压插管浇注的列线图解[J]. 推进技术, 1988(5): 62-65+80.
[40]LI D F.The nomogram of pressure offset casting for composite solid propellant [J]. Journal of Propulsion Technology, 1988(5): 62-65+80. (in Chinese)
[41]朱号锋, 苏昌银, 王秀菊, 等.小型固体火箭发动机药柱连续浇注工艺技术研究[J].固体火箭技术, 2005, 2:130-132+156.
[42]ZHU H F, SU C Y, WANG X J, et al.Investigation on continuous-casting technology of propellant for small solid rocket motors [J]. Journal of Solid Rocket Tech-nology, 2005, 2:130-132+156. (in Chinese)
[43]苏昌银, 姚谦, 史旭辉, 等.固体发动机捆绑式加压成型装药工艺研究[J]. 固体火箭技术, 2006, 6: 432-434+450.
[44]SU C Y, YAO Q, SHI X H, et al.Study on strap-on pressure propellant loading process for solid rocket mo-tor [J]. Journal of Solid Rocket Technology, 2006, 6: 432-434 +450. (in Chinese)
[45]宗陆航, 杜聪, 卢山, 等.固体火箭发动机药柱加压固化仿真研究[J].固体火箭技术, 2015, 38(5):653-656
[46]ZONG L H, DU C, LU S, et al.Simulation on pressure cure of solid rocket motor grain[J].Journal of Solid Rocket Technology, 2015, 38(5):653-656
[47]CHASE C.Pioneers in propulsion-a history of CSD, Pratt Whitney' s solid rocket company [C]. Nashville:46th AIAA/ASME/SAE/ASEE Joint Propulsion Conference Exhibit, 2010.
[48]LUSHIS D V, KIRSCH T J.Space motor propulsion-A status report [R]. AIAA, 80-1271.
[49]RUSSELL A E, RALPH N H.Advanced space motor demonstration [R]. AIAA, 80-1270.
[50]JAMES S N.Solid propellant grain structural integrity analysis [R]. NASA SP-8073, 1973.
[51]HUNT D A.Computing pressure cure viscoelastic ef-fects in solid propellants[J].Journal of Spacecraft and Rockets, 1972, 9(12):937-938
[52]ARAI K J.Research on pressure cure of solid rocket motor (in Japanese)[J].Industry Powder, 1982, 43(6):360-367
[53]荒井敬司, 石秀发.固体火箭发动机加压固化的研究[J]. 固体火箭技术, 1984, 4: 54-62.
[54]HUANG J J S, SHI X F.Research on pressure curing of solid rocket motor [J]. Journal of Solid Rocket Tech-nology, 1984, 4: 54-62. (in Chinese)
[55]梁党通, 贾小锋, 胡子衍, 等.固体推进剂药柱加压固化工艺研究[C]. //2017航天先进制造技术国际研讨会论文集, 2017: 344-350.
[56]LIANG D T, JIA X F, HU Z Y, et al.Research on pres-sure curing process of solid propellant grain [C]. // Pro-ceedings of 2017 International Conference on Aerospace Advanced Manufacturing Technology, 2017: 344-350.(in Chinese)
[57]刘仔, 权恩, 褚佑彪, 等.固体火箭发动机加压固化理论及仿真研究[J].固体火箭技术, 2019, 42(5):576-596
[58]LIU Z, QUAN E, CHU Y B, et al.Theoretical and simu-lation research on pressure cure of solid rocket motor[J].Journal of Solid Rocket Technology, 2019, 42(5):576-596
[59]刘凯, 郜婕, 韩翔, 等.加压固化工艺对药柱结构完整性的影响[J].固体火箭技术, 2022, 45(4):648-652
[60]LIU K, GAO J, HAN X, et al.Influence of pressure curing on the integrity of grain structure[J].Journal of Solid Rocket Technology, 2022, 45(4):648-652
[61]仇志艳.颗粒增强铝基复合材料的组织性能及残余应力检测系统开发[D]. 上海: 上海应用技术大学, 2022.
[62]QIU Z Y.Development of microstructure, properties and residual stress detection system for Particle Reinforced Aluminum Matrix Composites [D]. Shanghai: Shanghai Institute of Technology, 2022. (in Chinese)
[63]ZHAO Q, CHEN K S, CHEN M Z, et al.Use of plastic correction formula to improve accuracy of welding resid-ual stress test with blind-hole method[J].Transactions of Tianjin University, 2018, 24(5):480-488
[64]YASHAR J, AHMADI M N.Comparison between contact and immersion ultrasonic method to evaluate welding residual stresses of dissimilar joints [J]. Materi-als and Design, 2012, 47: 473-482.
[65]LODH A, THOOL K, SAMAIDAR I.X-ray Diffrac-tion for the determination of residual stress of crystalline material: an overview[J].Transactions of the Indian In-stitute of Metals, 2022, 75(4):1-13
[66]DAEHEE S, GYUBAEK A, JEONGUNG P, et al.Welding residual stress distributions in the thickness di-rection under constraints using neutron diffraction and contour methods[J].Metals, 2022, 13(1):25-25
[67]邓新, 邱长军.云纹干涉法测量残余应力的研究现状[J]. 机械工程师, 2022, 2:78-80.
[68]DENG X, QIU C J.Research status of residual stress measurement by moire interferometry [J]. Mechanical Engineer, 2022, 2:78-80. (in Chinese)
[69]SULAIMAN S, TIM B, ELYAS G, et al.Assessment of corrosion fatigue in welded joints using 3D surface scans, digital image correlation, hardness measurements, and residual stress analysis [J]. International Journal of Fatigue, 2023, 176: 107866.
[70]陈金根.固体发动机无损检测新技术评述[J]. 推进技术, 1992, 4: 75-82.
[71]CHEN J G.A review of new techniques of NDT in solid rocket motor [J]. Journal of Propulsion Technology, 1992, 4: 75-82. (in Chinese)
[72]PAN Y, QU W Z, ZHANG S C, et al.A Nonlinear Ul-trasonic Method for Detection and Characterization of Dewetting Damage in Solid Propellant[J].Propellants, Explosives, Pyrotechnics, 2022, 47(10):e202200079-
[73]艾春安, 蔡笑风, 李剑, 等.时间反转的固体火箭发动机干耦合超声检测[J].哈尔滨工业大学学报, 2017, 49(2):145-150
[74]AI C A, CAI X F, LI J, et al.Dry-Coupled Ultrason-ic Detection of Solid Rocket Motor by Time Reversal Method[J].Journal of Harbin Institute of Technology, 2017, 49(2):145-150
[75]LI B J, LI J.Nondestructive testing technology of solid rocket engine based on acoustics [A]. 2022 IEEE Inter-national Conference on Electrical Engineering, Big Data and Algorithms (EEBDA) [C], Changchun, China, 2022.
[76]HUANG L C, LI J, LI B J.Experimental Research on Ultrasonic A-Scan Testing Technology of Composite Solid Propellant [J]. Journal of Physics: Conference Se-ries, 2022, 2338: 012011.
[77]JOHNSON E C, POLLCHIK J D.An Ultrasonic Test-ing Technique for Monitoring the Cure and Mechanical Properties of Polymeric Materials, Nondestructive Char-acterization of Materials VI [M]. 1994, Springer, 45-51.
[78]徐春广, 尹鹏, 张文君, 等.残余应力超声检测方法第五部分: 复合固体推进剂热固性浇注成型: Q/CNG226.5-2021[S]. 北京: 中国兵器工业集团有限公司, 2022.
[79]XU C G, YIN P, ZHANG W J, et al.Ultrasonic Testing Methods for Residual Stress Part 5: Thermosetting Cast-ing of Composite Solid Propellants: Q/CNG226.5-2021[S]. Beijing: China North Industries Group Corpo-ration Limited, 2022. (in Chinese)
[80]DAI J J, LI T B, XUAN Z L, et al.Automated Defect Analysis System for Industrial Computerized Tomogra-phy Images of Solid Rocket Motor Grains Based on YOLO-V4 Model[J].Electronics, 2022, 11(19):3215-3215
[81]王守道.射线法测定药柱的残余应力[J].含能材料, 1994, 2(4):35-39
[82]WANG S D.X-Ray Method of Residual Stress Meas-urement in Explosive Charges[J].Chinese Journal of Energetic Materials, 1994, 2(4):35-39
[83]陈靖华.塑料粘结炸药药柱残余应力的X射线衍射检测技术及应用[D]. 成都: 四川大学, 2008.
[84]CHEN J H.Studies on Technique and its Application of X-ray Diffraction Testing for Polymer Bonded Explo-sive [D]. Chengdu: Sichuan University, 2008. (in Chi-nese)
[85]NIU H, SUN W, LI R, et al.Quantifying the Crack-tip Residual Stress of Nickel-based Single-crystal Alloys at the Micron Scale by Focused Ion Beam and Digital Im-age Correlation [J]. Metallurgical and Materials Transac-tions, 2023, 54: 4215-4221.
[86]FATIH U, HECTOR B, KONSTANTINOS L, et al.Voxel-based Full-field Eigenstrain Reconstruction of Re-sidual Stresses in Additive Manufacturing Parts using Height Digital Image Correlation[J].Additive Manufac-turing, 2023, 77(5):103822-
[87]ALEXANDER J L, THOMAS A H, NASSIA T, et al.Measurement of Residual Stresses in Surrogate Coated Nuclear Fuel Particles Using Ring-core Focused Ion Beam Digital Image Correlation [J]. Nuclear Materials and Energy, 2023, 36: 101470.
[88]苏昂, 张大鹏, 张文沁, 等.线黏弹性材料数字图像相关实验教学探索[J].力学与实践, 2024, 46(1):201-207
[89]SU A, ZHANG D P, ZHANG W Q, et al.Experimental Teaching Exploration of Linear Viscoelastic Materials based on Digital Image Correlation[J].Mechanics in Engineering, 2024, 46(1):201-207
[90]巴德欣, 董永康.分布式光纤传感技术及其在航空航天领域的应用展望[J].宇航学报, 2020, 41(6):730-738
[91]BA D X, DONG Y K.Distributed Optical Fiber Sensor and Its Potential Applications in Health Monitoring of Aerospace Structures[J].Journal of Astronautics, 2020, 41(6):730-738
[92]张松涛, 金东晖, 屈文忠, 等.基于柔性传感器的固体火箭发动机界面应力监测[J].固体火箭技术, 2020, 43(4):511-517
[93]ZHANG S T, JIN D H, QU W Z, et al.Interface Stress Monitoring of Solid Rocket Motor with Embedded Flex-ible Sensor[J].Journal of Solid Rocket Technology, 2020, 43(4):511-517
[94]GAO Y, GUO F Y, CAO P, et a1.Winding-Locked Car-bon Nanotubes/Polymer Nanofibers Helical Yarn for Ul-trastretchable Conductor and Strain Sensor [J]. ACS Nano, 2020, 14:3442-3450.
[95]CHEN M J, AQUINO W, WALSH T F, et al.A General-ized Stress Inversion Approach with Application to Re-sidual Stress Estimation[J].Journal of applied mechan-ics, 2020, 87(11):111007-
[96]顾百骏, 陶祥泽, 赵颖涛.基于弹性理论的残余应力反演和变形计算[J].固体力学学报, 2024, 45(2):188-120
[97]GU B J, TAO X Z, ZHAO Y T.Residual Stress Inver-sion and Deformation Calculation Based on Theory of Elasticity[J].Chinese Journal of Solid Mechanics, 2024, 45(2):188-120
[98]HUANG J F, GUO K, LIU X T, et al.Residual Stress Prediction Across Dimensions using Improved Radial Basis Function based Eigenstrain Reconstruction [J]. Mechanics of Materials, 2023, 185: 104779.
[99]MORIN L, BRAHAM C, TAJDARY P, et al.Recon-struction of Heterogeneous Surface Residual-Stresses in Metallic Materials from X-Ray Diffraction Measure-ments [J]. Mechanics of Materials, 2021, 158: 103882.
[100]YUAN Z Y, WANG Y J, YANG G G, et al.Evolution of Curing Residual Stresses in Composite using Multi-Scale Method [J]. Composites Part B, 2018, 155: 49-61.
[101]HUI X Y, XU Y J, NIU J W, et al.Rapid Evaluation and Prediction of Cure-Induced Residual Stress of Compo-sites based on cGAN Deep Learning Model[J].Compo-site Structures, 2024, 330(15):117827-
[102]ZHANG W C, XU Y J, HUI X Y, et al.A Multi-Dwell Temperature Profile Design for the Cure of Thick CFRP Composite Laminates [J]. The International Journal of Advanced Manufacturing Technology, 2021, 117: 1133-1146.
[103]TANG W, XU Y, HUI X, et al.Multi-Objective Optimi-zation of Curing Profile for Autoclave Processed Com-posites: Simultaneous Control of Curing Time and Pro-cess-Induced Defects [J]. Polymers, 2022, 14: 2815.
[104]简力.复合固体推进剂药浆真空浇注除气过程仿真及参数优化[D]. 长沙: 国防科技大学, 2019.
[105]JIAN L.Simulation and Parameter Optimization of Vac-uum Casting Degassing Process for Composite Solid Propellant Slurry [D]. Changsha: National University of Defense Technology, 2019. (in Chinese)
[106]CUI Z X, LI H Y, SHEN Z B, et al.Analysis of Load Optimization in Solid Rocket Motor Propellant Grain with Pressure Curing [J]. International Journal of Aero-space Engineering, 2021, 2021, 5026878.
[107]MIAO Q W, ZHANG H H, SHEN Z B, et al.Multi-Objective Optimization of Stress-Release Boot of Solid Rocket Motor under Vertical Storage based on RBF Model [J]. International Journal of Aerospace Engineer-ing, 2022, 2022, 8475281.
[108]HAMED M R, SAEED T R, SEYED H M S, et al.Numerical Simulation of HTPB Resin Curing Process Using OpenFOAM and Study the Effect of Different Conditions on its Curing Time [J]. Propellants, Explo-sives, Pyrotechnics, 2021, 46, 1447.
[109]叶年辉, 胡少青, 李宏岩, 等.考虑性能及成本的固体火箭发动机多学科设计优化[J].推进技术, 2022, 43(7):75-84
[110]YE N H, HU S Q, LI H Y, et al.Multidisciplinary De-sign Optimization for Solid Rocket Motor Considering Performance and Cost[J].Journal of Propulsion Tech-nology, 2022, 43(7):75-84
[111]李文韬, 何允钦, 李文博, 等.固体火箭发动机三维装药的逆向设计与形状优化[J].航空学报, 2024, 45(11):529089-
[112]LI W T, HE Y Q, LI W B, et al.D Grain Reverse De-sign and Shape Optimization for Solid Rocket Motor[J].Acta Aeronautica et Astronautica Sinica, 2024, 45(11):529089-
[113]KAMRAN A, GUOZU L.An Integrated Approach for Optimization of Solid Rocket Motor[J].Aerospace Sci-ence and Technology, 2012, 17(1):50-64
[114]雷勇军, 袁端才, 何煌.固体发动机星形药柱的形状优化分析[J].国防科技大学学报, 2008, 30(4):6-10
[115]LEI Y J, YUAN D C, HE H.The Shape Optimization Analysis of Solid Motor Star Grain[J].Journal of Na-tional University of Defense Technology, 2008, 30(4):6-10
[116]蒙上阳, 唐国金, 雷勇军.低温环境下固体火箭发动机药柱伞盘结构设计[J].推进技术, 2004, 25(5):397-400
[117]MENG S Y, TANG G J, LEI Y J.Design for the Um-brella Slot Configuration of the Solid Rocket Motor Grain under Low Temperature Condition[J].Journal of Propulsion Technology, 2004, 25(5):397-400
[118]李磊.基于结构完整性分析的固体火箭发动机药形改进与优化设计[D]. 长沙: 国防科学技术大学, 2011.
[119]LI L.Shape Improvement and Optimization of Solid Rocket Motor Grain Based on Structural Integrity Anal-ysis [D]. Changsha: National University of Defense Technology, 2011. (in Chinese)
[120]彭超.复杂载荷下固体火箭发动机装药应力释放槽优化设计[D]. 南京: 南京理工大学, 2014.
[121]PENG C.Optimal Design of the Stress-Releaser Struc-ture of Propellant Gain under Complex Load [J]. Nan-jing: Nanjing University of Science and Technology, 2014. (in Chinese)
[122]王晨飞.大长径比复杂装药结构完整性分析[D]. 南京: 南京理工大学, 2018.
[123]WANG C F.Analysis on Structural Integrity of Com-plex Charge with Large Length-Diameter Ratio [J]. Nan-jing: Nanjing University of Science and Technology, 2018. (in Chinese)
[124]YANG H Z, HONG S H, WANG Y.A Sequential Multi-Fidelity Surrogate-Based Optimization Methodology Based on Expected Improvement Reduction[J].Struc-tural and Multidisciplinary Optimization, 2022, 65(5):153-170
[125]YANG J W, WU Z P, WANG W J, et al.A Surrogate-Based Optimization Method for Mixed-Variable Air-craft Design[J].Engineering Optimization, 2022, 54(1):113-133
[126]YOO K, HAN S.Modified ant colony optimization for topology optimization of geometrically nonlinear struc-tures[J].International Journal of Precision Engineering and Manufacturing, 2014, 15(4):679-687
[127]SHIRAZI N R M, MOLLAMAHMOUDI H, SEYEDPOOR M S.Structural Damage Identification Using an Adaptive Multi-Stage Optimization Method Based on a Modified Particle Swarm Algorithm[J].Journal of Optimization Theory and Applications, 2014, 160(3):1009-1019
[128]ZHU L, LUO H W, WANG P C, et al.Uncertainty Anal-ysis and Design Optimization of Solid Rocket Motors with Finocyl Grain [J]. Structural and Multidisciplinary Optimization, 2020, 62:3521–3537.
[129]AN H C, YOUN D B, SOO H K.Variable-Stiffness Composite Optimization Using Dynamic and Exponen-tial Multi-Fidelity Surrogate Models [J]. International Journal of Mechanical Sciences, 2023, 257: 108547.
[130]HU J, ZHANG L, LIN Q, et al.A Conservative Multi-Fidelity Surrogate Model-Based Robust Optimization Method for Simulation-Based Optimization [J]. Structur-al and Multidisciplinary Optimization, 2021, 64: 2525-2551.
[131]LI K P, LI Q Y, LV L Y, et al.A Nonlinearity Integrated Bi-fidelity Surrogate Model Based on Nonlinear Map-ping [J]. Structural and Multidisciplinary Optimization, 2023, 66: 196.
Outlines

/