飞行器复合材料结构优化设计研究进展
|
摘要
随着飞行器设计要求的日益提高,且服役环境异常严酷,发展新型材料和新结构迫在眉睫,而复合材料凭借高比强度、高比刚度、耐疲劳、抗腐蚀等优点,在现代飞行器结构的设计与制造中得到了广泛应用.复合材料结构的可设计性为设计人员提供了更为广阔的设计空间.因此,复合材料结构的优化设计问题逐渐受到国内外科研工作者的热烈讨论.本文针对国内外在复合材料结构优化设计理论方面取得的成果进行了系统的综述,主要内容包括安全系数优化设计、可靠性优化设计及鲁棒优化设计,分别阐述了以上优化理论在复合材料结构优化设计领域的应用,探讨了3种优化设计理念之间的继承与发展关系,并分析了复合材料结构优化设计当前存在的主要问题和今后的发展方向.
With the increasing requirements of aircraft design, the service condition becomes more and more harsh, development for new material is imminent, and composite material has been widely used in the design and manufacture in the modern aircraft structure by virtue of high specific strength, high specific stiffness, fatigue resistance, and corrosion resistance. The advantage to be designed of composite material provides designers with more broad space for development of its potential abilities; therefore, the optimal design of the composite material gradually is aroused heated discussion among researchers both domestic and abroad. On the issue that optimization theory for composite materials at domestic and abroad, in this paper, the author introduce the development process of composite structure optimization design, and systematically reviews the achievements that researchers have obtained currently. The main contents include the safety factor-based design optimization, reliability-based design optimization and robust optimization design, elaborate the application of the above methods in composite structure optimization design region, discuss the relations among the three optimization design theories, and then the current structure optimization design of the composites presented some problems and the future development direction is analyzed.
With the increasing requirements of aircraft design, the service condition becomes more and more harsh, development for new material is imminent, and composite material has been widely used in the design and manufacture in the modern aircraft structure by virtue of high specific strength, high specific stiffness, fatigue resistance, and corrosion resistance. The advantage to be designed of composite material provides designers with more broad space for development of its potential abilities; therefore, the optimal design of the composite material gradually is aroused heated discussion among researchers both domestic and abroad. On the issue that optimization theory for composite materials at domestic and abroad, in this paper, the author introduce the development process of composite structure optimization design, and systematically reviews the achievements that researchers have obtained currently. The main contents include the safety factor-based design optimization, reliability-based design optimization and robust optimization design, elaborate the application of the above methods in composite structure optimization design region, discuss the relations among the three optimization design theories, and then the current structure optimization design of the composites presented some problems and the future development direction is analyzed.
引文
1 Cheng C X,Yan Y.NASA of advanced composite material technology(ACT)study design and the development of textile composites(in Chinese).In:The National Conference on Composite Material.Shanghai,1998[成传贤,燕瑛.美国宇航局(NASA)的先进复合材料技术(ACT)的研究设计及纺织复合材料的发展.见:全国复合材料学术会议.上海,1998]
2 Wang W,Yang C.Aircraft Composite Wing Surface Structure Optimization Design Theory and Application(in Chinese).Beijing:National Defence Industry Press,2014.12-27[王伟,杨常.飞机复合材料翼面结构优化设计理论与应用.北京:国防工业出版社,2014.12-27]
3 Kang E.The Strength Calculation of Plane(in Chinese).Beijing:National Defence Industry Press,1960.42-63[康恩.飞机强度计算.北京:国防工业出版社,1960.42-63]
4 Wu T M.Determination the safety coefficient of composite material structure(in Chinese).Aeron Sci Tech,1998.26-27[吴铁民.复合材料结构安全系数的确定.航空科学技术,1998.26-27]
5 Yan F F.Performance of Composite Material Dispersion and Safety Coefficient(in Chinese).Dissertation for Master Degree.Nanjing:Nanjing University of Aeronautics and Astronautics,2009.4-11[颜芳芳.复合材料性能的分散性与安全系数.硕士学位论文.南京:南京航空航天大学,2009.4-11]
6 Schmit L A,Miura H.Approximation concepts for efficient structural synthesis.AIAA J,1976,12:8508-8515
7 Ashley H.On making things the best-aeronautical uses of optimization.J Aircraft,1982,19:5-28
8 Lansing W,Lerner E,Taylor R F.Applications of structural optimization for strength and aeroelastic design requirements.Med Chir Trans,1978,6:221-262
9 Akbulut M,Sonmez F O.Design optimization of laminated composites using a new variant of simulated annealing.Comp Struct,2011,89:1712-1724
10 McDonald M,Mahadevan S.Reliability based design optimization formulations for component and system reliability.In:Proceedings of 49th AIAA/ASME/ASCE/AHS/ASC Structures,Structural Dynamics,and Materials Conference.Schaumburg,2008
11 Singha M K,Ramachandra L S,Bandyopadhyay J N.Optimum design of laminated composite plates for maximum thermal buckling loads.J Comp Mater,2000,34:1982-1997
12 Irisarri F X,Bassir D H,Carrere N,et al.Multiobjective stacking sequence optimization for laminated composite structures.Comp Sci Tech,2009,69:983-990
13 Lopez R H,Lemosse D,de Cursi J E S,et al.An approach for the reliability based design optimization of laminated composites.Eng Optim,2011,43:1079-1094
14 Liu K L,Yao W X,Yu X Q,et al.Safety factor of the composite statistical analysis(in Chinese).J Nanjing Univ Aeron Astron,2004,36:22-28[刘克龙,姚卫星,余雄庆,等.复合材料的安全系数统计分析.南京航空航天大学学报,2004,36:22-28]
15 Yang L,Ma Z K,Fu G Z.Safety factor and reliability of composite laminate(in Chinese).Chin J Aeron,1991,12:631-634[羊姈,马祖康,符国政.复合材料层压板的安全系数与可靠度.航空学报,1991,12:631-634]
16 Mu P G.Ant colony algorithm for composite laminated plate design and optimaziton(in Chinese).J Mech Strength,2009,31:410-413[穆朋刚.蚁群算法在复合材料层合板优化设计中的应用.机械强度,2009,31:410-413]
17 Zhuang S S.An optimization method for aero-engine composite casing based on DSA-FEM(in Chinese).Mech Sci Tech Aerospace Eng,2012,31:1573-1577[庄三少.基于DSA-FEM的航空发动机复合材料机匣优化方法.机械科学与技术,2012,31:1573-1577]
18 Zhang Y K,Zhang D.Research on the composite structure optimization prooedure(in Chinese).J Solid Rocket Techn,2003,26:69-71[张彦考,张铎.大型复合材料结构优化设计方法研究.固体火箭技术,2003,26:69-71]
19 Wang X Y,Chen J Q,Wei J H.Advances in the reliability-based optimization study for laminated composites(in Chinese).Adv Mech,2005,35:541-548[王向阳,陈建桥,魏俊红.复合材料层合板的可靠性和优化问题的研究进展.力学进展,2005,35:541-548]
20 Mayer A,Sykes A.A Probability Model for Analysing Complexity Metrics Data.London:Michael Faraday House,1989.254-258
21 Freudenthal H.Didactical Phenomenology of Mathematical Structures.Netherlands:Springer,2002
22 Kam T Y,Chang E S.Reliability formulation for composite laminates subjected to first-ply failure.Comp Struct,1997,38:447-452
23 Dey A,Tryon R,Mahadevan S,et al.Fatigue reliability prediction of tapered composites.In:40th Structures,Structural Dynamics,and Materials Conference and Exhibit.St.Louis,1999
24 Kogiso N,Shao S,Murotsu Y.Reliability analysis of simply supported symmetric laminated plate subject to buckling load.JSMET,1997,63:138-145
25 Kogiso N,Murotsu Y,Shao S.Effect of correlation on reliability-based design of composite plate for buckling.AIAA J,1998,36:1706-1713
26 Kogiso N,Murotsu Y,Nakagawa S.Lamination parameters applied to reliability-based in-plane strength design of composites.AIAA J,2003,41:2200-2207
27 Chen J Q,Xu Y R,Wei J H.Probabilistic optimum design of laminated composites based on the last ply failure criterion(in Chinese).J Mech Strength,2007,29:241-246[陈建桥,许玉荣,魏俊红.复合材料层合板的极限强度分析与可靠性优化设计.机械强度,2007,29:241-246]
28 An W G,Zhao W T,Yang D H.A method of reliability a analysis for composite laminate(in Chinese).J Asrton,2005,26:672-675[安伟光,赵维涛,杨多和.复合材料层合板的可靠性分析方法.宇航学报,2005,26:672-675]
29 Onkar A K,Upadhyay C S,Yadav D.Probabilistic failure of laminated composite plates using the stochastic finite element method.Compos Struct,2007,77:79-91
30 Venugopal S M.Stochastic Mechanics and Reliability of Composite Laminates Based on Experimental Investigation and Stochastic FEM.Dissertation for Master Degree.Montreal:Concordia University,2003
31 Song Y L,Li S J.The reliability analysis of structure of enhanced fiber composite material plate(in Chinese).J Harbin Eng Univ,1999,20:63-71[宋云连,李树军.加强纤维复合材料板结构的可靠性分析.哈尔滨工程大学学报,1999,20:63-71]
32 Li Y B,Yao W X.Fatigue reliability analysis on structural elements based on SFEM(in Chinese).J Nanjing Univ Aeron Astron,2007,39:461-464[李应波,姚卫星.基于SFEM的结构元件疲劳可靠性分析.南京航空航天大学学报,2007,39:461-464]
33 Chen S X,Hao Z M.Neumann stochastic finite element analysis of the reliability of the composite structure of cyclotron(in Chinese).J Aeron Mater,1998,18:47-52[陈顺祥,郝志明.用纽曼随机有限元分析复合材料回旋结构的可靠性.航空材料学报,1998,18:47-52]
34 Chen X X,Shen Z H,Zhu C Y.Reliability analysis for fiber winding chamber of solid rocket motor via stochastic finite element method(in Chinese).J Aeron Mater,2006,26:113-116[陈顺祥,沈志辉,朱成永.基于SFEM的SRM纤维缠绕结构的可靠性分析.航空材料学报,2006,26:113-116]
35 Ibnabdeljalil M,Curtin W A.Strength and reliability of notched fiber-reinforced composites.Acta Mater,1997,45:3641-3652
36 Jeong H K,Shenoi R A.Probabilistic strength analysis of rectangular FRP plates using Monte Carlo simulation.Comp Struct,2000,76:219-235
37 Yao L J,Tong X Y.The reliability analysis of fatigue life of composite laminates(in Chinese).J Mech Strength,1998,4:268-270[姚磊江,童小燕.复合材料层合板疲劳寿命的可靠性分析.机械强度,1998,4:268-270]
38 Hao Z M,Chen S X,Zhang D,et al.The relaibility analysis of composite convolution structure by neumann expansion Monte-Carloβball method(in Chinese).In:National Conference on Composite Material,Shanghai,1998[郝志明,陈顺祥,张铎,等.分析复合回旋结构可靠性的纽曼展开蒙特卡罗β球法.见:全国复合材料学术会议.上海,1998]
39 Ben-Haim Y,Elishakoff I.Discussion on:A non-probabilistic concept of reliability.Struct Safety 1995,17:195-199
40 Ben-Haim Y.A non-probabilistic concept of reliability.Struct Safety,1994,14:227-245
41 Ben-Haim Y.A non-probabilistic measure of reliability of linear systems based on expansion of convex models.Struct Safety,1995,17:91-109
42 Qiu Z P.Convex Method Based on Non-Probabilistic Set-Theory and Its Application(in Chinese).Beijing:National Defence Industry Press,2005.11-18[邱志平.非概率集合理论凸方法及其应用.北京:国防工业出版社,2005.11-18]
43 Wang X J,Qiu Z P,Wu Z.Non-probabilistic set-based model for structural reliability(in Chinese).Chin J Theor Appl Mech,2007,39:641-646[王晓军,邱志平,武哲.结构非概率集合可靠性模型.力学学报,2007,39:641-646]
44 Gu X D,Wang X J,Qiu Z P.Dynamic response analysis of composite plate with uncertain parameters via interval analysis method(in Chinese).In:The National Conference on Composite Material.Yichang,2006[顾笑冬,王晓军,邱志平.具有不确定参数复合材料板动力响应的非概率区间分析法.见:全国复合材料学术会议.宜昌,2006]
45 Guo S X,Zhang L,Li Y.Procedures for computing the non-probabilistic reliability index of uncertain structures(in Chinese).Chin J Comput Mech,2005,22:227-231[郭书祥,张陵,李颖.结构非概率可靠性指标的求解方法.计算力学学报,2005,22:227-231]
46 Guo S X,Lv Z Z,Feng Y S.Anon-probabilistic model of structural reliability based on interval analysis(in Chinese).Chin J Comput Mech,2001,18:56-60[郭书祥,吕震宙,冯元生.基于区间分析的结构非概率可靠性模型.计算力学学报,2001,18:56-60]
47 Wang X Y,Chen J Q.Probability and non-probability model of laminated composite plate structures(in Chinese).Huazhong Univ Sci Tech(Nat Sci Ed),2006,34:71-73[王向阳,陈建桥.复合材料层合板结构的概率与非概率模型.华中科技大学学报(自然科学版),2006,34:71-73]
48 Kang Z,Luo Y.Non-probabilistic reliability-based topology optimization of geometrically nonlinear structures using convex models.Comp Methods Appl Mech Eng,2009,198:3228-3238
49 Luo Y,Kang Z,Luo Z,et al.Continuum topology optimization with non-probabilistic reliability constraints based on multi-ellipsoid convex model.Struct Multidisc Opt,2009,39:297-310
50 Jiang C,Zhao M H,Cao W G.Non-probabilistic reliability research on uncertain parameters in rock mechanics.J Hunan Univ Nat Sci,2008,35:11-14
51 Zhao M H,Jiang C,Cao W G.Non-probabilistic reliability analysis of retaining walls based on interval(in Chinese).Chin J Geotech Eng,2008,30:467-472[赵明华,蒋冲,曹文贵.基于区间理论的挡土墙稳定性非概率可靠性分析.岩土工程学报,2008,30:467-472]
52 Li Y L,Wang X J,Huang R.Non-probabilistic reliability analysis of active control system for structural vibration(in Chinese).J Beijing Univ Aeron Astron,2015,41:259-266[李云龙,王晓军,黄仁.结构振动主动控制系统的非概率可靠性分析.北京航空航天大学学报,2015,41:259-266]
53 Guo S X,Lv Z Z.Comparison between the non-probabilistic and probabilistic reliability methods for uncertain structure design(in Chinese).Chin J Applied Mech,2003,20:107-110[郭书祥,吕震宙.结构的非概率可靠性方法和概率可靠性方法的比较.应用力学学报,2003,20:107-110]
54 Sun H L,Yao W X.A retrospect for structural reliability measure methods(in Chinese).Mech Sci Tech Aerospace Eng,2007,26:140-146[孙海龙,姚卫星.概率体系和非概率体系下结构元件的可靠性分析方法回顾.机械科学与技术,2007,26:140-146]
55 Kogiso N.Reliability analysis and reliability-based optimization of composite laminated plate subject to buckling.Dissertation for Doctoral Degree.Osaka:Osaka Prefecture University,1997
56 Kogiso N,Katou S,Murotsu Y.Reliability-based optimization of thin composite structure.In:8th ASCE Specialty Conference on Probabilistic Mechanics and Structural Reliability.South Bend,2001:219-222
57 Eamon C D,Rais-Rohani M.Integrated reliability and sizing optimization of a large composite structure.Mar Struct,2009,22:315-334
58 Li W J.Optimal design of composite laminates(in Chinese).J Northwestern Polytech Univ,1986:35-44[李为吉.复合材料层板的优化设计.西北工业大学学报,1986:35-44]
59 Han X,Lei L,Yuan W,et al.Optimization of the composite hat-stiffened panel based on equivalent model(in Chinese).In:2009 China International Conference on Advanced Materials and Technology.Beijing,2009[韩旭,雷磊,袁伟,等.基于等效模型的帽型复合材料加筋壁板优化设计.见:2009暨中国国际先进材料与工艺技术学术研讨会.北京,2009]
60 Xiu Y S,Cui D G.Ply optimization design for stability of composite laminates(in Chinese).Eng Mech,2005,22:212-216[修英姝,崔德刚.复合材料层合板稳定性的铺层优化设计.工程力学,2005,22:212-216]
61 Chang N,Yang W,Wang W,et al.New method of ply optimization design for stability of composite laminates(in Chinese).J Mech Strength,2008,30:148-151[常楠,杨伟,王伟,等.基于复合材料层板稳定性的铺层参数优化设计方法.机械强度,2008,30:148-151]
62 Fang X,Feng Y L,Liu X M,et al.Two level optimization method for large aspect ratio composite wing structure(in Chinese).In:2015 Aviation Test Technology Proceedings of Academic Exchange.Beijng,2015[方雄,冯玉龙,刘晓明,等.大展弦比复合材料机翼结构的两级优化方法.见:2015航空试验测试技术学术交流会论文集.北京,2015]
63 Zhang Y K.Composite Wing,Segment Combination Structure Optimization Design(in Chinese).Dissertation for Master Degree.Xi'an:Northwestern Polytechnical University,2002.10-18[张彦考.全复合材料弹翼、舱段组合结构优化设计.硕士学位论文.西安:西北工业大学,2002.10-18]
64 Hou Y P.Composite Laminated Board Spreading Layer Design and Selection and Discrete Optimization Method Research(in Chinese).Dissertation for Master Degree.Dalian:Dalian University of Technology,2013.4-12[侯玉品.复合材料层合板铺层设计与离散结构选型优化方法研究.硕士学位论文.大连:大连理工大学,2013.4-12]
65 Wang S P,Gao X S,Gan J,et al.Two-level optimization on layout and ply for composite airtight port of airplane(in Chinese).Chin J Appl Mech,2014,3:24-29[王帅培,高行山,甘建,等.飞机复合材料气密舱门布局和铺层的两级优化设计.应用力学学报,2014,3:24-29]
66 Wang P Y,Dong Y P,Wang F S,et al.District and level optimization method for a high aspect-ratio composite wing(in Chinese).In:Composite Materials:Innovation and Sustainable Development.Changsha,2010[王佩艳,董勇鹏,王富生,等.大展弦比复合材料机翼分区分级优化.见:复合材料:创新与可持续发展.长沙,2010]
67 Tang J,Zhang M Q.Research on small-sample fuzzy reliability simulation based on bayes Monte Carlo Method.J Syst Simul,2009,21:7557-7559,7563
68 Ding F,Yin J C,Dang J Q.Reliability assessment of the small sample aero-engine bearings.Adv Mater Res,2014,986-987:858-861
69 Zou X,Yao R.Small sample statistical theory and IC reliability assessment.Control Deci,2008,23:241-232
70 Xiong J,Shenoi R A,Gao Z.Small sample theory for reliability design.J Strain Anal Eng Des,2002,37:87-92
71 Fu H.Method for reliability assessment with very small sample.J Mech Strength,2005,3:12
72 Jin B,Qin D T,Hu J J.A bayes method of reliability synthesis evaluation based on the small sample-system.J Chongqing Univ,2007,9:4
73 Kang Z,Bai S.Structural optimization considering uncertainties and multi-field coupling(in Chinese).Sci Techn Innov Herald,2016,13:177-178[亢战,白嵩.考虑不确定性与多场耦合的结构优化.科技创新导报,2016,13:177-178]
74 Wang X J,Wang L,Qiu Z P.Response analysis based on smallest interval set of parameters for structures with uncertainty(in Chinese).Appl Math Mech,2012,33:1078-1090[王晓军,王磊,邱志平.基于最小参数区间集的不确定结构响应分析.应用数学和力学,2012,33:1078-1090]
75 Wang X J,Yang H F,Qiu Z P,et al.Fuzzy theory for uncertain structural analysis based on measurement data(in Chinese).J Beijing Univ Aeron Astron,2010,36:887-891[王晓军,杨海峰,邱志平,等.基于测量数据的不确定性结构分析的模糊理论.北京航空航天大学学报,2010,36:887-891]
76 Luo Y,Li A,Kang Z.Reliability-based design optimization of adhesive bonded steel-concrete composite beams with probabilistic and nonprobabilistic uncertainties.Eng Struct,2011,33:2110-2119
77 Kang Z,Luo Y J.On structural optimization for non-probabilistic reliability based on convex models(in Chinese).Chin J Theor Appl Mech,2006,38:807-815[亢战,罗阳军.基于凸模型的结构非概率可靠性优化.力学学报,2006,38:807-815]
78 Kang Z,Luo Y,Li A.On non-probabilistic reliability-based design optimization of structures with uncertain-but-bounded parameters.Struct Safety,2011,33:196-205
79 Chen L,Qiu Z P.Natural frequency analysis and optimization of composite laminates based on the non-probabilistic approach(in Chinese).In:The National Conference on Composite Material.Harbin,2009[陈亮,邱志平.复合材料板固有频率的非概率分析及优化.见:全国复合材料学术会议.哈尔滨,2009]
80 Xu M H,Qiu Z.Interval analysis and optimization for free vibration of all-composite lattice truss core sandwich beam(in Chinese).J Beijing Univ Aeron Astron,2013,39:1079-1085[许孟辉,邱志平.复合材料点阵夹芯梁振动特性区间分析与优化.北京航空航天大学学报,2013,39:1079-1085]
81 Wang X J,Wang L,Jia X,et al.Structural optimization design based on non-probabilistic convex modeling reliability(in Chinese).J Beijing Univ Aeron Astron,2012,38:630-635[王晓军,王磊,贾晓,等.基于非概率凸模型可靠性的结构优化设计.北京航空航天大学学报,2012,38:630-635]
82 Wang C,Qiu Z P,Wang X J.Composite structure-acoustic coupling interval reliability optimization(in Chinese).In:The Chinese Mechanical Conference.Xi'an,2013[王冲,邱志平,王晓军.复合材料结构-声耦合系统区间可靠性优化.见:中国力学大会.西安,2013]
83 Gomes H M,Awruch A M,Lopes P A M.Reliability based optimization of laminated composite structures using genetic algorithms and artificial neural networks.Struct Safety,2011,33:186-195
84 Tang Y,Chen J,Peng W.Probabilistic optimization of laminated composites considering both ply failure and delamination based on PSO and FEM.Tsinghua Sci Tech,2009,14:89-93
85 Ge R,Chen J Q.Reliability optimal design of composite materials based on the improved particle swarm optimization algorithm(in Chinese).Mech Sci Tech,2007,26:257-260[葛锐,陈建桥,魏俊红.基于改进粒子群优化算法的复合材料可靠性优化设计.机械科学与技术,2007,26:257-260]
86 Xu Y R,Chen J Q,Luo C,et al.Probabilistic optimum design of laminated plates based on genetic algorithms(in Chinese).Mech Sci Tech,2004,23:1344-1347[许玉荣,陈建桥,罗成,等.复合材料层合板基于遗传算法的可靠性优化设计.机械科学与技术,2004,23:1344-1347]
87 Wang X Y,Chen J Q,Luo C.Optimum design of the probability for composite laminates based on genetic algorithm(in Chinese).Huazhong Univ Sci Tech(Nat Sci Ed),2004,32:10-12[王向阳,陈建桥,罗成.基于遗传算法的层合板结构的可靠性优化设计.华中科技大学学报(自然科学版),2004,32:10-12]
88 Li S,Xun Y M,Zhang J.Conposite structural optimization design based on neural net work response surfaces(in Chinese).Acta Mater Comp Sin,2005,22:134-140[李烁,徐元铭,张俊.基于神经网络响应面的复合材料结构优化设计.复合材料学报,2005,22:134-140]
89 Wang X Y.Study on the Reliability-Based Optimum Design and the Robust Optimization for Laminated Composite Structures(in Chinese).Dissertation for Doctoral Degree.Huazhong University of Science and Technology,2004[王向阳.复合材料层合板结构的可靠性优化和鲁棒优化研究.博士学位论文.华中科技大学,2004]
90 Wang X Y,Chen J Q,Zhang X D.Probabilistic progressive failure analysis of CFRP laminated plates(in Chinese).J Wuhan Univ Tech(Transport Sci Eng),2004,28:863-865[王向阳,陈建桥,张谢东.纤维增强复合材料层合板的概率逐步失效分析.武汉理工大学学报(交通科学与工程版),2004,28:863-865]
91 Luo C.Reliability and Optimal Design of Fiber Composites Based on Ultimate Strength(in Chinese).Dissertation for Master Degree.Wuhan:Huazhong University of Science and Technology,2003[罗成.纤维复合材料基于最终强度的可靠性及其优化设计.硕士学位论文.武汉:华中科技大学,2003]
92 Gadade A M,Lal A,Singh B N.Finite element implementation of Puck's failure criterion for failure analysis of laminated plate subjected to biaxial loadings.Aerospace Sci Tech,2016,55:227-241
93 Kumar A,Chakrabarti A.Failure analysis of laminated composite skew laminates.Procedia Eng,2017,173:1560-1566
94 Wang X.Reliability-based optimum study on FRP laminated plates with genetic algorithm.In:Proceedings of International Symposium on Distributed Computing and Applications To Business,Engineering and Science.Bangalore,2007
95 Romeo G,Danzi F,Cestino E,et al.Optimization of advanced composite wing box structures subjected to combined loads and impact.In:Proceedings of 1st International Conference on Engineering and Applied Sciences Optimization.Kos,2014
96 Taguchi G,Cariapa V.Taguchi on robust technology development.J Pressure Vessel Technol,1993,115:336
97 Sundaresan S,Ishii K,Houser D R.A robust optimization procedure with variations on design variables and constraints.Eng Opt,1995,24:101-117
98 Sundaresan S,Ishii K,Houser R.Automatic differentiation in robust optimization.AIAA J,1997,35:1072-1079
99 Chen W,Wiecek M M,Zhang J.Quality utility—A compromise programming approach to robust design.J Mech Des,1999,121:179
100 Gabrel V,Murat C,Thiele A.Recent advances in robust optimization:An overview.Eur J Oper Res,2014,235:471-483
101 Makkapati S.Robust Design Optimization with Applications to Composite-Material Structures.Dissertation for Doctoral Degree.Morgantown:West Virginia University,1997
102 Henrichsen S R,Lindgaard E,Lund E.Robust buckling optimization of laminated composite structures using discrete material optimization considering"worst"shape imperfections.Thin-Walled Struct,2015,94:624-635
103 Phelan S L,Mavris D N.Robust design of aeroelastically tailored composite plates using a new formulation of anti-optimization and optimization.In:56th AIAA/ASCE/AHS/ASC Structures,Structural Dynamics,and Materials Conference.Kissimmee,2015
104 Xiao Z P,Wan Z Q,Yang C,et al.Robust aeroelastic optimization design of a composite wing(in Chinese).Acta Mater Comp Sin,2010,27:127-132[肖志鹏,万志强,杨超,等.复合材料机翼鲁棒气动弹性优化设计.复合材料学报,2010,27:127-132]
105 Wang X Y,Chen J Q.Robust design of laminated composite plates cased on the last-ply failure criterion(in Chinese).J Mech Strength,2004,26:675-679[王向阳,陈建桥.基于最终失效强度的层合板结构的鲁棒优化分析.机械强度,2004,26:675-679]
106 Zhang Z F,Chen H R,Bai R X.Robust optimization of advanced grid composite cylindrical shell considing initial imperfect effect(in Chinese).Acta Mech Solid Sin,2006,27:58-64[张志峰,陈浩然,白瑞祥.含初始缺陷复合材料格栅加筋圆柱壳的鲁棒优化设计.固体力学学报,2006,27:58-64]
107 Tang Y F.Robust reliability analysis and optimization algorithms for composite structure(in Chinese).Wuhan:Huazhong University of Science and Technology,2012.10-18[唐远富.复合材料结构可靠性鲁棒分析及优化算法研究.武汉:华中科技大学,2012.10-18]
108 Zhao X F.Considering Load Uncertainty and Stiffness Uncertainty of Robust Optimization Problem(in Chinese).Dissertation for Master Degree.Dalian:Dalian University of Technology,2015.4-12[赵晓芳.考虑载荷不确定性和刚度不确定性的鲁棒优化问题.硕士学位论文.大连:大连理工大学,2015.4-12]
2 Wang W,Yang C.Aircraft Composite Wing Surface Structure Optimization Design Theory and Application(in Chinese).Beijing:National Defence Industry Press,2014.12-27[王伟,杨常.飞机复合材料翼面结构优化设计理论与应用.北京:国防工业出版社,2014.12-27]
3 Kang E.The Strength Calculation of Plane(in Chinese).Beijing:National Defence Industry Press,1960.42-63[康恩.飞机强度计算.北京:国防工业出版社,1960.42-63]
4 Wu T M.Determination the safety coefficient of composite material structure(in Chinese).Aeron Sci Tech,1998.26-27[吴铁民.复合材料结构安全系数的确定.航空科学技术,1998.26-27]
5 Yan F F.Performance of Composite Material Dispersion and Safety Coefficient(in Chinese).Dissertation for Master Degree.Nanjing:Nanjing University of Aeronautics and Astronautics,2009.4-11[颜芳芳.复合材料性能的分散性与安全系数.硕士学位论文.南京:南京航空航天大学,2009.4-11]
6 Schmit L A,Miura H.Approximation concepts for efficient structural synthesis.AIAA J,1976,12:8508-8515
7 Ashley H.On making things the best-aeronautical uses of optimization.J Aircraft,1982,19:5-28
8 Lansing W,Lerner E,Taylor R F.Applications of structural optimization for strength and aeroelastic design requirements.Med Chir Trans,1978,6:221-262
9 Akbulut M,Sonmez F O.Design optimization of laminated composites using a new variant of simulated annealing.Comp Struct,2011,89:1712-1724
10 McDonald M,Mahadevan S.Reliability based design optimization formulations for component and system reliability.In:Proceedings of 49th AIAA/ASME/ASCE/AHS/ASC Structures,Structural Dynamics,and Materials Conference.Schaumburg,2008
11 Singha M K,Ramachandra L S,Bandyopadhyay J N.Optimum design of laminated composite plates for maximum thermal buckling loads.J Comp Mater,2000,34:1982-1997
12 Irisarri F X,Bassir D H,Carrere N,et al.Multiobjective stacking sequence optimization for laminated composite structures.Comp Sci Tech,2009,69:983-990
13 Lopez R H,Lemosse D,de Cursi J E S,et al.An approach for the reliability based design optimization of laminated composites.Eng Optim,2011,43:1079-1094
14 Liu K L,Yao W X,Yu X Q,et al.Safety factor of the composite statistical analysis(in Chinese).J Nanjing Univ Aeron Astron,2004,36:22-28[刘克龙,姚卫星,余雄庆,等.复合材料的安全系数统计分析.南京航空航天大学学报,2004,36:22-28]
15 Yang L,Ma Z K,Fu G Z.Safety factor and reliability of composite laminate(in Chinese).Chin J Aeron,1991,12:631-634[羊姈,马祖康,符国政.复合材料层压板的安全系数与可靠度.航空学报,1991,12:631-634]
16 Mu P G.Ant colony algorithm for composite laminated plate design and optimaziton(in Chinese).J Mech Strength,2009,31:410-413[穆朋刚.蚁群算法在复合材料层合板优化设计中的应用.机械强度,2009,31:410-413]
17 Zhuang S S.An optimization method for aero-engine composite casing based on DSA-FEM(in Chinese).Mech Sci Tech Aerospace Eng,2012,31:1573-1577[庄三少.基于DSA-FEM的航空发动机复合材料机匣优化方法.机械科学与技术,2012,31:1573-1577]
18 Zhang Y K,Zhang D.Research on the composite structure optimization prooedure(in Chinese).J Solid Rocket Techn,2003,26:69-71[张彦考,张铎.大型复合材料结构优化设计方法研究.固体火箭技术,2003,26:69-71]
19 Wang X Y,Chen J Q,Wei J H.Advances in the reliability-based optimization study for laminated composites(in Chinese).Adv Mech,2005,35:541-548[王向阳,陈建桥,魏俊红.复合材料层合板的可靠性和优化问题的研究进展.力学进展,2005,35:541-548]
20 Mayer A,Sykes A.A Probability Model for Analysing Complexity Metrics Data.London:Michael Faraday House,1989.254-258
21 Freudenthal H.Didactical Phenomenology of Mathematical Structures.Netherlands:Springer,2002
22 Kam T Y,Chang E S.Reliability formulation for composite laminates subjected to first-ply failure.Comp Struct,1997,38:447-452
23 Dey A,Tryon R,Mahadevan S,et al.Fatigue reliability prediction of tapered composites.In:40th Structures,Structural Dynamics,and Materials Conference and Exhibit.St.Louis,1999
24 Kogiso N,Shao S,Murotsu Y.Reliability analysis of simply supported symmetric laminated plate subject to buckling load.JSMET,1997,63:138-145
25 Kogiso N,Murotsu Y,Shao S.Effect of correlation on reliability-based design of composite plate for buckling.AIAA J,1998,36:1706-1713
26 Kogiso N,Murotsu Y,Nakagawa S.Lamination parameters applied to reliability-based in-plane strength design of composites.AIAA J,2003,41:2200-2207
27 Chen J Q,Xu Y R,Wei J H.Probabilistic optimum design of laminated composites based on the last ply failure criterion(in Chinese).J Mech Strength,2007,29:241-246[陈建桥,许玉荣,魏俊红.复合材料层合板的极限强度分析与可靠性优化设计.机械强度,2007,29:241-246]
28 An W G,Zhao W T,Yang D H.A method of reliability a analysis for composite laminate(in Chinese).J Asrton,2005,26:672-675[安伟光,赵维涛,杨多和.复合材料层合板的可靠性分析方法.宇航学报,2005,26:672-675]
29 Onkar A K,Upadhyay C S,Yadav D.Probabilistic failure of laminated composite plates using the stochastic finite element method.Compos Struct,2007,77:79-91
30 Venugopal S M.Stochastic Mechanics and Reliability of Composite Laminates Based on Experimental Investigation and Stochastic FEM.Dissertation for Master Degree.Montreal:Concordia University,2003
31 Song Y L,Li S J.The reliability analysis of structure of enhanced fiber composite material plate(in Chinese).J Harbin Eng Univ,1999,20:63-71[宋云连,李树军.加强纤维复合材料板结构的可靠性分析.哈尔滨工程大学学报,1999,20:63-71]
32 Li Y B,Yao W X.Fatigue reliability analysis on structural elements based on SFEM(in Chinese).J Nanjing Univ Aeron Astron,2007,39:461-464[李应波,姚卫星.基于SFEM的结构元件疲劳可靠性分析.南京航空航天大学学报,2007,39:461-464]
33 Chen S X,Hao Z M.Neumann stochastic finite element analysis of the reliability of the composite structure of cyclotron(in Chinese).J Aeron Mater,1998,18:47-52[陈顺祥,郝志明.用纽曼随机有限元分析复合材料回旋结构的可靠性.航空材料学报,1998,18:47-52]
34 Chen X X,Shen Z H,Zhu C Y.Reliability analysis for fiber winding chamber of solid rocket motor via stochastic finite element method(in Chinese).J Aeron Mater,2006,26:113-116[陈顺祥,沈志辉,朱成永.基于SFEM的SRM纤维缠绕结构的可靠性分析.航空材料学报,2006,26:113-116]
35 Ibnabdeljalil M,Curtin W A.Strength and reliability of notched fiber-reinforced composites.Acta Mater,1997,45:3641-3652
36 Jeong H K,Shenoi R A.Probabilistic strength analysis of rectangular FRP plates using Monte Carlo simulation.Comp Struct,2000,76:219-235
37 Yao L J,Tong X Y.The reliability analysis of fatigue life of composite laminates(in Chinese).J Mech Strength,1998,4:268-270[姚磊江,童小燕.复合材料层合板疲劳寿命的可靠性分析.机械强度,1998,4:268-270]
38 Hao Z M,Chen S X,Zhang D,et al.The relaibility analysis of composite convolution structure by neumann expansion Monte-Carloβball method(in Chinese).In:National Conference on Composite Material,Shanghai,1998[郝志明,陈顺祥,张铎,等.分析复合回旋结构可靠性的纽曼展开蒙特卡罗β球法.见:全国复合材料学术会议.上海,1998]
39 Ben-Haim Y,Elishakoff I.Discussion on:A non-probabilistic concept of reliability.Struct Safety 1995,17:195-199
40 Ben-Haim Y.A non-probabilistic concept of reliability.Struct Safety,1994,14:227-245
41 Ben-Haim Y.A non-probabilistic measure of reliability of linear systems based on expansion of convex models.Struct Safety,1995,17:91-109
42 Qiu Z P.Convex Method Based on Non-Probabilistic Set-Theory and Its Application(in Chinese).Beijing:National Defence Industry Press,2005.11-18[邱志平.非概率集合理论凸方法及其应用.北京:国防工业出版社,2005.11-18]
43 Wang X J,Qiu Z P,Wu Z.Non-probabilistic set-based model for structural reliability(in Chinese).Chin J Theor Appl Mech,2007,39:641-646[王晓军,邱志平,武哲.结构非概率集合可靠性模型.力学学报,2007,39:641-646]
44 Gu X D,Wang X J,Qiu Z P.Dynamic response analysis of composite plate with uncertain parameters via interval analysis method(in Chinese).In:The National Conference on Composite Material.Yichang,2006[顾笑冬,王晓军,邱志平.具有不确定参数复合材料板动力响应的非概率区间分析法.见:全国复合材料学术会议.宜昌,2006]
45 Guo S X,Zhang L,Li Y.Procedures for computing the non-probabilistic reliability index of uncertain structures(in Chinese).Chin J Comput Mech,2005,22:227-231[郭书祥,张陵,李颖.结构非概率可靠性指标的求解方法.计算力学学报,2005,22:227-231]
46 Guo S X,Lv Z Z,Feng Y S.Anon-probabilistic model of structural reliability based on interval analysis(in Chinese).Chin J Comput Mech,2001,18:56-60[郭书祥,吕震宙,冯元生.基于区间分析的结构非概率可靠性模型.计算力学学报,2001,18:56-60]
47 Wang X Y,Chen J Q.Probability and non-probability model of laminated composite plate structures(in Chinese).Huazhong Univ Sci Tech(Nat Sci Ed),2006,34:71-73[王向阳,陈建桥.复合材料层合板结构的概率与非概率模型.华中科技大学学报(自然科学版),2006,34:71-73]
48 Kang Z,Luo Y.Non-probabilistic reliability-based topology optimization of geometrically nonlinear structures using convex models.Comp Methods Appl Mech Eng,2009,198:3228-3238
49 Luo Y,Kang Z,Luo Z,et al.Continuum topology optimization with non-probabilistic reliability constraints based on multi-ellipsoid convex model.Struct Multidisc Opt,2009,39:297-310
50 Jiang C,Zhao M H,Cao W G.Non-probabilistic reliability research on uncertain parameters in rock mechanics.J Hunan Univ Nat Sci,2008,35:11-14
51 Zhao M H,Jiang C,Cao W G.Non-probabilistic reliability analysis of retaining walls based on interval(in Chinese).Chin J Geotech Eng,2008,30:467-472[赵明华,蒋冲,曹文贵.基于区间理论的挡土墙稳定性非概率可靠性分析.岩土工程学报,2008,30:467-472]
52 Li Y L,Wang X J,Huang R.Non-probabilistic reliability analysis of active control system for structural vibration(in Chinese).J Beijing Univ Aeron Astron,2015,41:259-266[李云龙,王晓军,黄仁.结构振动主动控制系统的非概率可靠性分析.北京航空航天大学学报,2015,41:259-266]
53 Guo S X,Lv Z Z.Comparison between the non-probabilistic and probabilistic reliability methods for uncertain structure design(in Chinese).Chin J Applied Mech,2003,20:107-110[郭书祥,吕震宙.结构的非概率可靠性方法和概率可靠性方法的比较.应用力学学报,2003,20:107-110]
54 Sun H L,Yao W X.A retrospect for structural reliability measure methods(in Chinese).Mech Sci Tech Aerospace Eng,2007,26:140-146[孙海龙,姚卫星.概率体系和非概率体系下结构元件的可靠性分析方法回顾.机械科学与技术,2007,26:140-146]
55 Kogiso N.Reliability analysis and reliability-based optimization of composite laminated plate subject to buckling.Dissertation for Doctoral Degree.Osaka:Osaka Prefecture University,1997
56 Kogiso N,Katou S,Murotsu Y.Reliability-based optimization of thin composite structure.In:8th ASCE Specialty Conference on Probabilistic Mechanics and Structural Reliability.South Bend,2001:219-222
57 Eamon C D,Rais-Rohani M.Integrated reliability and sizing optimization of a large composite structure.Mar Struct,2009,22:315-334
58 Li W J.Optimal design of composite laminates(in Chinese).J Northwestern Polytech Univ,1986:35-44[李为吉.复合材料层板的优化设计.西北工业大学学报,1986:35-44]
59 Han X,Lei L,Yuan W,et al.Optimization of the composite hat-stiffened panel based on equivalent model(in Chinese).In:2009 China International Conference on Advanced Materials and Technology.Beijing,2009[韩旭,雷磊,袁伟,等.基于等效模型的帽型复合材料加筋壁板优化设计.见:2009暨中国国际先进材料与工艺技术学术研讨会.北京,2009]
60 Xiu Y S,Cui D G.Ply optimization design for stability of composite laminates(in Chinese).Eng Mech,2005,22:212-216[修英姝,崔德刚.复合材料层合板稳定性的铺层优化设计.工程力学,2005,22:212-216]
61 Chang N,Yang W,Wang W,et al.New method of ply optimization design for stability of composite laminates(in Chinese).J Mech Strength,2008,30:148-151[常楠,杨伟,王伟,等.基于复合材料层板稳定性的铺层参数优化设计方法.机械强度,2008,30:148-151]
62 Fang X,Feng Y L,Liu X M,et al.Two level optimization method for large aspect ratio composite wing structure(in Chinese).In:2015 Aviation Test Technology Proceedings of Academic Exchange.Beijng,2015[方雄,冯玉龙,刘晓明,等.大展弦比复合材料机翼结构的两级优化方法.见:2015航空试验测试技术学术交流会论文集.北京,2015]
63 Zhang Y K.Composite Wing,Segment Combination Structure Optimization Design(in Chinese).Dissertation for Master Degree.Xi'an:Northwestern Polytechnical University,2002.10-18[张彦考.全复合材料弹翼、舱段组合结构优化设计.硕士学位论文.西安:西北工业大学,2002.10-18]
64 Hou Y P.Composite Laminated Board Spreading Layer Design and Selection and Discrete Optimization Method Research(in Chinese).Dissertation for Master Degree.Dalian:Dalian University of Technology,2013.4-12[侯玉品.复合材料层合板铺层设计与离散结构选型优化方法研究.硕士学位论文.大连:大连理工大学,2013.4-12]
65 Wang S P,Gao X S,Gan J,et al.Two-level optimization on layout and ply for composite airtight port of airplane(in Chinese).Chin J Appl Mech,2014,3:24-29[王帅培,高行山,甘建,等.飞机复合材料气密舱门布局和铺层的两级优化设计.应用力学学报,2014,3:24-29]
66 Wang P Y,Dong Y P,Wang F S,et al.District and level optimization method for a high aspect-ratio composite wing(in Chinese).In:Composite Materials:Innovation and Sustainable Development.Changsha,2010[王佩艳,董勇鹏,王富生,等.大展弦比复合材料机翼分区分级优化.见:复合材料:创新与可持续发展.长沙,2010]
67 Tang J,Zhang M Q.Research on small-sample fuzzy reliability simulation based on bayes Monte Carlo Method.J Syst Simul,2009,21:7557-7559,7563
68 Ding F,Yin J C,Dang J Q.Reliability assessment of the small sample aero-engine bearings.Adv Mater Res,2014,986-987:858-861
69 Zou X,Yao R.Small sample statistical theory and IC reliability assessment.Control Deci,2008,23:241-232
70 Xiong J,Shenoi R A,Gao Z.Small sample theory for reliability design.J Strain Anal Eng Des,2002,37:87-92
71 Fu H.Method for reliability assessment with very small sample.J Mech Strength,2005,3:12
72 Jin B,Qin D T,Hu J J.A bayes method of reliability synthesis evaluation based on the small sample-system.J Chongqing Univ,2007,9:4
73 Kang Z,Bai S.Structural optimization considering uncertainties and multi-field coupling(in Chinese).Sci Techn Innov Herald,2016,13:177-178[亢战,白嵩.考虑不确定性与多场耦合的结构优化.科技创新导报,2016,13:177-178]
74 Wang X J,Wang L,Qiu Z P.Response analysis based on smallest interval set of parameters for structures with uncertainty(in Chinese).Appl Math Mech,2012,33:1078-1090[王晓军,王磊,邱志平.基于最小参数区间集的不确定结构响应分析.应用数学和力学,2012,33:1078-1090]
75 Wang X J,Yang H F,Qiu Z P,et al.Fuzzy theory for uncertain structural analysis based on measurement data(in Chinese).J Beijing Univ Aeron Astron,2010,36:887-891[王晓军,杨海峰,邱志平,等.基于测量数据的不确定性结构分析的模糊理论.北京航空航天大学学报,2010,36:887-891]
76 Luo Y,Li A,Kang Z.Reliability-based design optimization of adhesive bonded steel-concrete composite beams with probabilistic and nonprobabilistic uncertainties.Eng Struct,2011,33:2110-2119
77 Kang Z,Luo Y J.On structural optimization for non-probabilistic reliability based on convex models(in Chinese).Chin J Theor Appl Mech,2006,38:807-815[亢战,罗阳军.基于凸模型的结构非概率可靠性优化.力学学报,2006,38:807-815]
78 Kang Z,Luo Y,Li A.On non-probabilistic reliability-based design optimization of structures with uncertain-but-bounded parameters.Struct Safety,2011,33:196-205
79 Chen L,Qiu Z P.Natural frequency analysis and optimization of composite laminates based on the non-probabilistic approach(in Chinese).In:The National Conference on Composite Material.Harbin,2009[陈亮,邱志平.复合材料板固有频率的非概率分析及优化.见:全国复合材料学术会议.哈尔滨,2009]
80 Xu M H,Qiu Z.Interval analysis and optimization for free vibration of all-composite lattice truss core sandwich beam(in Chinese).J Beijing Univ Aeron Astron,2013,39:1079-1085[许孟辉,邱志平.复合材料点阵夹芯梁振动特性区间分析与优化.北京航空航天大学学报,2013,39:1079-1085]
81 Wang X J,Wang L,Jia X,et al.Structural optimization design based on non-probabilistic convex modeling reliability(in Chinese).J Beijing Univ Aeron Astron,2012,38:630-635[王晓军,王磊,贾晓,等.基于非概率凸模型可靠性的结构优化设计.北京航空航天大学学报,2012,38:630-635]
82 Wang C,Qiu Z P,Wang X J.Composite structure-acoustic coupling interval reliability optimization(in Chinese).In:The Chinese Mechanical Conference.Xi'an,2013[王冲,邱志平,王晓军.复合材料结构-声耦合系统区间可靠性优化.见:中国力学大会.西安,2013]
83 Gomes H M,Awruch A M,Lopes P A M.Reliability based optimization of laminated composite structures using genetic algorithms and artificial neural networks.Struct Safety,2011,33:186-195
84 Tang Y,Chen J,Peng W.Probabilistic optimization of laminated composites considering both ply failure and delamination based on PSO and FEM.Tsinghua Sci Tech,2009,14:89-93
85 Ge R,Chen J Q.Reliability optimal design of composite materials based on the improved particle swarm optimization algorithm(in Chinese).Mech Sci Tech,2007,26:257-260[葛锐,陈建桥,魏俊红.基于改进粒子群优化算法的复合材料可靠性优化设计.机械科学与技术,2007,26:257-260]
86 Xu Y R,Chen J Q,Luo C,et al.Probabilistic optimum design of laminated plates based on genetic algorithms(in Chinese).Mech Sci Tech,2004,23:1344-1347[许玉荣,陈建桥,罗成,等.复合材料层合板基于遗传算法的可靠性优化设计.机械科学与技术,2004,23:1344-1347]
87 Wang X Y,Chen J Q,Luo C.Optimum design of the probability for composite laminates based on genetic algorithm(in Chinese).Huazhong Univ Sci Tech(Nat Sci Ed),2004,32:10-12[王向阳,陈建桥,罗成.基于遗传算法的层合板结构的可靠性优化设计.华中科技大学学报(自然科学版),2004,32:10-12]
88 Li S,Xun Y M,Zhang J.Conposite structural optimization design based on neural net work response surfaces(in Chinese).Acta Mater Comp Sin,2005,22:134-140[李烁,徐元铭,张俊.基于神经网络响应面的复合材料结构优化设计.复合材料学报,2005,22:134-140]
89 Wang X Y.Study on the Reliability-Based Optimum Design and the Robust Optimization for Laminated Composite Structures(in Chinese).Dissertation for Doctoral Degree.Huazhong University of Science and Technology,2004[王向阳.复合材料层合板结构的可靠性优化和鲁棒优化研究.博士学位论文.华中科技大学,2004]
90 Wang X Y,Chen J Q,Zhang X D.Probabilistic progressive failure analysis of CFRP laminated plates(in Chinese).J Wuhan Univ Tech(Transport Sci Eng),2004,28:863-865[王向阳,陈建桥,张谢东.纤维增强复合材料层合板的概率逐步失效分析.武汉理工大学学报(交通科学与工程版),2004,28:863-865]
91 Luo C.Reliability and Optimal Design of Fiber Composites Based on Ultimate Strength(in Chinese).Dissertation for Master Degree.Wuhan:Huazhong University of Science and Technology,2003[罗成.纤维复合材料基于最终强度的可靠性及其优化设计.硕士学位论文.武汉:华中科技大学,2003]
92 Gadade A M,Lal A,Singh B N.Finite element implementation of Puck's failure criterion for failure analysis of laminated plate subjected to biaxial loadings.Aerospace Sci Tech,2016,55:227-241
93 Kumar A,Chakrabarti A.Failure analysis of laminated composite skew laminates.Procedia Eng,2017,173:1560-1566
94 Wang X.Reliability-based optimum study on FRP laminated plates with genetic algorithm.In:Proceedings of International Symposium on Distributed Computing and Applications To Business,Engineering and Science.Bangalore,2007
95 Romeo G,Danzi F,Cestino E,et al.Optimization of advanced composite wing box structures subjected to combined loads and impact.In:Proceedings of 1st International Conference on Engineering and Applied Sciences Optimization.Kos,2014
96 Taguchi G,Cariapa V.Taguchi on robust technology development.J Pressure Vessel Technol,1993,115:336
97 Sundaresan S,Ishii K,Houser D R.A robust optimization procedure with variations on design variables and constraints.Eng Opt,1995,24:101-117
98 Sundaresan S,Ishii K,Houser R.Automatic differentiation in robust optimization.AIAA J,1997,35:1072-1079
99 Chen W,Wiecek M M,Zhang J.Quality utility—A compromise programming approach to robust design.J Mech Des,1999,121:179
100 Gabrel V,Murat C,Thiele A.Recent advances in robust optimization:An overview.Eur J Oper Res,2014,235:471-483
101 Makkapati S.Robust Design Optimization with Applications to Composite-Material Structures.Dissertation for Doctoral Degree.Morgantown:West Virginia University,1997
102 Henrichsen S R,Lindgaard E,Lund E.Robust buckling optimization of laminated composite structures using discrete material optimization considering"worst"shape imperfections.Thin-Walled Struct,2015,94:624-635
103 Phelan S L,Mavris D N.Robust design of aeroelastically tailored composite plates using a new formulation of anti-optimization and optimization.In:56th AIAA/ASCE/AHS/ASC Structures,Structural Dynamics,and Materials Conference.Kissimmee,2015
104 Xiao Z P,Wan Z Q,Yang C,et al.Robust aeroelastic optimization design of a composite wing(in Chinese).Acta Mater Comp Sin,2010,27:127-132[肖志鹏,万志强,杨超,等.复合材料机翼鲁棒气动弹性优化设计.复合材料学报,2010,27:127-132]
105 Wang X Y,Chen J Q.Robust design of laminated composite plates cased on the last-ply failure criterion(in Chinese).J Mech Strength,2004,26:675-679[王向阳,陈建桥.基于最终失效强度的层合板结构的鲁棒优化分析.机械强度,2004,26:675-679]
106 Zhang Z F,Chen H R,Bai R X.Robust optimization of advanced grid composite cylindrical shell considing initial imperfect effect(in Chinese).Acta Mech Solid Sin,2006,27:58-64[张志峰,陈浩然,白瑞祥.含初始缺陷复合材料格栅加筋圆柱壳的鲁棒优化设计.固体力学学报,2006,27:58-64]
107 Tang Y F.Robust reliability analysis and optimization algorithms for composite structure(in Chinese).Wuhan:Huazhong University of Science and Technology,2012.10-18[唐远富.复合材料结构可靠性鲁棒分析及优化算法研究.武汉:华中科技大学,2012.10-18]
108 Zhao X F.Considering Load Uncertainty and Stiffness Uncertainty of Robust Optimization Problem(in Chinese).Dissertation for Master Degree.Dalian:Dalian University of Technology,2015.4-12[赵晓芳.考虑载荷不确定性和刚度不确定性的鲁棒优化问题.硕士学位论文.大连:大连理工大学,2015.4-12]