摘要
在航空航天结构中,结构重量是重要的性能指标之一,减重可以提高飞行器的机动性和续航性,还可节约燃油。作为飞机结构的重要组成部分,翼面结构型式多样,加筋板结构已被广泛应用于各种翼面结构中,它的布局优化设计日益受到航空航天界的关注。
布局优化本身就是优化设计的难点。对于复合材料翼面结构而言,设计变量多,不仅有结构的型式、筋条、梁、肋的个数、位置、尺寸,还有铺层厚度、铺层顺序等等,种类复杂,既有连续变量,又有离散变量;约束类型多样,这些都使得布局优化问题求解难度大。
针对翼面结构的布局优化问题,本文提出了一种二级优化设计技术:第一级采用基于近似模型的优化方法实现布局和尺寸的综合优化,其优化思想为构建一个初始铺层确定的辅助层合板,将梁、肋、筋条的个数、位置、筋条型式、截面形状等作为布局设计变量进行试验设计,铺层厚度作为尺寸设计变量,各试验点对应的最轻重量作为响应值,根据试验点及响应值建立近似模型,利用多岛遗传算法优化求解结构最轻重量对应的最佳布局,然后对其进行尺寸优化得各铺层厚度,并计算出此时层合板的弯曲刚度系数;第二级铺层顺序优化,考虑层合板的制造和工艺约束,层合板各分层的厚度必须是单层材料厚度的整数倍,铺层角通常取一些标准的角度,各分层在层合板厚度方向上的相对位置可以任意变化。本级的思想是将铺层顺序优化等效为对铺层角度的整数规划问题,采用基于等效弯曲刚度的方法,以层合板的各铺层角作为设计变量,以层合板弯曲刚度系数与上一级优化所给最优弯曲刚度系数之间的误差最小为目标,应用多岛遗传算法,求出满足给定层合板铺层厚度和最优弯曲刚度要求的层合板最优铺层结构;最后在二级优化的基础上,通过协调稳定性约束,实现综合优化。
本文利用上述方法,分别研究了复合材料加筋壁板和某型飞机水平安定面的布局优化问题,验证本文方法的有效性与实用性。
Weight is an important performance index for aerospace structure. Weight reduction can not only improve the mobility and endurance capability of aircraft, but also save fuel. As a significant component of airplane structure, wing structure configuration types vary. Among them, stiffened plate structure has been widely used, and its layout optimization design is concerned increasingly in aviation realm.
Layout optimization is a difficulty of design. For composite wing configuration, there are many design variables, including the type, the number of reinforced bars, beams and ribs, thickness and stacking sequence, etc, varying from continuous to discrete specie. Together with the various constraints, all of these make layout optimization problem difficult.
In this paper a layout optimum design formation for wing configuration is proposed. This formation composed of three steps. Firstly parametric finite element model was set up and approximate model is used to construct the weight function of layout variables and size variables, and then to optimize the weight function to obtain the layout and size of the stiffened panel under given stacking sequence. Secondly the equivalent bending stiffness and GA were employed to deal with the ply stacking sequence optimization, where the requirements of manufacture and etc. were considered. And finally the buckling constrain results given by the layout optimization and stacking sequence optimization were collaboratively optimized and thus the optimal composite stiffened panel was determined.
The layout optimization design of the composite stiffened plate and the horizontal stabilizer of certain airplane are studied in this paper using the above method. The method proposed in this paper is proved to be efficient and practical by comparing the final result with the initial solution.
引文
[1]王志谨,姚卫星.飞机结构设计[M].北京:国防工业出版社. 2004.
[2]中国航空研究院.复合材料结构稳定性分析指南[M].北京:航空工业出版社, 2002.
[3]陈念众,张圣坤,孙海虹.复合材料帽型加筋板极限承载能力[J].玻璃钢/复合材料, 2001, 46~48.
[4]李芳,凌道盛.工程结构优化设计发展综述[J].工程设计学报, 2002, 9(5): 229~234.
[5]秦东晨,陈江义,胡滨生等.机械结构优化设计的综述与展望[J].工程论坛, 2005, 9: 90~91.
[6] Maxwell J C. Scientific Papers. Vol.2[C], New York: Dover Publications, 1952: 175~177.
[7] Schmit L A. Structural design by systematic syntheris [J]. Proc. 2nd Conf. Electronic Computation, ASCE, 1960: 105~132.
[8]钱令希,钱万拐,程耿东等.工程结构优化的序列二次规划[J].固体力学学报, 1983, 4(4): 469~480.
[9]许素强,夏人伟.结构优化方法综述[J].航空学报, 1995, 16(4): 385~396.
[10] Azid I A, Kwan A S K, Seetharamu K N. A GA-based technique for layout optimization of truss with stress and displacement constrains [J]. Int J Num Meth Eng, 2002, 53: 1641~1674.
[11]李昊,胡云昌,曹宏铎.桁架结构智能布局优化系统[J].中国工程科学, 2003, 5(2): 75~79.
[12]王跃方,孙焕纯.离散变量桁架结构的布局优化设计[J].大连理工大学学报, 1995, 35(5): 458~462.
[13]梁醒培,王辉.基于有限元法的结果优化设计——原理与工程应用[M].北京:清华大学出版社, 2010: 4~5.
[14]李为吉,辜曦.复合材料结构的优化设计[J].航宇学报, 1990, 2(1): 35~44.
[15]刘福江.复合材料翼面结构多级优化设计方法[J].中国民航学院学报, 1997, 15(1): 15~21.
[16]常楠,刘江,赵美英.复合材料蒙皮/长桁壁板结构优化设计[J].飞机设计, 2007, 27(6): 28~32.
[17]张彦考,张铎.大型复合材料结构优化设计方法研究[J].固体火箭技术, 2003, 26(3): 69~71.
[18]李太鹏,徐元铭.基于PATRAN/NASTRAN的复合材料结构铺层的分级优化设计方法[J].固体火箭技术, 2004, 27(4) : 308~311.
[19]白小涛,李为吉.基于近似技术的协同优化方法在机翼设计优化中的应用[J].航空学报, 2006, 27(5): 847~850.
[20]刘克龙,姚卫星,余雄庆.运用低自由度协同优化的机翼结构气动多学科设计优化[J].航空学报, 2007, 28(5): 1025~1032.
[21]曲晓东,赵丽红.离散变量结构优化设计方法的研究进展与展望[J].辽宁工学院学报, 2004, 24(5): 40~43.
[22]黎观生,潘丙辰,尤其豪.翼面结构满应力设计[J].航空学报, 1978, 2: 20~23.
[23]王小同,范立础.基于模式联想的结构布局优化方法[J].计算力学学报, 1997, 14: 28~35.
[24] M. Blair, S. Hill, T.A. Weisshaar. Rapid Modeling with Innovative Structural Concepts[C]. American Institute of Aeronautics and Astronautics, AIAA-98-1755. U.S, 1998.
[25]王伟,赵美英,常楠.某型机翼内翼结构几何优化设计[J].强度与环境, 2006, 33(3): 56~60.
[26]张仲祯,余雄庆,胡添元.飞翼式飞行器结构布局与构件尺寸的两级优化[J].计算机辅助工程, 2009, 18(l): 27~30.
[27] L. Berke, S.N. Patnaik, P.L.N. Murthy. Optimum Design of Aerospace Structural Components Using Neural Networks[J]. Computers & Structures, 1993, 48(6): 1001~1010.
[28]王伟,赵美英,赵锋.基于人工神经网络技术的结构布局优化设计[J].机械设计, 2006, 23(12): 7~10.
[29]邓扬晨,詹光,高彤.飞机翼面结构布局综合设计方法研究[J].飞机设计, 2004, (2): 18~21.
[30]邓扬晨,张卫红,章怡宁.基于分级优化的飞机翼面结构布局综合技术研究[J].强度与环境, 2005, 32(1):27~35.
[31]王伟,赵美英,常楠.基于杂交算法的机翼结构布局优化设计[J].西北工业大学学报, 2007, 25(1): 46~50.
[32]王伟.考虑气动弹性约束的机翼结构布局优化设计[J].飞机设计, 2009, 29(1): 10~16.
[33]王伟,杨伟,穆朋刚.基于蚁群算法的机翼结构布局优化方法[J].中国机械工程, 2009, 20(5): 542~545.
[34]何林涛,万小朋,赵美英.基于改进粒子群算法的复合材料机翼结构布局优化设计[J].机械设计, 2008, 25(5): 9~11.
[35]何林涛,万小朋,赵美英,王伟.布局优化和尺寸优化相结合的复合材料机翼优化设计[J].中国机械工程, 2008, 19(17): 2077~2080.
[36] W. Liu, R. Butler, A.R. Mileham, et al. Optimum Design, Experimental Testing and Post-Buckling Analysis of Thick Composite Stiffened Panel[R]. 2005, AIAA-2005-1826.
[37] S. Nagendra, D. Jestin, Z. Gurdal, et al. Improved Genetic Algorithm for the Design ofStiffened Composite Panels [J]. Computers and Structures, 1996, 58(3): 543~555.
[38] R. Rikards, H. Abramovich, J. Auzins, et al. Surrogate models for optimum design of stiffened composite shells [J]. Composite Structures, 2004, 63: 243~251
[39] R. Rikards, H. Abramovich, K. Kalnins, et al. Surrogate modeling in design optimization of stiffened composite shells [J]. Composite Structures, 2006, 73: 244~251
[40] H. Langer, T. Puhlhofer, H. Baier. A Multi-objective Evolutionary Algorithm with intergrated Response Surface Functionaltities for Configuration Optimization with Discrete Variables [J].2004, AIAA-2004-4326.
[41]穆雪峰,姚卫星,余雄庆,刘克龙,薛飞.多学科设计优化中常用代理模型的研究[J].计算力学学报, 2005, 22(5): 608~612.
[42]张成成,姚卫星.基于响应面的结构抗疲劳优化设计方法[J].南京航空航天大学学报, 2007, 39(1): 37~40.
[43]刘克龙,姚卫星,穆雪峰.基于Kriging代理模型的结构形状优化方法研究[J].计算力学学报, 2006, 23(3): 344~347
[44]张柱国,姚卫星,刘克龙.基于进化Kriging模型的金属加筋板结构布局优化方法[J].南京航空航天大学学报, 2008, 40(4): 497~500.
[45]乔巍,姚卫星.复合材料加筋板铺层优化设计的等效弯曲刚度法[J].计算力学学报, 2011, 28(1):发表.
[46]张铁亮,丁运亮.复合材料加筋壁板的结构布局优化设计[J].南京航空航天大学学报,2010,42(1):8~12.
[47]赵群,丁运亮,金海波.一种基于复合材料加筋板结构效率的稳定性优化方法[J].复合材料学报, 2010, 27(3): 169~176.
[48]赵群,丁运亮,金海波.基于压弯刚度匹配论则的复合材料加筋板结构优化设计[J].南京航空航天大学学报, 2010, 42(3): 357~362.
[49]唐焕文,秦学志.实用最优方法[M].大连理工大学出版社, 2004.
[50]修英姝,崔德刚.复合材料层合板稳定性的铺层优化设计[J].工程力学, 2005, 22(6): 212~216.
[51]晏飞,李为吉.基于自适应遗传算法的复合材料层合板铺层顺序优化方法[J].西北工业大学学报, 2001. 19(1): 156~159.
[52]罗志军,乔新.基于遗传算法的复合材料层压板固有频率的铺层顺序优化[J].复合材料学报, 1997, 14(4):114~118.
[53]唐文艳,顾元宪,赵国忠.复合材料层合板铺层顺序优化遗传算法[J].大连理工大学学报, 2004, 44(2): 186~189.
[54] Weaver P M. On Laminate Selection and Design. AIAA-2002-1220.
[55]任茶仙,张铎.复合材料层合结构铺层顺序优化设计的免疫遗传算法[J].强度与环境,2007, 34(2): 43~50.
[56] I. Visser. Aeroelastic and Strength Optimization of a Composite Aircraft Wing Using a Multilevel Approach [J]. AIAA-99-1258:601~610.
[57]金海波,丁运亮.复合材料飞机结构综合优化设计系统研究[D].南京:南京航空航天大学, 2003.
[58] Y. Hirano, A. Todoroki. Fractal Branch and Bound Method for Stacking-Sequence Optimization of Composite Delta Wing [J]. 2004, AIAA-2004-6439:1~13.
[59] Miki M.Optimum design of laminated composite plates using lamination parameters.AIAA Journal, 1993, 31(5): 275~283.
[60] B. Liu, R.T. Haftka. Maximization of buckling loads of composite panels using flexural lamination parameters[R]. Structural and Multidisciplinary Optimization, 2004, 26(2):28~36.
[61] R.T. Haftka, R.L. Walsh. Stacking-sequence optimization for buckling of laminated plates by integer programming[R]. AIAA Journal, 1992, 30(3): 814~819.
[62]王小妮.基于代理模型的结构外形优化[J].飞机设计, 2008, 28(3): 13~15.
[63]方开泰.均匀试验设计的理论、方法和应用—历史回顾[J].数理统计与管理, 2004, 23(3): 69~80.