基于代理模型的加筋板结构布局优化设计
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摘要
加筋板结构可大大地节省结构材料,减轻结构重量,从而提高结构效率,因而已被广泛地应用于航空航天等工程领域。当承受压缩、剪切载荷时,加筋板结构可能发生屈曲甚至导致破坏。加筋板结构失效模式众多,且对其进行优化的设计变量众多,其有限元模型、结构分析以及优化设计非常复杂。因此,对加筋板结构进行优化设计具有重要的研究价值。
本文基于代理模型技术,提出了一种金属加筋板结构稳定性优化设计方法,实现了金属加筋板结构布局优化设计。其基本思想是采用试验设计法选取样本点,进行有限元分析得到该样本点的重量、屈曲因子等,利用这些样本点和响应建立kriging代理模型,并采用更新技术提高kriging模型的精度,基于Kriging模型应用折衷法和遗传算法获得最优解。并在此基础上,本文分析了加筋板结构的后屈曲特性,实现了结构后屈曲优化设计。本文又通过引入层合板弯曲刚度参数,提出了对称均衡复合材料铺层顺序优化设计方法,并将其和前述加筋板结构优化设计相结合,发展了基于代理模型技术的二级优化方法,实现了层合板结构铺层顺序优化的复合材料加筋板结构优化设计。算例表明优化效果比较明显,也同时验证了本文所提方法的可行性和有效性。
Stiffened panel structure is widely used in the engineering fields of aeronautics and astronautics as they can save the structural materials, reduce the structural weight, and raise the structural efficiency. Stiffened panel structure may result in buckling or even collapse when undertaking compressive load or shear load or the both. Because of the numerous failure modes and optimum design variables, modeling, analysis and optimization are complicated. So the research of the optimum design of stiffened panel is very important.
In this thesis, an optimum design method of metallic stiffened panel was built up based on surrogate model. It can be applied to the layout optimization of metallic stiffened panel structure. In this method, the initial samples were firstly created by design of experiment (DOE), secondly the responses corresponding to the initial samples, including the weight and the buckling factor, were computed by FEA, then the initial Kriging model was derived through the samples, late the samples were updated if the Kriging model was not satisified, and a new Kriging model was rederived with the updated samples. Finally the optimal solution was obtained with Trade off Method and Genetic Algorithms (GA) based on the Kriging model. Based on this method, the post -buckling optimization problem of metallic stiffened panel was also accomplished by introducing post-buckling analysis. Besides, a stacking sequence optimization method of symmetrical and balanced composite laminate was proposed in this thesis based on the above presented optimization method and bending lamination parameter. And then a two-level optimization algorithm was developed. All the examples demonstrate that they can find out the optimal solution and can verify the feasibility and validity of these methods proposed in this thesis.
本文基于代理模型技术,提出了一种金属加筋板结构稳定性优化设计方法,实现了金属加筋板结构布局优化设计。其基本思想是采用试验设计法选取样本点,进行有限元分析得到该样本点的重量、屈曲因子等,利用这些样本点和响应建立kriging代理模型,并采用更新技术提高kriging模型的精度,基于Kriging模型应用折衷法和遗传算法获得最优解。并在此基础上,本文分析了加筋板结构的后屈曲特性,实现了结构后屈曲优化设计。本文又通过引入层合板弯曲刚度参数,提出了对称均衡复合材料铺层顺序优化设计方法,并将其和前述加筋板结构优化设计相结合,发展了基于代理模型技术的二级优化方法,实现了层合板结构铺层顺序优化的复合材料加筋板结构优化设计。算例表明优化效果比较明显,也同时验证了本文所提方法的可行性和有效性。
Stiffened panel structure is widely used in the engineering fields of aeronautics and astronautics as they can save the structural materials, reduce the structural weight, and raise the structural efficiency. Stiffened panel structure may result in buckling or even collapse when undertaking compressive load or shear load or the both. Because of the numerous failure modes and optimum design variables, modeling, analysis and optimization are complicated. So the research of the optimum design of stiffened panel is very important.
In this thesis, an optimum design method of metallic stiffened panel was built up based on surrogate model. It can be applied to the layout optimization of metallic stiffened panel structure. In this method, the initial samples were firstly created by design of experiment (DOE), secondly the responses corresponding to the initial samples, including the weight and the buckling factor, were computed by FEA, then the initial Kriging model was derived through the samples, late the samples were updated if the Kriging model was not satisified, and a new Kriging model was rederived with the updated samples. Finally the optimal solution was obtained with Trade off Method and Genetic Algorithms (GA) based on the Kriging model. Based on this method, the post -buckling optimization problem of metallic stiffened panel was also accomplished by introducing post-buckling analysis. Besides, a stacking sequence optimization method of symmetrical and balanced composite laminate was proposed in this thesis based on the above presented optimization method and bending lamination parameter. And then a two-level optimization algorithm was developed. All the examples demonstrate that they can find out the optimal solution and can verify the feasibility and validity of these methods proposed in this thesis.
引文
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[10]孙焕纯,王跃方,黄吉锋.离散变量桁架的形状优化设计[J].大连理工大学学报,1995,35(1):10-16
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[12]刘军伟,姜节胜.桁架动力学形状优化的统一设计变量方法[J].振动工程学报,2000,13(1):84-88
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[14]赵丽红,郭鹏飞,孙洪军等.结构拓扑优化设计的发展、现状及展望[J].辽宁工学院学报,2004,24(1):46-49
[15]陈建军,曹一波,段宝岩.基于可靠性的桁架结构拓扑优化设计[J].力学学报,1998,30(3):277-284
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[17] Kawamura H, Ohmori H, Kito N. Truss Topology Optimization by a Modified Genetic Algorithm [J]. Struct Optim,2002,(23):467-472
[18] Lipson S L, Gwin L B. Discrete sizing of trusses for optimal geometry [J]. ASCE J StructDiv,1977,103(5):1031-1046
[19] Rozvany G I N, Birker T. Generalized Michell structures: exact least-weight truss layouts for combined stress and displacement constraints: Part 1: general theory for plane trusses [J]. Structural Optimization,1994,9(2):178-188
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[21]谭中富,张作泉.关于桁架结构布局优化理论和方法的探讨[J].科技通报,1995,11(3):167-170
[22] 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
[23] Azid I A, Kwan A S K, Seetharamu K N. An evolutionary approach for layout optimization of a three-dimensional truss [J]. Struct Multidisc Optim,2002,24:333-337
[24]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
[25] Venkataraman S, Haftka R T. Optimization of Composite Panel-A Review [J]. Proceeding of the 14th Annual Technical Conference of the American Society of Composites. Dayton, OH, 1999
[26] Sridharan S. A finite strip analysis of locally buckled plate structures subject to nonuniform compression [J]. Eng Struct,4,249-255
[27] Li L Y, Bettess P. Buckling of stiffened plates and design of stiffeners [J]. Int J Ves&Piping,1997,74:177-187
[28] Jung J H, Jeong S K, Yoon S J. Buckling strength of longitudinally stiffened orthotropic rectangular plate under in-plane compressive forces [A], International Conference on Advances in Structural Engineering and Mechanics [C], 1st, Seoul, Republic of Korea, Proceedings, Taejon, Republic of Korea,1999,1:431-437
[29] Fujikubo M. Elastic local buckling strength of stiffened plate considering plate/stiffener interaction and welding residual stress [J]. Marine Strcutures,1999,12,(9):543-564
[30]胡毓仁,陈伯真,孙久龙.纵向受压加筋板架有侧向压力时加强筋的扭转屈曲[J].上海交通大学学报,2000,12:1717-1732
[31]朴春雨,章怡宁.典型加筋板的优化设计[J].飞机设计, 2003, 4:29-32
[32] Liu W, Butler R, Mileham A R, et al. Optimum Design,Experimental Testing and Post-Buckling Analysis of Thick Composite Stiffened Panel[R]. 2005, AIAA-2005-1826
[33] Lanzi L, Bisagni C. Post-buckling Experimental Tests and Numerical Analyses on Composite Stiffened Panels [J].2003, AIAA-2003-1795.
[34] Bisagni C, Giavotto V. Experimental and Analyses on Post-buckling Behavior of Stringer-Stiffened Laminated Composite Helicopter Tailplane [J].2005, AIAA-2005-1866.
[35] Sjoerd V, Murphy A, Benedictus R. Post-buckling failure of welded aluminum panels[J].2006, AIAA-2006-2273.
[36] Lanzi L. An Experimental Investigation on the Post-buckling Behavior of Composite Stiffened Panels [J].2004, AIAA-2004-1566.
[37] Nagendra S, Jestin D, Gurdal Z,et al. Improved Genetic algorithm for the Design of Stiffened Composite Panels [J]. Computers and Structures,1996,58(3):543-555
[38] Rikards R, Abramovich H, Kalnins K, et al. Surrogate modeling in design optimization of stiffened composite shells [J]. Composite Structures, 2006, 73:244-251
[39] Fatemi J, Trompette P. Optimization of stiffened plates using a modified genetic algorithm[R]. 1998, AIAA-98-4973
[40] Kang J H, Kim C G. Minimum-Weight Design of Compressively Loaded Composite Plates and Stiffened Panels for Post-buckling Strength by Genetic Algorithm[R]. Composite Structures , 2005,69:239-246
[41] Lanzi L, Bisagni C. Minimum Weight Optimization of Composite Stiffened Panel Using Neural Networks[R].2003, 2003, AIAA-2003-1698
[42] Vitali R, Park O, et al. Structural Optimization of a Hat Stiffened Panel by Response Surface Techniques[R].1997, AIAA-97-1151:2983-2993
[43] Merval A, Samuelides M, Grihon S. Application of Response Surface Methodology to Stiffened Panel Optimization [J]. AIAA2006-1815
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