| 基于代理模型的复合材料带加强筋板铺层优化 |
| 刘哲1, 金达锋1, 范志瑞2 |
| 1. 清华大学 汽车安全与节能国家重点实验室, 北京 100084; 2. 中北大学 机械与动力工程学院, 太原 030051 |
| Laminate optimization of a composite stiffened panel based on surrogate model |
| LIU Zhe1, JIN Dafeng1, FAN Zhirui2 |
| 1. State Key Laboratory of Automotive Safety and Energy, Tsinghua University, Beijing 100084, China; 2. School of Mechanical and Power Engineering, North University of China, Taiyuan 030051, China |
摘要:
| |||
| 摘要该文基于遗传算法对复合材料带加强筋板中加强筋的铺层顺序进行了优化, 使结构在质量一定的情况下结构屈曲载荷最大。为了减少优化过程中有限元模型的调用次数, 引入径向基神经网络作为代理模型对结构屈曲载荷进行估计, 并且将铺层参数作为其输入以降低目标函数的非线性。由于设计空间形状不规则, 采用D-optimal实验设计方法确定训练径向基神经网络的采样点集。考虑到代理模型存在估计误差, 提出了加强代理模型在暂定最优区域估计精度的方法。算例表明: 以铺层参数为输入的径向基神经网络在建立代理模型方面具有较高的精度和效率; 代理模型的局部精度加强可进一步提高代理模型在暂定最优区域的精度。 | |||
| 关键词 ：复合材料,加强筋板,优化,遗传算法,代理模型 | |||
| Abstract：This study optimized the stacking sequence of stiffeners in a composite stiffened panel to maximize the buckling load of the panel assuming a constant mass panel. The number of finite element models was reduced by using a radial basis function neural network (RBF) as the surragate model with the lamination parameters as inputs to estimate the buckling load. The lamination input parameters reduced the nonlinearities of the objective function. Due to the irregular shape of the design space, the D-optimal method was used to determine the sample points for training the RBF. The model errors were reduced by constructing a zoomed RBF to enhance the RBF accuracy near the provisional optimal laminate. A numerical example shows the accuracy and efficiency of the RBF with the lamination parameters as inputs and how the model accuracy is increased by the zoomed RBF near the optimal region. | |||
| Key words：compositestiffened paneloptimizationgenetic algorithmsurrogate model | |||
| 收稿日期: 2014-08-07 出版日期: 2015-09-18 | |||
| |||
| 通讯作者:金达锋,副教授,E-mail:jindf@tsinghua.edu.cnE-mail: jindf@tsinghua.edu.cn | |||
| 引用本文: |
| 刘哲, 金达锋, 范志瑞. 基于代理模型的复合材料带加强筋板铺层优化[J]. 清华大学学报（自然科学版）, 2015, 55(7): 782-789. LIU Zhe, JIN Dafeng, FAN Zhirui. Laminate optimization of a composite stiffened panel based on surrogate model. Journal of Tsinghua University(Science and Technology), 2015, 55(7): 782-789. |
| 链接本文: |
| http://jst.tsinghuajournals.com/CN/或 http://jst.tsinghuajournals.com/CN/Y2015/V55/I7/782 |
图表:
 |
| 图1 加强筋铺层优化流程图 |
 |
| 图2 铺层参数在设计空间内的分布图 |
 |
| 图3 带加强筋平板几何尺寸 |
 |
| 表1 T800/924C碳纤维环氧材料性能[12] |
 |
| 图4 实验测得与有限元法得到的屈曲载荷分布对比图 |
 |
| 图5 实验设计所得采样点分布图 |
 |
| 图6 初始径向基神经网络误差分析结果 |
 |
| 表2 由初始径向基神经网络确定的暂定最优铺层的临近铺层参数及误差 |
 |
| 表3 由局部加强径向基神经网络确定的暂定最优铺层的临近铺层参数及误差 |
参考文献:
| [1] Irisarri F X, Laurin F, Leroy F H, et al. Computational strategy for multiobjective optimization of composite stiffened panels [J]. Composite Structures, 2011, 93(3): 1158-1167. [2] Marín L, Trias D, Badalló P, et al. Optimization of composite stiffened panels under mechanical and hygrothermal loads using neural networks and genetic algorithms [J]. Composite Structures, 2012, 94(11): 3321-3326. [3] Faggiani A, Falzon B G. Optimization strategy for minimizing damage in postbuckling stiffened panels [J]. AIAA Journal, 2007, 45(10): 2520-2528. [4] Rikards R, Abramovich H, Kalnins K, et al. Surrogate modeling in design optimization of stiffened composite shells [J]. Composite Structures, 2006, 73(2): 244-251. [5] Blom A W, Setoodeh S, Hol J M A M, et al. Design of variable-stiffness conical shells for maximum fundamental eigenfrequency [J]. Computers & Structures, 2008, 86(9): 870-878. [6] Wang G G, Dong Zuoming, Aitchison P. Adaptive response surface method: A global optimization scheme for approximation-based design problems [J]. Engineering Optimization, 2001, 33(6): 707-734. [7] Abouhamze M, Shakeri M. Multi-objective stacking sequence optimization of laminated cylindrical panels using a genetic algorithm and neural networks [J]. Composite Structures, 2007, 81(2): 253-263. [8] Apalak M K, Yildirim M, Ekici R. Layer optimisation for maximum fundamental frequency of laminated composite plates for different edge conditions [J]. Composites Science and Technology, 2008, 68(2): 537-550. [9] Todoroki A, Ishikawa T. Design of experiments for stacking sequence optimizations with genetic algorithm using response surface approximation [J]. Composite Structures, 2004, 64(3): 349-357. [10] Todoroki A, Sasai M. Stacking sequence optimizations using GA with zoomed response surface on lamination parameters [J]. Advanced Composite Materials, 2002, 11(3): 299-318. [11] De Aguiar P F, Bourguignon B, Khots M S, et al. D-optimal designs [J]. Chemometrics and Intelligent Laboratory Systems, 1995, 30(2): 199-210. [12] Falzon B G, Stevens K A, Davies G O. Postbuckling behaviour of a blade-stiffened composite panel loaded in uniaxial compression [J]. Composites Part A: Applied Science and Manufacturing, 2000, 31(5): 459-468. |
相关文章:
|
