基于负泊松比蜂窝的复合式柔性蒙皮优化技术

郭瑜超; 聂小华; 宋晨; 艾森; 常亮

基于负泊松比蜂窝的复合式柔性蒙皮优化技术

郭瑜超^{1, 2, ,},
聂小华²,
宋晨³,
艾森²,
常亮²

1.
西北工业大学国家卓越工程师学院, 西安 710072
2.
中国飞机强度研究所强度与结构完整性全国重点实验室, 西安 710065
3.
北京航空航天大学航空科学与工程学院, 北京 100191

基金项目: 工信部民机科研(MJZ3-2N21)；陕西省重点研发计划(2022ZDLGY02-03)

详细信息

通讯作者:
郭瑜超，硕士，高级工程师，研究方向为航空结构仿真技术及结构分析CAE软件　E-mail: guoyuchao1986@163.com

中图分类号: TB124
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- 文章访问数: 38
- HTML全文浏览量: 23
- 被引次数: 0
出版历程
- 收稿日期: 2024-07-09
- 修回日期: 2024-09-15
- 录用日期: 2024-09-28
- 网络出版日期: 2024-10-19

Optimization technology for composite flexible skin based on negative Poisson's ratio honeycomb

1.
National Elite Institute of Engineering, Northwestern Polytechnical University, Xi'an 710072, China
2.
National Key Laboratory of Strength and Structural Integrity, Aircraft Strength Research Institute of China, Xi'an 710065, China
3.
School of Aeronautic Science and Engineering, Beihang University, Beijing 100191, China

Funds: Civil Aircraft Research Projects (MJZ3-2N21)； Key R & D Program of Shaanxi Province (2022ZDLGY02-03)

摘要

摘要: 针对由负泊松比蜂窝夹芯和弹性表皮构成的复合式柔性蒙皮，提出了柔性蒙皮几何参数优化方法。首先，将柔性蒙皮的胞壁长度、胞壁夹角、蜂窝高度、胞壁厚度、表皮厚度等几何参数作为变量，设计了柔性蒙皮结构参数化建模方法；其次，通过均实验设计方法获取样本点，利用参数化方法构建柔性蒙皮结构有限元模型，并通过仿真获取各几何参数组合状态对应的结构性能；然后，基于响应面方法构造柔性蒙皮几何参数与结构性能关系的近似模型，并对近似模型的精度进行了定量评估；最后，以近似模型为基础，以柔性蒙皮几何参数为优化变量，综合考虑面内应变、泊松比、面外挠度、质量等因素，采用加权系数法构造了综合优化目标函数，并采用遗传算法进行优化，得到了柔性蒙皮结构综合性能最优的构型。构建了复合式柔性蒙皮有限元模型，进行优化方法验证，结果显示，优化后的构型与初始构型相比，面内变形能力提升30.73%，面外承载能力提高30%，结构质量减轻22.77%，泊松比降低20.73%。
- 变体飞机 /
- 复合材料 /
- 柔性蒙皮 /
- 负泊松比蜂窝 /
- 优化技术 /
- 近似模型 /
- 遗传算法
Abstract: The geometric parameter optimization method of flexible skin composed of negative Poisson's ratio honeycomb core and elastic skin was proposed. Firstly, a parameterized modeling method for the flexible skin structure was designed, with geometric parameters such as cell wall length, cell wall Angle, honeycomb height, cell wall thickness and skin thickness. Secondly, the sample points were obtained by uniform experimental design method, the finite element models of flexible skin structure were constructed using the parameterized method, and the structural performance corresponding to various combinations of geometric parameters was obtained through simulation. Then, an approximate model for the relationship between the geometric parameters of the flexible skin and the structural performance was constructed using the response surface method, and the accuracy of the approximate model was quantitatively evaluated. Finally, based on the approximate model, taking the geometric parameters of the flexible skin as optimization variables, and considering the factors such as internal strain, Poisson's ratio, out-of-plane deflection, and mass, a comprehensive optimization objective function was constructed using the weighted coefficient method, and the optimal configuration of the flexible skin structure was obtained by genetic algorithm. A finite element model of the composite flexible skin was constructed to validate the optimization. The results show that compared with the initial configuration, the in-plane deformation capacity is increased by 30.73%, the out-of-plane load capacity is increased by 30%, the structural mass is reduced by 22.77%, and the Poisson’s ratio is reduced by 20.73%.
- variant aircraft /
- composite material /
- flexible skin /
- negative Poisson's ratio honeycomb /
- optimization technology /
- approximate model /
- genetic algorithms

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图 1 PDMS-Nylon6复合材料柔性蒙皮及蜂窝胞元

Figure 1. PDMS-Nylon6 composite flexible skin structure and honeycomb cell

${L_1}$ and ${L_2}$ are the lengths of the walls of the cell; $\theta $ is the angle between the walls; $t$ is the thickness of the walls

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图 2 PDMS-Nylon6复合材料柔性蒙皮厚度方向尺寸

Figure 2. Thickness of the PDMS-Nylon6 composite flexible skin

${t_{\text{f}}}$ is the thickness of the elastic skin; $H$ is the height of the honeycomb

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图 3 PDMS-Nylon6复合材料柔性蒙皮结构综合优化流程

Figure 3. Optimization process of PDMS-Nylon6 composite flexible skin structure

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图 4 PDMS-Nylon6复合材料柔性蒙皮参数化模型边界条件

Figure 4. Boundary conditions of the parametric model of PDMS-Nylon6 composite flexible skin

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图 5 PDMS-Nylon6复合材料柔性蒙皮模型的变形计算结果

Figure 5. Deformation calculation results of the PDMS-Nylon6 composite flexible skin model

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图 6 PDMS-Nylon6复合材料柔性蒙皮响应面方法建模流程图

Figure 6. PDMS-Nylon6 composite flexible skin response surface method modeling process diagram

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图 7 遗传算法流程图

Figure 7. Process of Genetic Algorithm

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图 8 优化前后PDMS-Nylon6复合材料柔性蒙皮变形结果对比

Figure 8. Comparison of the deformation results of the PDMS-Nylon6 composite flexible skin before and after optimization

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表 1 聚二甲基硅氧烷(PDMS)-Nylon6复合材料力学性能

Table 1. Mechanical properties of Polydimethylsiloxane (PDMS)-Nylon6 composite materials

Material	Elastic modulus/ MPa	Poisson's ratio	Density/ ($kg \cdot m{m^{ - 3}}$)
Nylon6	1.06	0.35	$1.14 \times {10^{ - 6}}$
PDMS	1.8	0.49	$2.33 \times {10^{ - 6}}$

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表 2 PDMS-Nylon6复合材料柔性蒙皮模型边界条件

Table 2. Boundary conditions of the PDMS-Nylon6 composite flexible skin model

Boundary	Boundary of in-plane load conditions	Boundary of out-plane load conditions
A	${u_x} = {u_y} = {u_{\textit{z}}} = 0$ ${\gamma _x} = {\gamma _y} = {\gamma _z} = 0$	${u_x} = {u_y} = {u_{\textit{z}}} = 0$ ${\gamma _x} = {\gamma _y} = {\gamma _{\textit{z}}} = 0$
B	${F_x}$ ${\gamma _x} = {\gamma _y} = {\gamma _{\textit{z}}} = 0$	${u_x} = {u_y} = {u_{\textit{z}}} = 0$ ${\gamma _x} = {\gamma _y} = {\gamma _{\textit{z}}} = 0$
C	Free	Free
D	Free	Free
E	Free	Free
F	Free	${P_{\text{n}}} = 0.001{\text{MPa}}$

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表 3 PDMS-Nylon6复合材料柔性蒙皮均匀实验设计

Table 3. Uniform experimental design for PDMS-Nylon6 composite flexible skin

Parameters	Levels
Parameters	1	2	3	4	5
${L_1}$/mm	4.5	4.75	5	5.25	5.5
${L_2}$/ mm	6.75	7.125	7.5	7.875	8.25
$\theta $ /(°)	31.5	33.25	35	36.75	38.5
H /mm	1.8	1.9	2	2.1	2.2
t /mm	0.45	0.475	0.5	0.525	0.55
${t_{\text{f}}}$/ mm	0.9	0.95	1	1.05	1.1
F / N	450	475	500	525	550
Notes: F is the external load.

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表 4 PDMS-Nylon6复合材料柔性蒙皮近似模型的评估

Table 4. Evaluation of the approximated model for PDMS-Nylon6 composite flexible skin

	${\varepsilon _x}$	μ	ω	G
R	0.9996	0.9999	0.9999	1.0
$\bar e$	0.99%	0.32%	0.83%	0.05%
${\sigma _e}$	1.20%	0.24%	0.67%	0.06%
Notes: ${\varepsilon _x}$ is the in-plane tensile strain; μ is the Poisson’s ratio; ω is the out-of-plane deflection; G is the structural mass; R is the correlation coefficient; $\bar e$ is the mean of the relative error; ${\sigma _e}$ is the standard deviation of the relative error.

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表 5 优化前后PDMS-Nylon6复合材料柔性蒙皮的几何参数对比

Table 5. Comparison of geometric parameters of PDMS-Nylon6 composite flexible skin before and after optimization

Variable	Initial value	Optimized value
${L_1}$/mm	5	4.5
${L_2}$/ mm	7.5	7.3164
$\theta $ /(°)	35	38.5
H /mm	2	2.2
t /mm	0.65	0.45
${t_{\text{f}}}$/ mm	1	0.9

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表 6 优化前后PDMS-Nylon6复合材料柔性蒙皮的性能对比

Table 6. Comparison of PDMS-Nylon6 composite flexible skin performance before and after optimization

Variable	Initial value	Optimized value	Percent change
${\varepsilon _x}$	23.92%	31.27%	30.73%
$\mu $	1.3886	1.1008	-20.73%
$\omega $	1.6%	1.12%	-30%
G	0.0584	0.0451	-22.77%
F(x)	0.3522	0.0740	-78.99%

下载: 导出CSV

[1]	Weisshaar T A. Morphing aircraft systems: historical perspectives and future challenges[J]. Journal of Aircraft, 2013, 50(2): 337-353. doi: 10.2514/1.C031456
[2]	Sofla A, Meguid S A, Tan K T, et al. Shape morphing of aircraft wing: status and challenges[J]. Materials and Design, 2010, 31(3): 1284-1292. doi: 10.1016/j.matdes.2009.09.011
[3]	Joshi S P, Tidwell Z, Crossley W A, et al. Comparison of morphing wing strategies based upon aircraft performance impacts[J]. Proceedings of the 45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Palm Springs, CA: AIAA, 2004, 1722: 1-7.
[4]	Jha A K, Kudva J N. Morphing aircraft concepts, classifications, and challenges. Anderson E H, Proc. SPIE 5388, Smart Structures and Materials 2004: Industrial and Commercial Applications of Smart Structures Technologies, San Diego, CA: International Society for Optics and Photonics, 2004: 213-224.
[5]	Reich G, Sanders B. Introduction to morphing aircraft research[J]. Journal of Aircraft, 2007, 44(4): 1059. doi: 10.2514/1.28287
[6]	任鑫, 张相玉, 谢亿民. 负泊松比材料和结构的研究进展[J]. 力学学报, 2019, 51(3): 656-687. doi: 10.6052/0459-1879-18-381 Ren Xin, Zhang Xiangyu, Xie Yimin. Research progress in auxetic materials and structures[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(3): 656-687(in Chinese). doi: 10.6052/0459-1879-18-381
[7]	沈元, 昂海松, 刘卫东. 用于变形机翼夹心式柔性伸缩蒙皮的梯形蜂窝支撑结构[J]. 复合材料学报, 2015, 32(3): 8158-22. She Y, Ang HS, Liu W D. Trapezoidal cellular support structure applied to flexible telescopic sandwich skin of morphing wing[J]. Acta Materiae Compositae Sinica, 2015, 32(3): 8158-22(in Chinese).
[8]	Olympio K R, Gandhi F. Flexible skins for morphing aircraft using cellular honeycomb cores[J]. Journal of Intelligent Material Systems and Structures, 2010, 21(17): 1719-1735. doi: 10.1177/1045389X09350331
[9]	Olympio K R, Gandhi F. Zero Poisson’s ratio cellular honeycombs for flex skins undergoing one-dimensional morphing[J]. Journal of intelligent material systems and structures, 2010, 21(17): 1737-1753. doi: 10.1177/1045389X09355664
[10]	Bubert E A, Woods B K, Lee K, et al. Design and fabrication of a passive 1D morphing aircraft skin[J]. Journal of Intelligent Material Systems and Structures, 2010, 21(17): 1699-1717. doi: 10.1177/1045389X10378777
[11]	Murugan S, Saavedra Flores E I, Adhikari S, et al. Optimal design of variable fiber spacing composites for morphing aircraft skins[J]. Composite Structures, 2012, 94(5): 1626-1633 doi: 10.1016/j.compstruct.2011.12.023
[12]	Olympio K R, Gandhi F. Skin designs using multi-objective topology optimization[J]. Proceedings of the 49th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Schaumburg, IL: AIAA, 2008, 1793: 1-26.
[13]	Liu Weidong, Zhu Hua, Zhou Shengqiang, Bai Yalei, Zhao Chunsheng. Topology Optimization of Support Structure of Telescope Skin Based on Bit-matrix Representation NSGA-II[J]. Chinese Journal of Aeronautics, 2013, 26(6): 1422-1429 doi: 10.1016/j.cja.2013.07.046
[14]	刘明, 李永新, 吴金玺, 等. 基于响应面法的负泊松比蜂窝芯结构多目标优化[J]. 现代制造工程, 2015, (10): 1-4. doi: 10.3969/j.issn.1671-3133.2015.10.001 Liu Ming, Li Yongxin, Wu Jinxi, et al. Structure multi-objective optimization of negative Poisson’s ratio honeycomb core based on response surface method[J]. Modern Manufacturing Engineering, 2015, (10): 1-4(in Chinese). doi: 10.3969/j.issn.1671-3133.2015.10.001
[15]	De shanShan, Qiao Li, InamullahKhan, et al. A novel finite element mo del updating method based on substructure and response surface model[J]. Enginee ring Structures, 2015, 103.
[16]	Henikar G, Palmer G M. Response-Surface Methodology-Revisited[J]. Cereal Food Science, 1976, 21: 432-445.
[17]	Henikar G, Use of Response-Surface Methodology in Sensory Evaluation[J]. Food Technology, 1982, 36: 96-101.
[18]	Bucher C G, Bourgund U. A Fast and Efficient Response Surface Approach for Structural Reliability Problems[J]. Structural Safety, 1990, 7(1): 57-66. doi: 10.1016/0167-4730(90)90012-E
[19]	Goldberg D E, Holland J H. Genetic algorithms and machine learning[J]. machine learning, 1988, 3(2): 95-99.
[20]	Wright A H. Genetic algorithms for real parameter optimization[J]. Foundations of Genetic Algorithms, 1991, 1: 205-218.
[21]	胡春幸, 侯玉亮, 铁瑛, 等. 基于遗传算法的碳纤维增强树脂复合材料层合板单搭胶接结构的多目标优化[J]. 复合材料学报, 2021, 38(6): 1847-1858. HU Chunxing, HOU Yuliang, TIE Ying, et al. Multi-objective optimization of adhesively bonded single-lap joints of carbon fiber reinforced polymer laminates based on genetic algorithm[J]. Acta Materiae Compositae Sinica, 2021, 38(6): 1847-1858(in Chinese).