复合材料星载天线反射面热变形有限元模拟及拓扑优化

谭昆林; 曹静; 黄宏才; 魏培君; 张从发

复合材料星载天线反射面热变形有限元模拟及拓扑优化

1.
北京科技大学数理学院, 北京 100083
2.
北京空间飞行器总体设计部, 北京 100086

详细信息

通讯作者:
魏培君，教授，博导，研究方向为弹性波传播、声子晶体及超材料　E-mail: weipj@ustb.edu.cn

中图分类号: TB332
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- 被引次数: 0
出版历程
- 收稿日期: 2023-12-26
- 修回日期: 2024-02-21
- 录用日期: 2024-03-11
- 网络出版日期: 2024-04-16
- 刊出日期: 2024-11-15

Finite element simulation and topology optimization of thermal deformation of reflector of composite spaceborne antenna

1.
School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China
2.
Beijing Space Vehicle General Design Department, Beijing 100086, China

摘要

摘要: 为控制星载天线反射面的热变形，本文以一口径为1200 mm的正方形格栅反射面为研究对象，首先，确定了预测反射面热变形的有限元建模策略，计算了反射面在三种不同温度荷载下的型面热变形均方根(RMS)。在此基础上提供了一种新的有限元建模策略——层合板等效方式，求出层合板的等效弹性模量和等效热膨胀系数。其次，以正方形格栅反射面为原型对格栅芯子进行拓扑优化，并与其他三种几何形状的芯子进行了比较，发现正方形格栅反射面为最优的结构形式。然后，对正方形格栅反射面做参数优化，找出了最优的正方形格栅单胞尺寸、蒙皮铺层方式、正方形格栅铺层方式和胶层厚度。最后，对正方形格栅反射面做热稳定性指标置信度分析，得到RMS的概率密度函数分布图和各个设计参数的贡献率Pareto图，找出了影响反射面型面热变形的关键因素。
- 反射面 /
- RMS /
- 层合板等效 /
- 拓扑优化 /
- 参数优化 /
- 置信度分析
Abstract: In order to control the thermal deformation of satellite-borne antenna reflector, a square grille reflector with a diameter of 1200 mm was taken as the research object. Firstly, the finite element modeling strategy for predicting the thermal deformation of the reflector was determined, and the thermal deformation RMS of the reflector under three different temperature loads was calculated. On this basis, a new finite element modeling strategy, the equivalent method of laminates, was provided to obtain the equivalent elastic modulus and equivalent thermal expansion coefficient of laminates. Secondly, the grid core was optimized topologically using the square grid reflector as prototype, and compared with the other three geometries, it is found that the square grid reflector is the best structure. Then, the parameters of the square grating reflector were optimized, and the optimal square grating cell size, skin laying mode, square grating laying mode and adhesive layer thickness were found out. Finally, the probability density function distribution of RMS and the contribution rate Pareto diagram of each design parameter were obtained by the confidence analysis of the thermal stability index of the square grating reflector, and the key factors affecting the thermal deformation of the reflector profile were found out.
- reflecting surface /
- RMS /
- laminated board equivalent /
- topology optimization /
- parameter optimization /
- confidence analysis

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图 1 反射面结构：(a)整体结构；(b)瓜瓣单元结构

Figure 1. Reflector structure: (a) Overall structure; (b) Melon petal unit structure

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图 2 反射面瓜瓣单元的有限元模型

Figure 2. Finite element model of reflecting surface melon petal element

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图 3 反射面热变形型面误差计算示意图

Figure 3. Schematic diagram of error calculation of thermal deformation profile of reflector

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图 4 反射面在三种温度荷载下的z向位移：(a)均匀温升80℃；(b)面内温度梯度0~100℃；(c)面外温度梯度0~2℃

Figure 4. z displacement of the reflector under three temperature loads: (a) Uniform temperature rise of 80℃; (b) In-plane temperature gradient 0-100℃; (c) Out-of-plane temperature gradient 0-2℃

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图 5 整体坐标系与局部坐标系的关系

Figure 5. Relation between global coordinate system and local coordinate system

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图 6 四种拓扑结构：(a)正方形格栅单胞；(b)蜂窝单胞；(c)三角形格栅单胞；(d)圆管单胞

Figure 6. Four topological structures: (a) Square grid cell; (b) Honeycomb monocytes; (c) Triangular grid cell; (d) Cylindrids

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图 7 $ {a}_{1} $与RMS和等效密度

Figure 7. $ {a}_{1} $ to RMS and equivalent density

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图 8 蒙特卡洛模拟：(a)RMS的概率密度函数分布图；(b)各个设计参数的贡献率Pareto图

Figure 8. Monte Carlo simulation: (a) RMS probability density function distribution; (b) Pareto diagram of contribution rate of each design parameter

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表 1 M55 J型CFRP单层板性能参数

Table 1. Performance parameters of M55 J CFRP single-layer plate

Elasticity modulus /GPa		Poisson's ratio	Shear elasticity /GPa			CTE/(×10⁻⁶·⁻¹)
$ {E}_{1} $	$ {E}_{2} $	$ \nu $	$ {G}_{12} $	$ {G}_{13} $	$ {G}_{23} $	$ {\alpha }_{1} $	$ {\alpha }_{2} $	$ {\alpha }_{3} $
290	10	0.27	4.5	4.5	2.1	−1	35	35
Notes: CTE—coefficient of thermal expansion

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表 2 胶的性能参数

Table 2. Performance parameters of adhesive

Elasticity modulus /GPa	Poisson's ratio	CTE/(×10⁻⁶·⁻¹)
2.5	0.3	50

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表 3 三种温度荷载下的RMS

Table 3. RMS under three temperature loads

Temperature load	Uniform temperature rise of 80℃	0-100℃ inside the surface	0-2℃ outside the surface
RMS/$ \mathrm{\mu }\mathrm{m} $	90.59	116.3	0.92

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表 4 蒙皮和格栅的等效材料参数

Table 4. Equivalent material parameters of skin and grille

Structure	Elasticity modulus /GPa		Poisson's ratio	shear elasticity /GPa			CTE/(×10⁻⁶·⁻¹)
Structure	$ {E}_{x} $	$ {E}_{y} $	$ {\nu }_{xy} $	$ {G}_{xy} $	$ {G}_{x{\textit{z}}} $	$ {G}_{y{\textit{z}}} $	$ {\alpha }_{x} $	$ {\alpha }_{y} $	$ {\alpha }_{{\textit{z}}} $
Stressed skin [0,90,45,−45]	48.77	48.77	0.762	13.8	3.3	3.3	−2.9	−2.9	222.6
Grid[0,90,45,−45,0,90,45,−45,0,90]	59.81	59.81	0.708	10.17	3.3	3.3	5.56	38.98	2400

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表 5 单层板铺层方式和层合板等效方式下的RMS

Table 5. RMS of single layer and laminated board equivalent mode

Structure	Uniform temperature rise of 80℃RMS/$ \mathrm{\mu }\mathrm{m} $	0-100℃ inside the surface RMS/$ \mathrm{\mu }\mathrm{m} $	0-2℃ outside the surface RMS/$ \mathrm{\mu }\mathrm{m} $
Single ply	90.59	116.3	0.92
Laminate equivalent	82.34	125.81	0.73

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表 6 四种拓扑结构下的RMS

Table 6. RMS in four topologies

Load structural style	Temperature rise 80℃ $ \mathrm{R}\mathrm{M}\mathrm{S}/\mathrm{\mu }\mathrm{m} $	0-100℃ inside the surface $ \mathrm{R}\mathrm{M}\mathrm{S}/\mathrm{\mu }\mathrm{m} $	0-2℃ outside the surface $ \mathrm{R}\mathrm{M}\mathrm{S}/\mathrm{\mu }\mathrm{m} $
Square grating	90.59	116.3	0.92
Honeycomb	108	148.5	1.18
Triangular grating	103.5	128.3	1.04
circular tube	116.8	176.7	1.32

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表 7 $ {a}_{1} $与RMS和等效密度的关系

Table 7. Relation of $ {a}_{1} $ to RMS and equivalent density

$ {a}_{1}/\mathrm{m}\mathrm{m} $	Temperature rise 80℃ $ \mathrm{R}\mathrm{M}\mathrm{S}/\mathrm{\mu }\mathrm{m} $	0-100℃ inside the surface $ \mathrm{R}\mathrm{M}\mathrm{S}/\mathrm{\mu }\mathrm{m} $	0-2℃ outside the surface $ \mathrm{R}\mathrm{M}\mathrm{S}/\mathrm{\mu }\mathrm{m} $	Equivalent density$ \left(\mathrm{k}\mathrm{g}/{\mathrm{m}}^{3}\right) $
20	66.7	92.2	0.4	1700$ \times $0.19=323
25	74.6	100.4	0.63	1700$ \times $0.15=255
30	90.59	116.3	0.92	1700$ \times $0.13=221
40	103.1	125.9	1.13	1700$ \times $0.10=170
Notes: $ {a}_{1} $-Square grille cell outer length

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表 8 正交实验因素水平

Table 8. Orthogonal experimental factor levels

Factor	Skin laying method	Grid laying method
Level 1	$ \left[{\left(0，90\right)}_{5}\right] $	$ \left[{\left(0，90\right)}_{5}\right] $
Level 2	$ {\left(0，90，0，90，0\right)}_{s} $	$ {\left(0，90，0，90，0\right)}_{s} $
Level 3	$ \left[{\left(\pm 45\right)}_{5}\right] $	$ \left[{\left(\pm 45\right)}_{5}\right] $
Level 4	$ \left[{\left(45,-\mathrm{45,45},-\mathrm{45,45}\right)}_{s}\right] $	$ \left[{\left(45,-\mathrm{45,45},-\mathrm{45,45}\right)}_{s}\right] $
Level 5	$ \left[\left(\begin{array}{c}\mathrm{0,45,90},-\mathrm{45,0},\\ \mathrm{45,90},-\mathrm{45,0},45\end{array}\right)\right] $	$ \left[\left(\begin{array}{c}\mathrm{0,45,90},-\mathrm{45,0},\\ \mathrm{45,90},-\mathrm{45,0},45\end{array}\right)\right] $

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表 9 正交实验结果

Table 9. Orthogonal experiment results

Serial number	Skin laying method	Grid laying method	RMS/$ \mathrm\;{\mu }\mathrm{m} $
1	$ \left[{\left(0，90\right)}_{5}\right] $	$ \left[{\left(0，90\right)}_{5}\right] $	36.4
2	$ \left[{\left(0，90\right)}_{5}\right] $	$ {\left(0，90，0，90，0\right)}_{s} $	30.8
3	$ \left[{\left(0，90\right)}_{5}\right] $	$ \left[{\left(\pm 45\right)}_{5}\right] $	68.6
4	$ \left[{\left(0，90\right)}_{5}\right] $	$ \left[{\left(45,-\mathrm{45,45},-\mathrm{45,45}\right)}_{s}\right] $	68.8
5	$ \left[{\left(0，90\right)}_{5}\right] $	$ \left[\left(\begin{array}{c}\mathrm{0,45,90},-\mathrm{45,0},\\ \mathrm{45,90},-\mathrm{45,0},45\end{array}\right)\right] $	27.4
6	$ {\left(0，90，0，90，0\right)}_{s} $	$ \left[{\left(0，90\right)}_{5}\right] $	40
7	$ {\left(0，90，0，90，0\right)}_{s} $	$ {\left(0，90，0，90，0\right)}_{s} $	34.1
8	$ {\left(0，90，0，90，0\right)}_{s} $	$ \left[{\left(\pm 45\right)}_{5}\right] $	71.5
9	$ {\left(0，90，0，90，0\right)}_{s} $	$ \left[{\left(45,-\mathrm{45,45},-\mathrm{45,45}\right)}_{s}\right] $	71.6
10	$ {\left(0，90，0，90，0\right)}_{s} $	$ \left[\left(\begin{array}{c}\mathrm{0,45,90},-\mathrm{45,0},\\ \mathrm{45,90},-\mathrm{45,0},45\end{array}\right)\right] $	29.9
11	$ \left[{\left(\pm 45\right)}_{5}\right] $	$ \left[{\left(0，90\right)}_{5}\right] $	40.4
12	$ \left[{\left(\pm 45\right)}_{5}\right] $	$ {\left(0，90，0，90，0\right)}_{s} $	36.8
13	$ \left[{\left(\pm 45\right)}_{5}\right] $	$ \left[{\left(\pm 45\right)}_{5}\right] $	74.4
14	$ \left[{\left(\pm 45\right)}_{5}\right] $	$ \left[{\left(45,-\mathrm{45,45},-\mathrm{45,45}\right)}_{s}\right] $	93.9
15	$ \left[{\left(\pm 45\right)}_{5}\right] $	$ \left[\left(\begin{array}{c}\mathrm{0,45,90},-\mathrm{45,0},\\ \mathrm{45,90},-\mathrm{45,0},45\end{array}\right)\right] $	36.9
16	$ \left[{\left(45,-\mathrm{45,45},-\mathrm{45,45}\right)}_{s}\right] $	$ \left[{\left(0，90\right)}_{5}\right] $	39.6
17	$ \left[{\left(45,-\mathrm{45,45},-\mathrm{45,45}\right)}_{s}\right] $	$ {\left(0，90，0，90，0\right)}_{s} $	36.1
18	$ \left[{\left(45,-\mathrm{45,45},-\mathrm{45,45}\right)}_{s}\right] $	$ \left[{\left(\pm 45\right)}_{5}\right] $	73.6
19	$ \left[{\left(45,-\mathrm{45,45},-\mathrm{45,45}\right)}_{s}\right] $	$ \left[{\left(45,-\mathrm{45,45},-\mathrm{45,45}\right)}_{s}\right] $	73.1
20	$ \left[{\left(45,-\mathrm{45,45},-\mathrm{45,45}\right)}_{s}\right] $	$ \left[\left(\begin{array}{c}\mathrm{0,45,90},-\mathrm{45,0},\\ \mathrm{45,90},-\mathrm{45,0},45\end{array}\right)\right] $	36.2
21	$ \left[\left(\begin{array}{c}\mathrm{0,45,90},-\mathrm{45,0},\\ \mathrm{45,90},-\mathrm{45,0},45\end{array}\right)\right] $	$ \left[{\left(0，90\right)}_{5}\right] $	38.9
22	$ \left[\left(\begin{array}{c}\mathrm{0,45,90},-\mathrm{45,0},\\ \mathrm{45,90},-\mathrm{45,0},45\end{array}\right)\right] $	$ {\left(0，90，0，90，0\right)}_{s} $	33.4
23	$ \left[\left(\begin{array}{c}\mathrm{0,45,90},-\mathrm{45,0},\\ \mathrm{45,90},-\mathrm{45,0},45\end{array}\right)\right] $	$ \left[{\left(\pm 45\right)}_{5}\right] $	69.7
24	$ \left[\left(\begin{array}{c}\mathrm{0,45,90},-\mathrm{45,0},\\ \mathrm{45,90},-\mathrm{45,0},45\end{array}\right)\right] $	$ \left[{\left(45,-\mathrm{45,45},-\mathrm{45,45}\right)}_{s}\right] $	69.8
25	$ \left[\left(\begin{array}{c}\mathrm{0,45,90},-\mathrm{45,0},\\ \mathrm{45,90},-\mathrm{45,0},45\end{array}\right)\right] $	$ \left[\left(\begin{array}{c}\mathrm{0,45,90},-\mathrm{45,0},\\ \mathrm{45,90},-\mathrm{45,0},45\end{array}\right)\right] $	29.3
$ {K}_{1} $	46．4	39.06	-
$ {K}_{2} $	49.42	34.24	-
$ {K}_{3} $	56.48	71.56	-
$ {K}_{4} $	51.72	75.44	-
$ {K}_{5} $	48.22	31.88	-
R	10.08	43.56	-
Notes:$ {K}_{i}(i=\mathrm{1,2},\mathrm{3,4},5) $ represents the mean of the RMS when the factors are at each level, and R represents the range of the factors.

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表 10 胶层厚度与RMS的关系

Table 10. Relation between adhesive layer thickness and RMS

Bondline thickness /mm	0.1	0.2	0.3	0.4	0.5
Temperature rise 80℃RMS/$ \mathrm{\mu }\mathrm{m} $	27.4	28.2	29.4	30.4	31.4

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表 11 M55 J平纹布/氰酸酯和T300碳纤维/氰酸酯复合材料单层板性能参数

Table 11. Performance parameters of M55 J plain cloth/cyanate and T300 carbon fiber/cyanate composite monolayers

Material	Elasticity modulus /GPa		Poisson's ratio	Shear elasticity /GPa			CTE/(×10⁻⁶·⁻¹)
Material	$ {E}_{1} $	$ {E}_{2} $	$ \upsilon $	$ {G}_{12} $	$ {G}_{13} $	$ {G}_{23} $	$ {\alpha }_{1} $	$ {\alpha }_{2} $	$ {\alpha }_{3} $
M55 J	113.6	113.6	0.11	8	4	4	0.14	0.14	30
T300	60	60	0.13	8.41	4	4	0.14	0.14	30

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表 12 不同复合材料下的RMS

Table 12. RMS under different composite materials

Material	M55 J type carbon fiber	M55 J plain cloth/cyanate ester	T300 Carbon fiber/cyanate
RMS/$ \mathrm\;{\mu }\mathrm{m} $	27.4	0.2	0.8

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参考文献(27)

[1]	陈传志, 董家宇, 陈金宝, 等. 空间大型星载抛物面天线研究进展[J]. 航空学报, 2021, 42: 133-153. Chen Chuanzhi, Dong Jiayu, Chen Jinbao, et al. Research progress of large space-borne parabolic antennas[J]. Acta Aeronautica et Astronautica Sinica, 2021, 42: 133-153 (in Chinese).
[2]	张尉博, 张琦, 徐宏涛, 等. 高稳定碳纤维格栅夹层反射器结构设计及型面热变形优化[J]. 复合材料科学与工程, 2020, 5: 40-46. Zhang Yubo, Zhang Qi, Xu Hongtao, et al. Structural Design and Thermal Deformation optimization of high-stability carbon fiber sandwich reflector[J]. Composite Materials Science and Engineering, 2020, 5: 40-46(in Chinese).
[3]	Xu L, e Y, Wang Y, et al. Ultra-thin carbon fiber mirrors: nickel plated, optical fabrication and thermal deformation test[J]. Optik, 2019, 176: 85-92. doi: 10.1016/j.ijleo.2018.09.086
[4]	Kendrew S, Doel P, Brooks D, et al. Carbon fibre composite deformable mirrors: developments at UCL[J]. SPIE, 2006, 6272: 905-915.
[5]	Utsunomiya S, Kamiya T, Shimizu R. Development of CFRP mirrors for low-temperature application of satellite telescopes[J]. SPIE, 2012, 8450: 916-922.
[6]	Steeves J, Jackson K, Pellegrino S, et al. Multilayer active shell mirrors for space telescopes[J]. SPIE, 2016, 9912: 554-568.
[7]	Wei J, Zhang C, Qi X, et al. Ultra-high-precision reflectors-design concepts, structural optimization and zero-expansion composites[J]. International Journal of Computational Materials Science and Engineering, 2018, 7: 423-430.
[8]	周星驰, 周徐斌, 杜冬, 等. 碳纤维复合材料天线反射面低变形优化设计[J]. 航天器工程, 2018, 27: 83-88. Zhou Xingchi, Zhou Xubin, Du Dong, et al. Low Deformation optimization design of carbon fiber composite antenna reflector[J]. Spacecraft Engineering, 2018, 27: 83-88(in Chinese).
[9]	张弘弛, 梁旭豪, 钟业盛, 等. 复合材料格栅反射器结构热变形及精度分析[J]. 哈尔滨工业大学学报, 2019, 51: 35-39. Zhang Hongchi, Liang Xuhao, Zhong Yisheng, et al. Thermal Deformation and Precision Analysis of Composite grating reflector[J]. Journal of Harbin Institute of Technology, 2019, 51: 35-39(in Chinese).
[10]	Utsunomiya S, Kamiya T, Shimizu R. CFRP composite mirrors for space telescopes and their micro-dimensional stability[J]. SPIE, 2010, 7739: 962-968.
[11]	李岩咏, 韦娟芳, 江文剑. 星载高精度反射器工程模型在轨热变形分析及结构优化[J]. 应用数学和力学, 2018, 39: 657-664. Li Yanyong, Wei Juanfang, Jiang Wenjian. In-orbit Thermal Deformation Analysis and Structural Optimization of Spaceborne high-precision reflector Engineering Model[J]. Applied Mathematics and Mechanics, 2018, 39: 657-664(in Chinese).
[12]	王树宏, 庄纯, 史耀辉, 等. 太阳翼蜂窝夹层结构上蒙皮热变形的影响因素[J]. 理化检验-物理分册, 2022, 58: 1-5. Wang Shuhong, Zhuang Chun, Shi Yaohui, et al. Influence factors of thermal deformation on solar wing honeycomb sandwich structure[J]. Physical and Chemical Examination - Physics Branch, 2022, 58: 1-5(in Chinese).
[13]	邢思远, 刘洪新, 彭志刚, 等. 高精度复合材料天线反射器结构与热变形仿真优化分析[J]. 玻璃钢/复合材料, 2018, 8: 66-73. Xing Siyuan, Liu Hongxin, Peng Zhigang, et al. Simulation and Optimization Analysis of Structure and Thermal Deformation of High-precision Composite antenna reflector[J]. Glass Fiber Reinforced Plastic/Composite, 2018, 8: 66-73(in Chinese).
[14]	姚科, 杨军, 韦娟芳. 星载固面反射天线热变形分析[J]. 低温建筑技术, 2016, 38: 67-69 Yao Ke, Yang Jun, Wei Juanfang. Thermal deformation analysis of satellite-based Solid Surface Reflector antenna[J]. Cryogenic Building Technology, 2016, 38: 67-69(in Chinese).
[15]	王从思, 段宝岩. 反射面天线机电场耦合关系式及其应用[J]电子学报, 2011, 39: 1431-1435 Wang Congsi, Duan Baoyan. Electromechanical Field Coupling Relation of Reflector antenna and its Application[J]. Acta Electronica Sinica, 2011, 39: 1431-1435(in Chinese).
[16]	王猛. 面向机电耦合的微波天线随机与系统误差的分析与综合[D]. 西安电子科技大学, 2016. Wang Meng. Analysis and synthesis of random and systematic errors of microwave antennas for electromechanical coupling [D]. Xidian University, 2016(in Chinese).
[17]	孙华东, 林玉祥. 复合材料迭层板等效模量的计算分析[J]. 太原机械学院学报, 1993, 2: 113-119. Sun Huadong, Lin Yuxiang. Calculation and Analysis of Equivalent Modulus of Composite Laminates[J]. Journal of Taiyuan Institute of Machinery, 1993, 2: 113-119(in Chinese).
[18]	朱立平, 姜鹏飞, 武广哲, 等. 2.5D机织复合材料等效热膨胀系数参数化研究[J]. 玻璃纤维, 2021, 6: 8-10. Zhu Liping, Jiang Pengfei, Wu Guangzhe, et al. Parameterization of equivalent thermal expansion coefficient of 2.5D woven composites[J]. Fiberglass, 2021, 6: 8-10(in Chinese).
[19]	吴欣歌, 何智海, 赵思宇, 等. 可调热膨胀系数的复合材料层合结构预测与设计[J]. 应用力学学报, 2023, 40: 636-642. Wu Xinge, He Zhihai, Zhao Siyu, et al. Prediction and design of composite lamination structures with adjustable thermal expansion coefficient[J]. Chinese Journal of Applied Mechanics, 2023, 40: 636-642(in Chinese).
[20]	沈观林, 胡更开, 刘彬. 复合材料力学(第2版)[M]. 北京: 清华大学出版社, 2013: 233-234. Shen Guanlin, HU Gengkai, Liu Bin. Mechanics of Composite Materials (2nd edition) [M]. Beijing: Tsinghua University Press, 2013; 233-234(in Chinese).
[21]	Boudjemai A, Amri R, Mankour A, et al. Modal analysis and testing of hexagonal honeycomb plates used for satellite structural design[J]. Materials & Design, 2012, 35: 266-275.
[22]	Stocchi A, Colabella L, Cisilino A, et al. Manufacturing and testing of a sandwich panel honeycomb core reinforced with natural-fiber fabrics[J]. Materials & Design, 2014, 55: 394-403.
[23]	Reznik S V, Prosuntsov P V, Azarov A V. Substantiation of the structural-layout scheme of the mirror-space-antenna reflector with a high shape stability and a low density per unit length[J]. Journal of engineering physics and thermophysics, 2015, 88: 699-705. doi: 10.1007/s10891-015-1239-x
[24]	吴楠, 郝旭峰, 史耀辉, 等. 高精度碳纤维增强树脂复合材料夹层天线面板热变形影响参数仿真与实验[J]. 复合材料学报, 2020, 37: 1619-1628. Wu Nan, Hao Xufeng, Shi Yaohui, et al. Simulation and experiment on thermal deformation parameters of high precision carbon fiber reinforced resin composite sandwich antenna panel[J]. Journal of Composite Materials, 2019, 37: 1619-1628(in Chinese).
[25]	陈志华, 关富玲. 星载抛物面天线热变形敏感性分析[J]. 工程设计学报, 2010, 17: 263-267. Chen Zhihua, Guan Fuling. Thermal deformation sensitivity analysis of spaceborne parabolic antenna[J]. Chinese Journal of Engineering Design, 2010, 17: 263-267(in Chinese).
[26]	周涛, 叶周军, 史耀辉, 等. 星载蜂窝夹层结构固面天线反射器的热变形[J]. 复合材料学报, 2018, 35: 2065-2073. Zhou Tao, Ye Zhoujun, Shi Yaohui, et al. Thermal deformation of solid-surface antenna reflector with honeycomb sandwich structure on satellite[J]. Chinese Journal of Composites, 2018, 35: 2065-2073(in Chinese).
[27]	王丽. 星载抛物面天线在轨热—结构耦合分析[D]. 哈尔滨工业大学, 2012. Wang Li. In-orbit Thermal and Structural Coupling Analysis of spaceborne parabolic antenna [D]. Harbin Institute of Technology, 2012(in Chinese).