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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

谭昆林, 曹静, 黄宏才, 等. 复合材料星载天线反射面热变形有限元模拟及拓扑优化[J]. 复合材料学报, 2024, 42(0): 1-11.
引用本文: 谭昆林, 曹静, 黄宏才, 等. 复合材料星载天线反射面热变形有限元模拟及拓扑优化[J]. 复合材料学报, 2024, 42(0): 1-11.
TAN Kunlin, CAO Jing, HUANG Hongcai, et al. Finite element simulation and topology optimization of thermal deformation of reflector of composite spaceborne antenna[J]. Acta Materiae Compositae Sinica.
Citation: TAN Kunlin, CAO Jing, HUANG Hongcai, et al. Finite element simulation and topology optimization of thermal deformation of reflector of composite spaceborne antenna[J]. Acta Materiae Compositae Sinica.

复合材料星载天线反射面热变形有限元模拟及拓扑优化

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

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

  • 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。

     

  • 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

    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

    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

    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℃

    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

    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

    图  7  $ {a}_{1} $与RMS和等效密度

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

    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

    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
    下载: 导出CSV

    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
    下载: 导出CSV

    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
    下载: 导出CSV

    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)
    $ {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
    下载: 导出CSV

    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
    下载: 导出CSV

    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
    下载: 导出CSV

    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
    下载: 导出CSV

    表  8  正交实验因素水平

    Table  8.   Orthogonal experimental factor levels

    FactorSkin laying methodGrid 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] $
    下载: 导出CSV

    表  9  正交实验结果

    Table  9.   Orthogonal experiment results

    Serial numberSkin laying methodGrid laying methodRMS/$ \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} $46.439.06-
    $ {K}_{2} $49.4234.24-
    $ {K}_{3} $56.4871.56-
    $ {K}_{4} $51.7275.44-
    $ {K}_{5} $48.2231.88-
    R10.0843.56-
    Notes:$ {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.
    下载: 导出CSV

    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
    下载: 导出CSV

    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)
    $ {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
    下载: 导出CSV

    表  12  不同复合材料下的RMS

    Table  12.   RMS under different composite materials

    MaterialM55 J type carbon fiberM55 J plain cloth/cyanate esterT300 Carbon fiber/cyanate
    RMS/$ \mathrm\;{\mu }\mathrm{m} $27.40.20.8
    下载: 导出CSV
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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

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