Influence of the Ply Angle Deviation on the Out-of-Plane Deformation of the Composite Space Mirror

  • Qingnian LiuEmail author
  • Yong Cai
  • Xiaojing Liu
  • Zhiyong Yang
  • Shuai Jiang
  • Shuang Leng


In order to discuss the influence of the ply angle deviation, six symmetric quasi-isotropic layup sequences imposed the fixed or random angle deviation were studied based on the numerical analysis, such as Monte Carlo stochastic finite element method and statistic analysis. The out-of-plane deformation was observed in spite of the symmetric quasi-isotropic sequences subjected to a temperature change due to the ply angle deviation in the space mirror. The surface peak-to-valley (PV), which is one kind of out-of-plane deformation, is proportional to the magnitude of the fixed angle deviation, and the mean of PVs is also proportional to the standard deviation of the random angle deviation. The out-of-plane deformation resulting from two-ply angle deviation indirectly satisfies the parallelogram law, and if each ply angle deviation is random independently, the probability density of that satisfies the Rayleigh distribution. In this paper, it is found that the most effective method to improve the surface accuracy of the space mirror is decreasing the standard deviation of the angle deviation, next to decreasing ply thickness and optimizing layup sequence, which is useful for application in the space mirror.


CFRP Mirror Out-of-plane deformation MCSFEM Rayleigh distribution 



The authors will thank Dr. Hu Liqin for her great help in the statistical analysis. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  • Qingnian Liu
    • 1
    Email author
  • Yong Cai
    • 1
  • Xiaojing Liu
    • 2
  • Zhiyong Yang
    • 1
  • Shuai Jiang
    • 1
  • Shuang Leng
    • 1
  1. 1.Aerospace Research Institute of Materials & Processing TechnologyBeijingChina
  2. 2.Institute of High Energy PhysicsChinese Academy of SciencesBeijingChina

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