中文摘要：

充气天线的性能主要取决于其形面几何精度。该文以几何非线性有限元法为基础，对不同焦径比和口径的天线反射面进行分析，探讨了三种具有代表性的边界扰动分布形式（均匀扰动、局部扰动及波形扰动）对天线反射面几何形状及应力的影响特性及原因，并分别获得了形面精度对这三种扰动的敏感度。研究从影响区域、影响值大小、影响敏感度及褶皱分布等几个方面对三种扰动形式进行了定性和定量的比较，得到如下主要结论：均匀扰动及波形扰动对整个曲面形状均有影响，在边界影响区曲面会同时产生平移和曲率变化，中间区域则主要发生曲面平移。局部扰动则只对局部区域有影响；三种扰动形式中，在扰动值相同的情况下，均匀扰动引起的误差值最大，但形面误差值对局部扰动和波形扰动更敏感；除施加向外均匀扰动时无褶皱以外，其他扰动形式均会导致在影响区域内出现褶皱。此外，研究还探讨了天线焦径比和口径的影响。最后，在上述研究成果的基础上给出了反射面形面精度被动控制和主动控制的合理建议。

英文摘要：

The performance of inflatable antennas critically depended on the shape accuracy of the membrane reflectors. Based on the non-linear finite element method, this paper explores the effects of boundary perturbations on the shape and stress of inflatable antenna reflectors of different focal-length-to-diameter ratios and diameters, as well as the reasons for these effects. Three kinds of distributions of boundary are focused on, including uniform distribution, local distribution and waveform distribution. The sensitivity analyses are respectively conducted. The effects of three kinds of boundary perturbations are compared in effect region, effect extent, sensitivity value and wrinkling. The study shows that： the effects of uniform and waveform perturbations act on the whole reflector. In the edge effect regions, the translation and curvature change of surface coexist. In the central regions, only the translation occurs. The effect of local distribution is limited to a local area. Among three kinds of perturbations, the uniform perturbation imposes the largest effect on the shape accuracy. However, the local distribution and waveform distribution have higher sensitivity values. All kinds of distributions except outward uniform distribution lead to wrinkling in effect areas. In addition, the influences of focal-length-to-diameter ratios and diameters are discussed. Based on the work presented, suggestions are given on proper strategy in passive and active control of the shape accuracy of inflatable antenna reflectors.