中文摘要：

以轴对称圆薄板Karman方程以及钱伟长有关中心部分受载荷作用下的圆薄膜理论为基础，建立了薄膜上各点在外加载荷作用下的位移方程．对以聚对苯二甲酸乙二醇酯（PET）薄膜为基坯的膜基反射镜表面形变与初始边界条件和外加载荷-静电压强之间的关系、膜基反射镜面形与具有相同口径和，数的理想抛物面之间的偏差进行了理论计算和分析．所得结论对进一步开展膜基反射镜静电成形实验具有一定的指导意义．

英文摘要：

Based on Karman＇s equation for symmetrical circular membrane and Qian＇s theory of circular membrane under the action of uniformly distributed loads in its central portion, an equation of displacement on every point on a membrane is established. The relationship between the surface shape of membrane mirror on polyethylene terephthalate （PET） membrane substrate and the initial boundary condition,the relationship between the surface shape of membrane mirror and the pressure added on it, and the deviation between the surface shape of the membrane mirror and that of an parabolic mirror with the same diameter and F number are calculated and analyzed theoretically. The results obtained are significant for further experiments on membrane mirror by electrostatic configuration.