中文摘要：

介绍一种获得较精确的膜基反射镜挠度数值解的方法。通过非线性有限元分析，对三种有限元网格划分方法进行研究比较，建立符合实际情况的有限元模型，给出薄膜分析中施加预应力的方法，分析研究膜基反射镜的挠度特性。首先在简易边界条件下，验证有限元分析结果符合固定支撑圆板挠度弯曲问题的理论值；然后运用此方法分析复杂边界条件下膜基反射镜的表面位移情况，获得膜基反射镜面形特征数据。获得的挠度值相对误差小于0．04％，为深入研究膜基反射镜成型及面形控制做了准备。

英文摘要：

This paper introduces a more exact numeric method about solving bending problems in membrane mirror analysis. Through the analysis of the non-linear finite element, we compare three kinds of finite element mesh methods, create finite element model conformed to the actual membrane, list the steps of solving the initial stress problem in membrane analysis and study the bending characters of membrane mirrors. Firstly under the facility boundary conditions, we validate that the finite element analysis result is matching the academic value of large bending disk with fixed support; and then we use this method to analyse the surface displacement of membrane mirrors with complex boundary conditions, and get the characteristic data of its surface. The relative error of the obtained value can be less than 0. 04%, and it is benefit for further study on deformation and surface controlling of membrane mirrors.