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Based on the Karman’s equation for circular thin plate and Qian’s theory of membrane, the membrane mirror forming theory model is established. The effect of the high order disturbance for the shape of the membrane mirror is reduced by the way of variable thickness, so that the shape of the membrane is parabolic. The finite element method is used to verify the theory of the membrane mirror forming model. But the analysis results are not easy to convergence due to the flexibility characteristics of the membrane. So the reasonable solution parameters are necessary to ensure the correction of the finite element analysis result. The results show that the deviation between the finite element analysis and the theoretical results is small. The uniform thickness deviation is 0.73%, and the variable thickness deviation is 1.30%, thus the validity of the theoretical model is guaranteed. Then the membrane mirror design and optimization method is established on the basis of the theoretical model. Compare the theoretical surface and the optical design surface, and set the minimum root mean square error between the theoretical and the optical design surface as the optimization goal. The original shape and the surface shape control parameters of the membrane are optimized by using genetic algorithm. Finally, get the optimization model which can be used to optimize membrane mirror with any diameter. The genetic algorithm was used to optimize the thickness, boundary condition and the uniform loads. The result of membrane mirror accuracy is λ/4(λ=10um), which indicates that this membrane mirror can be applied in the infrared wavelength range for imaging. The main optimizing parameters are the variable thickness of the membrane, the boundary conditions and the surface loads. Finally, the optimization result of the membrane is the RMS<λ/4(λ=10μm), which indicates that the membrane can be used to long-wave infrared optical system. Based on the theory of mechanics of materials, this paper establishes a theoretical model and analyzes the relationship between the inflatable membrane mirror and the boundary conditions as well as the gas load. And the optimization design method is carried out for space-based optical applications. The model and method established in this paper is of great significance for the design and application of large optical payload based on the membrane mirror.
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