| Space exploration has heightened the need for large space antenna reflectors. Large-scale space inflatable structure made by inflatable membrane structure which has advantages of exceptional packaging efficiency and low stowed volume is one trend in development for future large deployment structures. In order to develop large space high precision paraboloid inflatable membrane antenna reflectors, establishing the inverse process by using the shape after inflation to determine the shape before inflation is needed. For the demands of shape with high precision and uniformed stress distribution, multi-objective optimization methods of inflatable membrane structure are required to research, which can improve the precision by adjusting the inflation pressure and boundary force. Therefore, in this paper analysis and optimization methods of shape and stress for high precision membrane reflector are investigated.For the sake of describing nonlinear couple relationship of shape and stress distribution of inflatable membrane after inflation well and truly, against the shape description method of membrane structure analysis model of inflatable membrane reflector based on geometry of nonlinear field theories is established in this paper and shape description of membrane structures are studied. Based on body coordinate system description method, the deformed configuration is set to reference standard, strain described model made of deformation and local rotation is built, the strain and displacement relationship is gained more accurate than the classical theory.Toward paraboloid shape demand of inflatable membrane structure after inflation, the ideal shape model and the uniform stress distribution model are established. Based on nonlinear geometry field theories, mechanical balance equations of inflatable membrane reflector are built, analytical solution of stress and displacement are obtained, the shape and stress distribution of inflatable membrane reflector before and after inflation are achieved. Utilizing the uniform stress model, the shape with the most uniform stress meet the surface precision requirement is gained. Based on the ideal shape model, variable thickness method is used to improve the uniformity of stress distribution of reflector, and the best thickness variation is determined.Inflatable membrane reflector is usually non-developable surface, made by a number of plain membranes splicing and paste into the overall membrane surface. In order to obtain the stress-free geometry configuration, inverse iteration and weighted form finding method is introduced. Based on FEA method and the initial shape set to the geometry configuration of the ideal shape model, inverse iteration analysis by weighting the local shrinkage and adjusting the initial geometry configuration, finally the obtained initial geometry configuration could meet the surface precision requirement. The results show inverse iteration and weighted form finding method in this paper could eliminate the "W-profile" error effectively in analysis of determined the initial configuration.High precision digital photogrammetry is used to measure the surface precision of inflatable membrane reflector. Surface precision, diameters, and the angle between upper surface and lower surface of inflatable antenna reflector under different boundary force are gained. The results from experiment verify the veracity of the inverse iteration and weighted form finding method. By analysis the experiment results, the relationship between boundary force and inflation pressure are determined.Considering the influencing factors such as initial geometry configuration, inflation pressure and the boundary force, the shape and stress distribution multi-parameter and multi-objective optimization model of inflatable membrane reflector is established based on genetic algorithms. This model optimizes the two objectives both the surface precision and uniform stress distribution simultaneously. Considering these two optimization objectives have different priority level, a method of layered solution is introduced to solve this multi-objective optimization problem, This multi-objective model enable to meet the precision requirement with the most uniform stress distribution, which could provide reference for design inflatable membrane reflectors.In this paper, shape and stress distribution analysis methods and multi-objective optimization method of inflatable membrane reflector are established, which could improve the surface precision of membrane reflector and provide theoretical foundation and technical support. |
