【作者】 毛丽娜；

【导师】 谭惠丰；

【作者基本信息】 哈尔滨工业大学 ， 工程力学， 2010， 博士

【摘要】 空间探索对大型星载天线反射面等大型轻型空间结构的需求日益强烈。利用充气膜结构技术构建的大型空间充气展开结构具有重量轻折叠体积小的优势,是未来空间大型展开结构的发展趋势之一。为了利用充气膜结构研制星载大口径高精度抛物面型的天线反射面,需要建立利用充气变形后形状确定充气变形前形状的逆过程分析方法,需要建立多目标优化模型,通过调整充气压力和边界拉力得到同时满足高精度形状要求和应力分布均匀要求的充气膜结构反射面。因此本文开展了高精度膜结构反射面的形态分析和优化方法研究。为了更为准确地描述在充气压力作用下充气膜结构形状和应力分布状态的非线性耦合关系,针对膜结构的形状描述方法进行了研究,建立了基于非线性几何场理论的充气膜结构反射面分析模型。基于随体坐标系描述法,以变形后的构形为参考基准,构建了变形和局部转动项组成的反射面应变描述模型,得到了比经典理论更为精确的应变-位移几何关系。针对充气膜结构反射面充气后的高精度抛物面形状要求,建立了理想状态形状模型和均匀应力分布模型。在非线性几何场理论的基础上,建立了充气膜结构反射面的平衡关系,求解了理想状态反射面应力和位移的解析解,获得了充气膜结构反射面变形前和变形后的形状和应力分布状态。建立了均匀应力分布模型,在满足形面精度要求条件下,获得了应力相对均匀的几何构形。在理想状态形状模型的基础上,提出了通过改变膜厚度方式改进反射面应力均匀度的方法,确定了最佳的反射面厚度变化规律。充气膜结构反射面通常是不可展曲面,需要由多个平面膜片拼接并粘贴成整体曲面。为获得最佳的初始无应力膜片几何形状,提出了高精度反射面初始构形确定的逆迭代加权找形法。利用非线性有限元数值计算工具,以理想状态形状模型的几何构形为起始形状,通过局部加权回缩量的方法修改初始几何构形进行分析。提出了正弦函数形式的权函数模型,确定了权函数表达式中的参数,进行迭代过程中几何形状调整,通过逆迭代分析,最后得到满足反射面形面精度要求的初始几何形状。分析结果表明,本文的逆迭代加权找形法确定的初始无应力平面膜片几何形状能够有效的减小反射面的“W形”误差。利用高精度非接触数字摄影测量法进行了充气膜结构反射面形面精度测量试验,得到了不同边界绳张力条件下充气天线反射面的形面精度、口径以及边界处天篷和反射面的夹角。试验结果验证了逆迭代加权找形法分析的准确性。通过试验结果分析,确定了边界绳张力、充气压力等影响因素和形面精度的关系。综合考虑初始几何构形、充气压力和边界拉力等形面精度的影响因素,建立了基于遗传算法的充气膜结构反射面的多参数、多目标形态优化分析模型,对形面精度和应力分布均匀两项目标同时进行优化分析。考虑这两个优化目标的优先级不同,提出了采用分层解法来解决多目标优化问题,实现了在满足形面精度要求范围内,获得应力最均匀的最优解集,为充气膜结构反射面的设计提供参考。本文建立的充气膜结构反射面形态分析方法和多目标优化方法,将为提高膜结构反射面的形面精度和控制提供理论基础和技术支持。更多还原

【Abstract】 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.更多还原