大型柔性薄膜天线局部褶皱变形的多场多尺度计算方法

Large flexible membrane antennae play an important role in signal detection and transmission in the task of deep space exploration, due to their light-weight, easily packable and deployable characteristics. Wrinkling in some local regions has a marked impact on the surface accuracy of membrane antennae. Strong nonlinearity and spatial multiscale characteristics of wrinkling bring great challenges to stability and efficiency of the numerical simulation methods. In this project, an efficient and stable multiscale finite element method (Multiscale FEM) will be proposed for numerical analysis of large membrane antennae under multiphysics conditions, in order to solve the problem of large-scale nonlinear iteration. A micro-macro two-scale finite element model will be proposed and the mechanical-electrical-thermal effect on wrinkling will be covered in the microscopic model. To improve the efficiency of solving, a multiscale base function that can describe the complicated macroscopic deformation is constructed to reduce the degree of computational freedoms. A two-scale iterative technique is proposed to solve the problem of numerical instability in downscale computation for wrinkled regions. The distribution and evolution of wrinkles can be studied by combining numerical simulation and experiment verification. The outcomes of the project will provide a new and powerful computational method for wrinkle-free design of large flexible membrane antennae structures and advance the study of multiphysics and multiscale FEM for heterogeneous plate/shell structures in finite deformation.

大型柔性薄膜天线由于其轻质和良好的收展性能在深空探测任务中扮演着信号探测及传输的重要角色。局部区域的褶皱变形会严重影响薄膜天线的形面精度，其强非线性与空间多尺度特征给数值模拟方法提出了稳定性和计算效率的挑战。本项目拟针对多物理场作用下的大型柔性薄膜天线局部褶皱问题发展一种高效、稳定的多尺度计算方法，解决该问题中大规模非线性迭代求解的难题。建立微观-宏观两尺度薄壳有限元模型，在微观模型中考虑力、电、热共同作用对褶皱变形的影响，构造出能够反映微观复杂变形的多尺度基函数，大幅降低计算自由度，提高求解效率。发展一种两尺度迭代求解技术，以克服褶皱区域降尺度计算的算法不稳定问题。结合数值模拟与验证性实验，研究多物理场作用下褶皱变形的分布及演化规律。研究成果将为大型柔性薄膜天线结构的褶皱抑制方案设计提供有力的计算力学新方法，并推动非均质板壳结构大变形分析的多场耦合多尺度有限元方法的深入研究。

大型柔性薄膜天线由于其轻质和良好的收展性能在深空探测任务中扮演着信号探测及传输的重要角色。局部区域的褶皱变形会严重影响薄膜天线的形面精度，其强非线性与空间多尺度特征给数值模拟方法提出了稳定性和计算效率的挑战。本项目首次将参变量变分原理拓展到充气薄膜结构大变形褶皱分析，所建立的参变量共旋有限元方法解决了商业软件的收敛困难。建立了一个高精度的褶皱幅值计算理论模型，揭示了薄膜拉致褶皱的新机理。该模型得到了实验验证。建立了薄膜结构分析的多尺度扩展有限元方法，大幅提高了大型薄膜天线褶皱分析的计算效率（约10~20倍）。提出了基于双模量材料本构关系的一致切线刚度方法，所发展的有限元方法具有二阶收敛性，提高了充气梁结构的数值模拟效率。该项目所形成的高效计算方法和有限元程序有望在航天薄膜结构分析与设计中得到工程应用。发表SCI论文7篇，EI论文２篇，获批软件著作权１项，培养毕业硕士生３名，培养博士生１名。

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