基于等几何分析的膜结构找形与褶皱分析研究

Membrane structures are widely used in building industry, aerospace industry and other fields, large complicated membrane structure and high accuracy aerospace membrane structure put forward higher requirements on the membrane structure design and manufacture, so the refinement and in-depth study on the membrane structure is very urgent. Currently, there are still many deficiencies in research work about membrane structure, such as the computational model has low accuracy geometry, calculated approximate membrane surface only meet the C0 continuous, stress calculation is not accurate. These deficiencies lead to mesh distortion and iteration non-convergence problems when membrane structure wrinkling behavior is simulated with strong geometrical nonlinearity. In this research project, we firstly adopt a new numerical simulation method - Isogeometric Analysis, study on mechanical behavior of membrane structure, this new method eliminates geometric discretization error from the source, and makes the analysis and design of membrane structure using the same exact geometric model. Based on this method, we study on form-finding of common tensioned cable-membrane structure and common inflatable membrane structure in engineering, the computational efficiency and accuracy of this method are investigated, the effect on initial equilibrium shape-state with different boundary conditions and pre-tension size is studied. We combine nonlinear buckling theory of thin shell structure, construct high-order continuous element, carry out accurate simulation of wrinkling process of membrane structure, study on wrinkling formation and expansion mechanism of membrane structure, the influence on thin membrane wrinkling is investigated with initial defects, prestresses, different boundary conditions and loading types and other factors. We combine with the experimental test to verify the computational model and analysis results, this research project provides the theoretical basis and guidance for the design and engineering application of membrane structure.

膜结构在建筑、航天等领域应用日益广泛，大型复杂结构和高精度空间结构对膜结构设计制造提出了更高的要求，因此对膜结构的精细化深入研究势在必行。针对当前研究中存在的计算模型几何精确度低，计算所得近似膜曲面仅满足C0连续性，应力计算不准确，模拟褶皱强几何非线性时存在网格畸变、迭代计算不收敛等问题，本项目引入一种新的数值计算方法—等几何分析方法，从源头消除几何离散误差，并使分析和设计采用同一精确几何模型。基于该方法，对工程中常见的张拉索膜结构和充气膜结构进行找形分析，考察该方法的计算精度和效率，研究不同边界条件类型、预张力大小等因素对初始平衡形态的影响；结合薄壳非线性屈曲理论，构造高阶连续协调单元，对薄膜褶皱过程进行精细化数值模拟，研究膜结构褶皱形成和扩展机理，考察初始缺陷、预应力、不同边界条件及荷载形式等因素对薄膜褶皱的影响，结合试验测试验证计算模型和分析结果，为膜结构工程设计提供理论依据和指导。

当前膜结构力学行为数值研究方法存在的主要问题是：对于只有膜张力作用的膜结构光滑空间曲面，采用有限元网格划分为若干个单元来近似表示，而且当前多采用平面常应变三角形单元，因此对复杂高级曲面无法给出精确的网格离散，根据有限元分析得到的膜曲面近似解几何精确度较低，膜面单元之间仅满足C0连续性，近似曲面不具有C1或更高阶连续性，导致进行强几何非线性计算时，容易出现网格极度扭曲、单元刚度矩阵奇异、迭代计算不易收敛等问题，同时后续应力计算中得到的应力不连续且精度低。. 本项目基于一种新的数值计算方法—等几何分析方法，提出了适用于膜结构三维复杂模型的等几何分析建模方法，开发了适用于膜结构力学行为分析的高精度、高阶连续协调膜单元和薄壳单元，主要成果如下：.（1）解决了传统采用有限元方法研究中计算模型几何精确度低、膜曲面近似解不光滑、模拟褶皱强几何非线性时网格畸变、迭代计算不收敛等问题。.（2）建立了统一分析与设计过程、几何模型精确、计算精度和效率高的膜结构等几何分析找形方法。.（3）改进了膜结构褶皱非线性屈曲数值分析中的刚度奇异性及算法稳定性问题，建立了精确、有效的膜结构褶皱非线性屈曲过程等几何分析数值模拟方法，探索揭示膜结构褶皱发生及拓展演化规律，对影响膜结构褶皱屈曲行为的主要因素进行了评估。. 等几何分析将结构设计与分析采用统一的精确几何模型描述，使产品的设计、分析和优化过程趋向集成和统一，开启了一条紧密联系分析、设计和优化的新途径。在建筑和空间膜结构研究中，引入和应用等几何分析方法，对丰富和加强膜结构的研究方法，推动膜结构的精细化深入研究和前沿发展，具有重要的学术意义和工程应用价值。