考虑热力耦合作用的薄膜褶皱分析稳定化算法研究

Flexible membranes have been used as some key components of spacecraft like solar panels and inflatable antenna reflectors which work in thermo-mechanical coupling environment. Wrinkling is a typically nonlinear deformation mode of thin membrane structures. Stability of numerical algorithms is very important to achieve numerical simulation of wrinkle deformation of membranes efficiently. Based on parametric variational principle and finite element method, the project will study a stabilized computational method for refined analysis of wrinkled membranes with thermo-mechanical coupling effects. Firstly, a thermo-mechanical coupling model and parametric variational principle of anisotropic bi-modulus materials will be proposed and then a stabilized quadratic programming algorithm will be developed. Subsequently, a simplified finite element model, which can capture wrinkle details, such as the number, wavelength and magnitude of wrinkles, will be proposed by combining a modified bi-modulus material model and stability theory of thin shells. With the wrinkling model embedded into developed quadratic programming algorithm, numerical simulation on wrinkled membranes with thermo-mechanical coupling effects can be achieved efficiently. The states of elements including tension, wrinkle and slack will be determined by solving a complementarity problem and thus stability of algorithm can be improved greatly. A typical experiment of wrinkled membranes will be carried out to validate the developed wrinkling model and algorithm. Finally, mechanisms of wrinkle formation and development will be studied by using the developed stabilized algorithm, which can provide scientific basis for design of scheme to restrain wrinkles.

柔性薄膜已经被用作太阳能电池帆板和充气反射天线等关键航天器部件，并且需要在热力耦合环境下服役。褶皱是薄膜结构的一种典型的非线性变形模式，数值算法的稳定性对于实现薄膜褶皱变形的高效数值模拟至关重要。本项目将基于参变量变分原理和有限单元法，开展热力耦合作用下薄膜褶皱变形精细分析的稳定化计算方法研究。首先，建立各向异性双模量材料的热力耦合模型及参变量变分原理，发展稳定的二次规划算法。其次，结合修正的双模量材料模型和薄壳稳定性理论，建立能够获取褶皱数目、幅值和波长的简化有限元模型。将该模型嵌入已发展的二次规划算法中，通过求解互补问题来确定单元的张紧、褶皱或松弛状态，从而改善算法稳定性，实现热力耦合作用下薄膜褶皱变形的高效数值模拟。进行薄膜褶皱典型实验，以验证模型与算法的正确性。最后，利用所发展的稳定化算法研究褶皱形成和发展的机理，为褶皱抑制方案的设计提供科学依据。

柔性薄膜已经被用作太阳能电池帆板和充气反射天线等关键航天器部件，并且需要在热力耦合环境下服役。褶皱是薄膜结构的一种典型的非线性变形模式，数值算法的稳定性对于实现薄膜褶皱变形的高效数值模拟至关重要。课题组首先测量了不同温度条件下薄膜材料的杨氏模量。进行了薄膜褶皱变形的三维散斑实验，测量了方形薄膜在对角拉伸条件下的全场三维变形形貌和应变场，定量地研究了褶皱幅值与波长随拉力、温度变化的变化规律。研究表明，在相同机械载荷作用下，温度越高，褶皱幅值越大。基于参变量变分原理，建立了三维双模量材料的最小势能表达式，通过变分计算和有限元离散，得了问题的有限元平衡方程，将原问题转化为标准的互补问题，很好地提高了该类问题非线性分析的算法收敛性和稳定性。该材料模型和算法被成功地应用到薄膜褶皱变形分析。利用ABAQUS软件，建立了多种形状的薄壳有限元模型，对薄壳进行了后屈曲分析，得到了褶皱变形形貌。将实验结果、ABAQUS模拟结果、程序计算结果三者进行了定量比较。室温条件下，三种结果在褶皱区域、方向、应力水平等指标上吻合良好。高温条件下薄膜褶皱变形的数值模拟并不能很好地重现实验所观测到的结果，有待进一步研究改进。对于具有大规模计算自由度的系统，算法的计算效率有待提高。

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