High Precision Simulation of Large Deployable Membrane Space Structure and Formulation of Similarity Rule

薄膜具有优良的可展开轻型结构性能，有望成为大型可展开空间结构。如果将膜应用于大型可展开空间结构，存在以下几个结构设计问题；(a)褶皱和塑性褶皱线非常小，膜的摩擦自冲击可能会对大膜的动力学产生不良影响；(b)膜展开后的动力稳定性得不到保证；(c)飞行模型（~ 100m）与地面可用的实验模型（~ 20m）之间的膜动力学没有适当的相似规则。本研究旨在提出定量获取这三个问题有价值知识的方法。研究结果总结如下：(1)相似规则的公式：建立了包含施加在膜上的扰动在轨道或地面实验中的影响的运动方程。利用该方程，导出了相似规则。实验结果表明了所建立的相似规则的有效性。(2)膜运动的参数化研究：研究者开发了一个高精度的有限元程序“NEDA”来模拟膜的展开。研究者利用商业软件“ABAQUS”和“NEDA”进行了仿真，评估了质量分布、折叠模式对部署和部署后稳定性的影响。(3)皱纹模型的验证：研究者提出了皱纹的数值模型，使我们能够有效地模拟膜。通过与壳单元模型的比较，验证了该模型的有效性。(4)折叠展开方法评价：针对折叠展开方法提出了综合评价方法。

Membrane has excellent property for deployable light structure, and has been expected as large deployable space structure. If membrane is applied to the large deployable space structure, there are several structural design problems as follows; (a) very small wrinkles and plastic fold lines, and the frictional self-impact of the membrane will be possibly give undesirable influence on the dynamics of the large membrane, (b) the dynamic stability of the membrane after the deployment is not guaranteed, (c) there is no appropriate similarity rule on the dynamics of membrane between the flight model (〜100m) and the experimental model that is available on the ground (〜20m). This research has aimed at proposing the method to get the valuable knowledge quantitatively about these three problems. The research results are summarized as follows;(1) Formulation of similarity rule : The equation of motion is formulated which includes the effect of the disturbances applied to the membrane on orbit or in the ground experiment. Using the equation, the similarity rule was derived. The validity of the formulated similarity rule was shown by the experimental results.(2) Parametric study of the membrane motion : The investigator had developed a highly precise FEM code "NEDA" to simulate the deployment of membranes. The investigator conducted the simulation by using the commercial software "ABAQUS" as well as "NEDA", and evaluated the influence of the mass-distribution, fold-pattern on the deployment and the stability after the deployment.(3) Verification of the wrinkle model: The investigator proposed the numerical model of the wrinkle that enables us the efficient simulation of the membrane. The validity of the proposed wrinkle model is shown by comparing the proposed model and the shell element model.(4) Evaluation of the folding and deploying method : The synthetic evaluation method was proposed concerned with the folding and deploying method.