Dynamics of Inflatable Space Structure

提出了一种充气膜结构展开动力学的数值分析方法，并编制了数值计算程序。提出了膜自接触的数学模型和膜褶皱线的粘弹塑性模型。这些模型的公式是在数字代码中实现的，这些代码直到去年才开发出来。膜的起皱问题是近年来最热门的研究课题，而本研究所分析的问题还没有被其他研究者研究过。然而。这将是在不久的将来制造大型膜结构的最严重的问题。本文的研究结果总结如下：(1)建立了局部起皱膜动力学的数值计算方法，并编制了数值计算程序。这种方法使我们可以进行精确保存能量、线性动量和角动量的数值时间积分，即时间积分是无条件稳定的。这是计算膜在零重力条件下的动力学的关键数值技术，一直是相当困难的。(2)建立了膨胀气体与膜管相互作用的数学模型。该模型能准确地保存能量，使积分在数值上保持稳定。(3)将膜的自接触效应落实到数值编码中。这也是获得准确仿真结果的关键数值技术。(4)建立了薄膜褶皱的粘弹塑性模型，这是模拟褶皱产生和发展的必要条件。研究表明，薄膜和充气膜结构的动力特性可以用数值方法进行预测，这在以前是不可能的。这是这项研究最重要的结果。

A numerical analysis method of deployment dynamics of inflatable membrane structures is proposed, and the numerical code is developed. A mathematical model of self-contact of the membrane and the visco-elastoplastic model of the fold line of the membrane are proposed. The formulation of these models is implemented into the numerical code that has already been developed until last year. The wrinkling problem f the membrane is the most popular research topics in these years, and the problem analyzed in this research has not investigated by other researchers yet. However. That problem will be the most serious problem to fabricate the large membrane structures in near future.The results of this research are summarized as follows; (1) Numerical method of the dynamics of membrane with partial wrinkling is formulated and a numerical code is developed. This method enables us to perform the numerical time integration that exactly conserves the energy, the linear momentum, and the angular momentum, i.e. the time integration is unconditionally stable. This is the key numerical technology to calculate the dynamics of the membrane in zero-gravity condition that has been quite difficult. (2) A mathematical model of the interaction between the inflation gas and the membrane tube is constructed. This model also conserves the energy exactly, which leads the numerically stable integration. (3) The effect of the self-contact of the membrane is implemented into the numerical code. This is also the key numerical technology to obtain the accurate results of the simulation. (4) A visco-elastoplastic model of the fold of the membrane is constructed, which is necessary to simulate the generation and growth of the fold.The research shows that the dynamic behavior of membranes and inflatable membrane structures can be predicted numerically, which has been understood impossible. That is the most important result of this research.