【作者】 李士民；

【导师】 董冰； 王祎；

【作者基本信息】 同济大学 ， 结构工程， 2008， 硕士

【摘要】 膜结构是20世纪中期出现的一种新型空间结构形式,它所能创造的丰富多彩的外部建筑造型是其他建筑结构所不具备的,因此自从它发展成为一种结构形式以后就被广大的建筑师、结构师广泛的应用于大型的体育场馆、展览场馆等空间结构体系中。而作为膜结构形式之一的充气膜结构,虽然具有一些难以回避的缺点,可是在一定领域内它的优势是明显的。随着科技水平的不断进步,充气设备的不断改善,我们有理由相信未来几年里充气膜结构会在我国得到迅速发展。针对充气膜结构的充气过程,本文通过分析膜结构的结构特点、膜材性能及力学性质,对其从完全未充气到完全充气这一过程进行了三维模拟。提出了基于两种不同理论的仿真技术,并对这两种技术方法进行详细深入地阐述。首先,运用杆件惯性的概念对充气膜结构的充气过程进行模拟。考虑到充气膜结构的截面特征,将膜截面简化为由有限个杆单元铰接而成的机构模型。为了确定机构模型的所有结点的运动情况,将每根杆的两端未知力作为总动力方程的未知量,利用动力学中杆单元的运动规律并结合整个机构的运动协调条件,得到简化机构模型的总的动力方程,求解此矩阵方程从而获得各个结点的位置和模型的实时运动状态,进而可以实现对充气膜结构的整个充气过程的计算机仿真。根据该理论获得的总动力方程,具有多元性、不规则性和稀疏性的特点。考虑到矩阵方程的性质,通过比较分析,本文采用十字链表存储方式来存储其系数矩阵,并选用量化的列选主元高斯消去法来对总动力矩阵方程进行数值求解,从而获得每一时刻各个结点的位置和模型的实时运动状态。此外,本文分析了用于柔性体建模的几何方法、物理方法后,将较为可行的基于弹性理论的弹簧-质点模型引用到充气膜结构的充气过程模拟中,从而可以有效的模拟三维充气膜结构。对弹簧-质点模型的结构特点和在充气过程中模型所受到的各种荷载等进行了详细的阐述,然后根据经典力学原理对模型的质点进行分析从而得到连续的膜面充气状态。对于在模拟充气过程中,出现一些异常的“超弹性”现象,如结构弹簧的过度拉伸、膜面的不稳定震荡等,找到了几种较为有效的处理方法,并对其进行了验证。对于所提出的上述两种方法,本文也分别作了部分实例进行检验。利用Visual C++进行算法实现,分别构造了充气膜结构的基于惯性理论和弹性理论的两种模型系统,其中在后者的建模过程里,本文还借助了ANSYS软件中较为成熟的建模和网格划分模块,用VC++编程构造了数据接口,完成了系统的初始阶段建模,最后结合OpenGL图形库将两种模型系统的整个充气过程进行了仿真动画实现。更多还原

【Abstract】 Membrane structure is a new kind of space structure styles appeared in the middle period of the 20th century. It can create lots of colorful outer architecture shapes which are quite different from other structure styles. Therefore, since membrane structure has been acquainted and develops into a kind of structure style, it has been widely used by lots of architects and civil engineers in the space structure buildings such as large gymnasiums, stadiums, exhibition halls and etc. Although pneumatic membrane structures, as one form of that, have some irrevocable shortcomings, its advantage in certain field is obvious. Developing with the progress of the level of technology and successive improvement of inflation equipment, it is believed that air-supported structures will be rapidly developed in our country during the next few years.For the inflating process of pneumatic membrane structures, this paper analyses the characteristic of structural style and material and mechanics in membrane structure, and simulates the entire process from little puffed to totally inflated in three-dimensions. Based on two different theories, simulation technique is presented and deeply expatiated.Firstly, the inflating process of pneumatic membrane structure is simulated with the pole inertia conception. Considering the section feature of pneumatic membrane structure, the membrane section is partitioned into finite elements and is predigested to a mechanical model which is formed of finite poles jointed by hinges. In order to acquire the real-time state of every node on the model, we regard forces on the ends of pole as unknown quantities of general dynamical equation. Using the dynamical laws of pole unit in dynamics and corresponding conditions, the general dynamical equation of the mechanical model can be founded. Then by solving the founded matrix equation, nodes’ positions and the real-time moving states of model are all obtained. Therefore, the simulation of entire process in which pneumatic membrane structure is inflating, can be achieved in this way. The general dynamical equation which is acquired in this theory has three characteristic, that is muti-unknowns, scrambling and sparsely. Considering this and comparative analysis, orthogonal list is used to storage coefficient matrix, and Improving Gaussian Elimination Method is used to numerically calculate dynamical equation. Therefore, nodes’ positions and the real-time moving states of model can be obtained in this way.Moreover, after the survey of cloth modeling methods in geometry and physics, mass-spring model based in elasticity theory is proposed to the inflating process simulation of pneumatic membrane structure. This paper expatiate the loads supported on mass-spring model, and then analyze particles in classical dynamics. In addition, some hyper-elasticity phenomena, such as, over-pull of structural springs and unstably shake of membrane surface etc. Some methods will be proposed to solve these problems and be proved.The author gives some examples to prove the methods above and program in visual C++. Two model system is constructed based in inertia and elastic theory. Besides, construction and gridding meshing of Mass-Spring model is solved by ANSYS modules. After programming data interface and constructing model originally, realistic simulation of inflating process is completed by OpenGL for two models.更多还原