【作者】 赵孟良；

【导师】 关富玲；

【作者基本信息】 浙江大学 ， 结构工程， 2007， 博士

【摘要】 可展结构作为一种新型结构形式，近些年来在宇航、建筑结构和军事工程等领域的应用越来越广泛，根据其用途不同可分为空间可展结构和地面可展结构。基于某几个科研项目，本文对空间可展结构展开过程动力学理论分析、仿真及试验进行了深入系统的研究。论文首先查阅了国内外大量相关文献，总结了国内外空间可展结构的应用情况及其展开过程研究现状，对课题的研究意义和研究思路进行了说明。接着阐述了空间可展结构展开过程分析的理论基础。对于在展开分析中具有重要应用的Moore-Penrose广义逆矩阵理论，详细介绍了其定义、求解方法、性质和应用。给出了可展结构运动学关系和准静态的形态解析方法，讨论了几何约束高阶项对展开分析精度的影响。周边环形桁架式可展天线具有收缩比大、重量轻的优点，已成为各国竟相研究的重点天线结构形式。为了对其展开过程进行动力学分析，结合缩比模型的制作简介了该天线结构设计过程，包括可动构件设计、杆件和驱动索设计、支撑索网设计等方面，阐述了其展开收纳机理。以笛卡儿坐标系下节点的自然坐标为未知量，建立了可展结构系统的动力学普遍方程，利用约束雅可比矩阵的零空间正交基引入一组准速率，得到独立的用于展开过程分析的动力学微分方程，结合广义逆矩阵与多体动力学理论分析可展桁架结构的展开运动过程。重点研究了约束系统动力学方程的建立及求解、计入库仑摩擦的展开过程动力学分析、结构各类约束条件下约束方程及其雅可比矩阵的建立、约束方程雅可比矩阵的讨论、数值误差的主动校正等，求得结构展开运动过程各特征参数的数值解，为结构设计优化提供了依据。对扭簧驱动四面体单元构架式可展天线结构设计进行了简要介绍，包括展开状态和收缩状态的形状拓扑；推导了扭簧驱动可展结构的展开动力学方程，方程能够反映展开过程中驱动力的变化情况；根据结构展开收纳机理，推导了该类可展结构的约束方程及其雅可比矩阵，特别针对该系统中出现的单向约束问题，提出了“预测—锁定”的计算方法，给出了程序流程图；结合实际结构的运动特性，分析了粘性摩擦对结构展开的影响；给出了构架式抛物面天线的形面精度计算方法，其可以预测不同弹簧刚度及结构设计对结构展开可靠性的影响；此外，论文还对最小可展开扭簧刚度进行了探讨。给出了在可展桁架结构展开分析中考虑弹性变形的计算方法。从可展桁架结构的运动学关系和平衡方程出发，基于广义逆矩阵理论提出了可展桁架结构机构运动和弹性变形混合分析方法，解决了机构运动和弹性变形的耦合问题。用细分的平面三角形单元组成的折板近似壳体的几何形状，将三角形板壳单元用两边和其夹角来描述，提出了可展板壳结构的运动学分析和求解刚体位移的基础方程式，然后结合广义逆矩阵理论和动力学普遍方程分析了可展板壳结构的展开过程，给出了结构展开动力学分析的详细方法。对常应用于空间可展板壳结构单元划分的平面四边形单元的运动学关系和刚体位移也进行了推导。给出了考虑可展板壳结构展开过程中弹性变形的近似方法，并应用仿真算例验证了分析方法的有效性。基于空间可展结构理论分析方面的研究成果，探讨了具备自身图形平台空间可展结构展开动力学仿真软件的开发，对开发过程中涉及的关键问题进行了描述，如系统框架、数据结构、类的构造与层次、核心分析模块的编制原理、可视化的实现过程等。运用VC++、MATLAB、OpenGL混合编程技术开发出空间可展结构展开动力学仿真软件(DSDSP)一套，用不同可展结构设计数据对该软件进行了测试，并将仿真算例结果与解析解、ADAMS分析解进行了对比，测试结果表明该软件分析过程正确，基本功能完整，错误处理恰当，操作流程方便。在进行了理论分析和仿真软件的研究之后，探讨了构架式可展天线展开过程动力试验方法；对扭簧刚度和初始角度进行了试验测试，针对设计制作出的构架式天线缩比模型进行了展开过程试验，介绍了相关试验设备，对不同试验方案进行了探讨，采集出运动过程测点的冲击加速度等数据，将试验结果与仿真分析软件分析结果进行了对比，分析了误差产生的原因。更多还原

【Abstract】 As a new kind of structure, the deployable structure is more and more widely used in the fields of astronautics, building structure and military engineering, etc. It can be divided into deployable space structures and deployable ground structures. Based on some projects, dynamic theory analysis, simulation and experiments had been studied systematically for the deployment process of deployable space structures in this dissertation.Firstly, after referring a lot of pertinent literature worldwidely, the application of deployable space structure and the research actuality of its deployment process were summarized, the research significance and approaches were presented.Afterward, this dissertation described the theoretical basis employed to analyze the deployment process of deployable space structures. As a significant theory to analyze the deployment analysis, the Moore-Penrose generalized inverse matrix theory’s definition, solving method, character and application were introduced detailedly. The kinetics relation and the quasi-static shape analysis of deployable structures were presented, and the influence of the geometric restriction’s higher order items to the deployment analysis accuracy was discussed.The circular truss deployable antenna has attracted more and more attention in some countries for its small package volume and light weight. For the sake of the dynamic analysis of its deployment process, a small proportional circular truss deployable antenna model was made, the designing of which was introduced simply: the moveable component design, the rod and driving cable design, and the supporting cable net design etc., and the deploying and stowing mechanism was explained completely. Dynamic equations of the structure were formulated with the idealized truss joints as variables in the Cartesian coordinates. Using the null space orthogonal basis vectors of the constraint equations’ Jacobian matrices, a set of quasi- velocity was integrated into the dynamic equations, then a group of independent dynamic equations with no coefficients were formulated. The deployment process was analyzed by combining the generalized inverse matrix and multi-body dynamics theory. The most attention was paid to the following: the formulation and solving method of dynamic equations of a constrained multi-body system, the deployment dynamic analysis with Coulomb friction, the formulation of kinematic constraint equations and the Jacobian matrix, the discussion of the Jacobian matrix, and the active correction of constraint violation and so on. So the numerical values of everycharacteristic parameters during structural deployment process were obtained, which could be an effective reference to the structural design and optimization.This dissertation introduced the structure design of a tetrahedral truss modular deployable antenna driven by torsional springs model briefly, and the shape topology of the deployed state and stowed state was also introduced. The dynamic equations of the deployable structure driven by torsional springs were deduced, which could reflect the variable driving force during deployment. According to the deploying and stowing mechanism of the structure, a new mathematic algorithm was developed to formulate the kinetic constraint equations and relevant Jacobian matrices, and the unilateral kinematic constraints of deployment were specifically solved by adopting a forcast-lock method, whose procedure flow chart was presented. Considering the actual movement of the structure, the influence of viscous friction damping to the structure deployment was analyzed. This dissertation presented the calculation method of the grid paraboloid antenna’ reflector accuracy which could be used to forecast the influence of different torsional springs stiffness and structure design to the deployment reliability. Moreover, the minimal stiffness of the torsional springs needed to deploy the structure was discussed.Deployment analysis of deployable truss structures with flexible deformation was discussed. Based on the kinetics relation and equilibrium equation of the structure, a new hybrid method was developed to analyze deployable truss structures with mechanism motion and flexible deformation by using the generalized inverse matrix theory, and the coupling between these two motions was calculated.The geometry shape of deployable spatial shell structure can be approximated by many plane triangle elements when the elements are small enough. The triangular shell element was described using two sides and the relevant angle, the kinematics relation and the basal equation used to solve rigid body displacement of the structure was presented, then the moving process of the structure under applied loads was analyzed by using the generalized inverse matrix theory and multi-body dynamics theory. This dissertation had also derived the kinematics relation and the basal equation used to solve rigid body displacement of a quadrangle element which is widely used to divide the structure. The approximate method was presented to analyze the flexible deformation of the structure during deployment, and the efficiency of the method was verified by simulation program based on it.According to the research above, the method of developing its deployment dynamic simulation software with self graphic platform was presented in detail in thisdissertation, some key technologies during developing process such as the system frame, the data structure, the constitution and arrangement of class, the development principle of core analysis module, and the procedure of visualization were included. Then by using VC++, MATLAB and OpenGL mixed programme technology, a deployment dynamic simulation software (DSDSP) was developed, whose validity of analytical process, completeness of its basic function, properness of its mistake disposing and convenientness of its operation were verified by some tests using different deployable structure design data and comparing them with the ADAMS analyses and theoretics solution.After studying the theory analysis and simulation software, the dynamic experiment method of deployment process for deployable truss antenna was discussed. The stiffness and initial angle of torsional springs were tested. With a small proportional deployable truss antenna model, this dissertation fulfilled the deployment process experiment, introduced the relevant experiment equipments, discussed the different experiment schemes, gathered the impulse acceleration of measure nodes during movement, compared the experiment result and the analytical result using the simulation software, and analyzed the reason of difference.更多还原