【作者】 常治国；

【导师】 张其林；

【作者基本信息】 同济大学 ， 结构工程， 2006， 博士

【摘要】 对于大型复杂钢结构需要研究施工时结构的变形和内力变化。因为系统中存在刚体位移，传统的有限元方法不能有效的解决这类特殊的结构计算问题。本文基于柔性多体系统动力学对索杆梁钢结构施工动力学的理论进行了研究并研制了相应的仿真软件系统。 大型复杂钢结构施工过程中同时存在刚体位移和弹性变形，传统的有限单元法只能应用于几何稳定的结构，不能用于解决这类特殊的问题。本文采用柔性多体系统动力学的基本理论来解决这类系统的动力学问题。用惯性坐标系作为整体坐标系描述多体系统的刚体位移，在每个柔性体上附着一个局部坐标系。局部坐标系随着柔性体的刚体位移(包括平动和转动)变化，柔性体相对于局部坐标系的运动定义为柔性体的弹性变形。本文采用的这种混合坐标的描述方法同时考虑了柔性体运动的刚体运动部分和弹性变形部分以及它们的耦合作用。本文的方法不受刚体运用的有无和刚体运动幅度大小的影响，算例表明这种方法具有较高的精度，同时验证了刚体运动和弹性变形之间的耦合作用是不能忽略的。 根据本文的基本方法，开发了两种柔性多体系统动力学计算的单元，索杆单元和梁单元。它们的空间方位分别用方向余弦和欧拉四元数表示；对每种单元选择适当的形函数描述单元的基本弹性模态。开发了不同单元之间的节点连接形式供建模时选择。对梁单元之间的刚性连接，相应的约束方程实际描述了两个梁单元对应的端点坐标系之间的关系。本文采用联立梁单元方位数学约束方程确定独立代数方程的方法，建立梁单元刚接的约束方程。 柔性多体系统动力学的控制方程是一类微分—代数混合方程，本文采用两套变量描述系统的运动过程，描述刚体运动的变量是大幅度的慢变分量，描述弹性变形的变量是小幅度的快变分量，两种变量的同时求解使控制方程呈严重的“刚性”，为了反映弹性变形的变化规律，积分步长必须取得很小，即使当弹性变形已经趋于收敛时，积分步长仍然不能放大。 本文研制了基于AutoCAD开发接口的三维实体仿真系统。该仿真系统能对各种索杆梁结构的施工过程进行仿真计算并给出完整的计算结果。更多还原

【Abstract】 For flexible large span steel structures, the investigation of the deformation and stress in construction process can not be neglected. Considering there is rigid body motion in this system, therefore, traditional FEM is incapable of solving the problem. In this thesis, based on the dynamics of flexible multi-body systems, the analysis of dynamical systems of cable-strut and beam steel structure and the corresponding simulation research is addressed.During the construction process of structures, rigid-body motion and elastic deflection occur simultaneously. Traditional FEM can only be applied to kinematically determinate structures, and it is incapable of solving the hoisting process problem. In this thesis, the calculation strategy based on dynamics of flexible multi-body systems is presented and applied to these engineering systems. An inertial frame serves as a global reference frame for describing the rigid body motion of the multi-body system. In addition, intermediate reference frames that are attached to each flexible component and follow the average local rigid body motion (rotation and translation) are used. The motion of the component relative to the intermediate frame is, approximately, due only to the deformation of the component. This hybrid description of this thesis can simultaneously consider the rigid-body motion and elastic deflection of the structure, including their coupling effects. The method is applicable to the conditions with or without rigid-body motion, and its performance is not affected by the extents of the rigid-body motion. Numerical examples demonstrate that the method of this thesis is with high precision, and validate that the coupling effects between rigid body motion and elastic deflection cannot be neglected.Based on the theory of dynamics of flexible multi-body systems, two elements, namely, cable-strut element and beam element are developed. The azimuths of the elements are described by direction cosine and Euler quaternion, respectively. The shape function of the element is selected to describe the basic elastic mode. For the更多还原