索杆体系的机构运动及其与弹性变形的混合问题

基于有限单元平衡方程推导了索杆体系机构运动的通解、特解及其路径跟踪的迭代求解列式，以及机构运动与弹性变形混合问题的迭代求解列式。从机构运动和弹性变形问题的比较角度出发，解释了机构运动中的若干基本定义，对索杆体系的机构运动和弹性变形混合问题作了分类。数值算例表明：采用本文方法可以非常有效地跟踪求解索杆体系机构运动、弹性变形及其混合问题的全过程路径，得到机构运动的静定状态和混合问题的平衡状态。

Mechanism motion and motion-deformation hybrid problems of cable-member systems

Cable-member system, as one of the typical pre-tension steel structures, is being widely applied in engineering. Based on nonlinear finite element equilibrium equations, the incremental iteration formulations of the mechanism motion, elastic deformation and motion-deformation mixed problem for cable-member system are set up in this paper. The complementary solution and the special solution are derived and proposed, and their physical meanings are graphically explained. Then some basic concepts on mechanism motion, such as motion restrain vector, stationary state of mechanism motion and stability of stationary state, are illustrated. In view of the comparison between the mechanism motion problem and the elastic deformation problem, two types of the motion-deformation mixed problem are classified. The first is that the system has motion and deformation at the same time. The second is that the system reaches a stationary state through a rigid-body motion process firstly, then elastically deforms under external loads. The methods and procedures for tracing the whole motion-deformation paths are given for the two kind problems, respectively. The four-member trusses with different initial geometry, the sagging cable, and the PANDA dome are taken as the numerical examples. Their motions and deformations are numerically analyzed and the corresponding paths are traced. Numerical examples show that the methods in this paper can effectively trace the whole processes of mechanism motions, elastic deformations, and the hybrid problems of cable-member systems. The stationary state of the mechanism motions and the equilibrium state of the hybrid problems can be also easily found.