一阶无穷小位移机构的刚化判定

Determination of Stiffening for First-order Infinite Mechanism

一阶无穷小位移机构是一类具有机构性能的特殊的新型空间结构,从工程结构的角度考虑,只有能够消除机构性而获得几何刚度的体系才是可承载的结构体系。一阶无穷小位移机构的几何刚度的获得是通过体系的相对机构位移而获得的,这与传统结构的几何刚度的概念是完全不同的。因此,研究一阶无穷小位移机构的刚化问题是非常重要的。Maxwell准则只从体系的拓扑关系来考虑体系的几何稳定性,这显然不能应用于一阶无穷小位移机构的刚化判定问题。本文基于矩阵向量空间分解的理论和一阶无穷小位移机构的概念,在体系的平衡矩阵引入了边界条件,对一阶无穷小位移机构的刚化判定问题进行了分析,运用功能原理给出了一阶无穷小位移机构刚化的等价条件和判定方法。通过几个数值算例验证了本文结论和方法是正确、可靠的。

The first-order infinite mechanism is a special kind of space structure, which possesses the character of mechanism. From the view point of engineering structure, only the system which has no mechanism and possesses geometrical stiffness can be used as a bearing load structure. The geometrical stiffness of first-order infinite mechanism is obtained by the relative motions of nodes, which is just different from the general structure. So the studies on the mechanism system are very important. Maxwell rules deal with geometrical stability only from the topology information of system, which apparently cannot be used as the rule of the stiffness determination standards of the first-order infinite mechanism. In this paper, based on the matrix decomposition theory and the concept of first-order infinite mechanism, the boundary condition of equilibrium was presented, and the stiffness determination of first-order infinite mechanism was analyzed. The equally condition of system stiffening and the determination method are given by using energy-work principle. By a few numerical examples, the conclusion and the method presented in this paper are proved.