满约束轴向拼接张拉整体结构的自稳定性分析

Self-stability analysis of a fully constrained axiallyspliced tensegrity structure

为获得更多张拉整体构型和拓扑结构,本文基于平衡方程,研究张拉整体拼接结构自稳定条件下的结构参数关系的求取方法。基于三杆张拉整体单元轴向拼接形成的臂状张拉整体结构,以减少结构节点约束数为目的去除索构件,获得一种新型满约束轴向拼接张拉整体结构;分析此结构的节点坐标、构件向量的求取方法,推导结构的平衡方程;依据节点和构件之间的连接关系,以获得方阵形式的平衡矩阵为目标,提出了平衡方程缩减原则;根据平衡方程有非零解,平衡矩阵行列式为零的原则,获得保证张拉整体结构自稳定的结构参数关系。通过具体实例分析,证明此方法正确,获得的结构参数关系能够保证确定的满约束轴向拼接张拉整体结构的自稳定性。

Based on the equilibrium equation,this paper examines the method for deriving the structural parameter relationship under the self-stabilizing condition of the tensegrity spliced structure,thus obtaining more overall configurations and topological structures of tensegrity.First,a new type of fully constrained axially spliced tensegrity structure is obtained based on the tensioned integral arm formed by axial splicing of three-bar tensegrity units.This was done by removing the cable members for the purpose of reducing the number of structural nodes.Then,the method of obtaining the node coordinates and component vectors of the structure is analyzed to reduce the equilibrium equation of the structure.To obtain a balance matrix in the form of a square matrix,a principle of reducing balance equations is proposed,considering the connection relationship between nodes and components.To ensure the self-stability of the overall tensegrity structure,the structural parameter relationship is obtained based on the principle stating that the equilibrium equation has a nonzero solution and that the determinant of the equilibrium matrix is zero.Finally,through analysis of specific examples,it is proven that this method is correct and that the obtained structural parameter relationship can ensure the self-stability of the determined,fully constrained,axially spliced tensile integral structure.