为深入研究三杆张拉整体基本单元结构的构建方法和稳定性判定问题。提出以结构外形几何参数为基础，应用节点广义坐标矢量矩阵、构件矢量矩阵和连接矩阵建立数学模型，并用MATLAB编程实现单元结构的自动构型。引入构件力密度标量，建立系统力平衡矢量矩阵方程，分析结构的稳定性，把非线性系统平衡问题转化为线性系统平衡问题。通过分析平衡矩阵，对结构系统进行分类，筛选出能够构建起稳定结构的几何参数的变化范围。本研究方法具有通用性，适用于其它张拉整体结构形式的构型和稳定性分析。%This paper focuses on the problem that how to build up basic 3 bars tensegrity unit structure and how to judge its stability. Based on the outer shape geometry parameters, using node general coordinates, member vector matrices, connectivity matrices, the mathematical model of basic 3 bars tensegrity unit is presented. To build up structures automatically, a program is established in the MATLAB software by which one can build any basic 3 bars tensegrity structure under the given outer shape geometry parameters. Then, the scalar parameters force densities are introduced. With the connectivity matrices and node general coordinates, the equilibrium matrix function is built. It is linear about force densities. The balance matrix specifies the given system as one of four kinds of structures, and the stable structure can be chosen out.
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