罗阿妮，伍承旭，刘贺平

(哈尔滨工程大学 机电学院，黑龙江 哈尔滨 150001)

三杆张拉整体的结构刚度分析

罗阿妮，伍承旭，刘贺平

(哈尔滨工程大学 机电学院，黑龙江 哈尔滨 150001)

三杆张拉整体结构是张拉整体结构体系的基础，为了更好的研究张拉整体结构体系的力学性能，本文对三杆张拉整体结构刚度影响因素进行了研究。根据张拉整体的构型理论，利用Matlab软件编程，建立了三杆张拉整体结构的数学模型以及有限元模型。通过数值仿真计算，分析了在轴向力和扭矩作用下，预紧力、材料弹性模量以及构件截面尺寸对结构轴向、径向、扭转变形的影响。由仿真计算数据结果得出：对张拉整体结构刚度的主要影响因素是预紧力，而材料弹性模量、构件截面尺寸等影响因素次之，该结论为改善张拉整体结构刚度提供了一定的理论支持。

张拉整体； 弹性刚度； 几何刚度； 预紧力； 弹性模量； 截面尺寸； 平衡矩阵

Abstract：Three- bar tensegrity structure is the basis of tensegrity system. In order to better study the mechanical performance of tensegrity system,the factors that influence the stiffness of a three- bar tensegrity structure were investigated in this study. Matlab software was utilized to establish the mathematical and finite- element models of the three- bar tensegrity structure in accordance with the structural theory of tensegrity. Numerical simulation calculations were performed to obtain the pretightening force; the elastic modulus of material; and the effects of the section size of the structure on axial, radial, and torsional deformation under axial force and torque. The analysis of simulation data revealed that tensegrity structural stiffness is mainly influenced by pretightening force, followed by the elastic modulus of the materials and the sectional size of structural parts. Results provide theoretical support for the improvement of the stiffness of the tensegrity structure.

Keywords：tensegrity structures; elastic stiffness; geometric stiffness; pretightening force; modulus of elasticity; sectional dimension; equilibrium matrix

自上世纪60年代美国建筑师Fuller提出张拉整体的概念至今，凭借其优越的结构特性，已经成为研究热点之一。Geiger在张拉整体概念的基础上发展出了索穹顶结构体系，在建筑领域得到广泛应用[1-5]；国内学者如袁行飞等提出的环形张拉整体结构[6]以及罗尧治等构建的平板型张拉整体结构[7]等，在张拉整体基本单元基础上进行的拓扑研究取得了一些进展。

国内外张拉整体结构的研究主要集中于结构的构型拓扑上，而对于结构力学性能方面的研究较少。……