张拉整体结构的稳定性判定及刚度分析  

Stability criterion and stiffness analysis of tensegrity structures

作　　者：张沛[1,2] 冯健[1,2] 

机构地区：[1]东南大学混凝土及预应力混凝土结构教育部重点实验室,江苏南京210096 [2]东南大学国家预应力工程技术研究中心,江苏南京210096

出　　处：《土木工程学报》2013年第10期48-57,共10页China Civil Engineering Journal

基　　金：国家自然科学基金(51278116)

摘　　要：张拉整体结构是一种由连续拉索和断续压杆构成的新型空间结构体系,结构刚度及稳定性主要靠预应力提供。以切线刚度矩阵的正定性为稳定判据,通过分析体系切线刚度矩阵解析表达式的构成,系统研究张拉整体结构的稳定条件。按稳定性由强到弱,给出张拉整体结构的实用分类法则。对于确定形态的张拉整体结构,只需验证几何刚度矩阵及其关于内部机构位移模态缩减形式的正定性即可判断其属于何种稳定等级,且预应力水平较低时,后者的最小特征根与切线刚度矩阵的最小特征根一样可用来度量张拉整体结构的刚度。通过考察系统总势能二阶增量(亦即切线刚度矩阵的二次型)随预应力水平的变化规律,详细阐述各稳定等级对应的刚度特性,为寻找真正适用于功能性建筑的张拉整体结构形式提供理论依据。最后通过对一系列张拉整体单元及一个由多单元组合而成的张拉整体结构进行算例分析验证文中理论的有效性。Tensegrity structure is a new type of space structure system which composes of continuous tension members and discontinuous compression members, and the stiffness and stability of structure are mainly provided by the prestress ~ In this study, the positive definiteness of tangent stiffness matrix was considered as the stability criterion, and stability conditions of tensegrity structures were systematically discussed through the investigation of analytical expression of tangent stiffness matrix. The practical classification rule of tensegrity structures was presented in view of their respective stability properties, in which only the positive definiteness of geometric stiffness matrix and its reduced form with respect to internal mechanism modes need be verified. Theoretical analysis showed that when the prestress level is low, the smallest eigenvalue of the reduced form can be used to evaluate the stiffness of tensegrity structures as the one of the tangent stiffness matrix. The variation of the second-order term increment of total potential energy （i. e. the quadratic form of tangent stiffness matrix） with prestress level was analyzed carefully to elaborate the stiffness characteristics at each stability level, providing the theoretical basis for the practical application of tensegrity structures as real building skeletons. Furthermore, some numerical examples were employed to illustrate all the main points of this work.

关 键 词：张拉整体结构 稳定条件 切线刚度矩阵 正定性 预应力水平 特征值分析 

分 类 号：TU323[建筑科学—结构工程]