平衡矩阵理论的探讨及一索杆梁杂交空间结构的静力和稳定性分析  

DISCUSSION ON THE EQUILIBRIUM MATRIX THEORY AND STATIC AND STABILITY ANALYSIS OF A HYBRID SPATIAL STRUCTURE COMPOSED OF CABLES, BARS AND BEAMS

作　　者：张志宏[1] 张明山[2] 董石麟[1] 

机构地区：[1]浙江大学空间结构研究中心,杭州310027 [2]浙江大学建筑设计研究院,杭州310027

出　　处：《工程力学》2005年第6期7-14,20,共9页Engineering Mechanics

基　　金：国家自然科学基金资助项目(50278086)

摘　　要：首先对索杆杂交结构采用平衡矩阵理论进行了探讨。对于索杆杂交结构而言,可以根据平衡矩阵确定体系在初状态几何下的整体预应力分布和大小,但是必须考虑变形相容条件和本构关系即各个单元的柔度分布。只有满足体系柔度分布的杆件截面尺寸的结构才能最终施工张成给定的预应力分布和设计几何。由相容方程和平衡方程提出了包含局部超静定结构的索杆杂交结构的柔度分布确定方法和独立柔度分布模态这一概念。算例分析结果验证了方法的正确性。其次,对一索杆梁杂交空间结构的计算分析方法及其初步的静力及其稳定性进行了研究。基于局部分析法对索杆梁体系的预应力分布和大小进行了优化分析。在优化目标下,最优的预应力分布是外环预应力较大,中环、内环预应力要小很多。并以预应力作为整体自平衡的初始内力情况下对其进行了初步静力和稳定性分析。结果表明柔性体系和刚性体系的杂交实际上只能为刚性体系提供大变形的安全储备,而并不能有效的降低体系的挠度,但是预应力的存在却可以有效的改变梁单元轴力的性质和水平。相比单层网壳,索杆梁体系的稳定性能有了较大提高。The equilibrium matrix theory in the analysis of cable-bar hybrid structures is discussed in this paper. For cable-bar hybrid structures the initial pre-stress distribution can be determined using the equilibrium matrix theory. The flexibility distribution of each cable or bar element should be considered at the same time. Bar elements with section sizes satisfying the flexibility distribution, can be used to construct the structure successfully eventually. A new method for flexibility distribution determination of cable-bar hybrid structures is proposed utilizing the compatible equation and the equilibrium equation. A new concept, independent flexibility distribution mode, is presented here. It is verified by a numerical example. In addition, a computational analysis method of a hybrid structure composed of cables, bars and beams and its preliminary static and stability properties are presented in this paper. Based on the local analysis method the distribution and magnitude of pre-stress of this hybrid structure is analyzed using optimal theory. The outmost ring has larger pre-stress than the middle one and the inner one. Static and stability properties are analyzed by taking the pre-stress as self-equilibrium initial internal force. It is found that the flexible cable-bar system and pre-stress in the whole structure cannot reduce the deflection dramatically. But the pre-stress can affect the axial force distribution in beams very much. In comparison with single-layer reticulated shells this type of hybrid structures has high stability.

关 键 词：找力分析 柔度分布 弦支穹顶 静力分析 稳定性 预应力 优化 

分 类 号：TU394[建筑科学—结构工程]