索网结构的弹性冗余度分析  

Elastic redundancy analysis of cable-net structures

作　　者：朱红飞[1] 陈务军[1] 董石麟[1] 

机构地区：[1]上海交通大学空间结构研究中心,上海200240

出　　处：《空间结构》2012年第3期49-55,40,共8页Spatial Structures

基　　金：国家自然科学基金资助项目(50878128;11172180)

摘　　要：主要介绍索网结构弹性冗余度的定义及其理论分析过程.冗余度的定义为可用的方程个数比求解时所必需的方程个数多出来的个数.索网结构属于柔性张力结构,不同于传统刚性结构,柔性张力结构的刚度主要由预应力提供,其刚度可分为弹性刚度和几何刚度,预应力主要影响几何刚度.索网的冗余度可分为弹性冗余度和几何冗余度,分别对应它的弹性刚度和几何刚度.本文通过对势能方程求解微分,得到索网结构的平衡方程、物理方程和几何协调方程,再将几何协调方程线性化,代入平衡方程和物理方程,推导弹性冗余度的计算公式,并采用MAT-LAB编程实现这一算法.最后通过算例,分析索网弹性冗余度的特性,得出一些有用的结论,对工程应用有一定的指导意义.The definition of elastic redundancy of cable-net structures as well as implementation procedure of its theoretical analysis are introduced in this paper. The definition of redundancy is the availability of more functional system components than necessary for meeting the requirements. In common sense, cablenet structure is a kind of flexible tensile structure. Apart from traditional rigid structure, the main source of stiffness for flexible tensile structure is prestress. As a result, its stiffness can be divided to elastic stiffness and geometric stiffness. The latter is affected by prestress condition. According to the stiffness, redundancy of cable-net structures also can be divided to elastic redundancy and geometric redundancy. In this paper, equilibrium equation, physical equation and geometric coordinate equation are obtained from differential equations solution through the potential energy equation. Then linearization of geometric coordinate equation is performed, the outcome of which is substituted into the other two equations. The redundancy formula is then formulated. Using MATLAB programming this algorithm, the redundancy can be calculated. At last, several examples are carried out. The character of elastic redundancy is analyzed. Some useful conclusions are summarized which will guide the further practice.

关 键 词：索网结构 冗余度 弹性冗余度 几何冗余度 势能方程 

分 类 号：TU351[建筑科学—结构工程]