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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.
This paper mainly introduces the definition of flexible redundancy of cable network and its theoretical analysis process.The redundancy is defined as the number of available equations which is more than the number of equations necessary for solving.The cable network structure belongs to flexible tension structure , Different from the traditional rigid structure, the stiffness of the flexible tension structure is mainly provided by the prestress, its stiffness can be divided into elastic stiffness and geometric stiffness, prestress mainly affect the geometric stiffness.The cable network redundancy can be divided into elastic redundancy and Geometric redundancy corresponding to its elastic stiffness and geometric stiffness respectively.Based on the differentiation of potential energy equation, the balance equation, physical equation and geometric coordination equation of cable network structure are obtained, and then the geometric coordination equation is linearized and substituted into the equilibrium equation and Physical equations, the formula for calculating the elastic redundancy is deduced, and MAT-LAB programming is used to realize this algorithm.At last, an example is given to analyze the characteristics of elastic network redundancy and some useful conclusions are obtained, The guiding significance.