非概率可靠性指标的存在性研究及其半解析解法

针对具有非线性功能函数的广义结构系统的基于区间分析的非概率可靠性指标难以求取的问题,证明了可靠性指标只可能存在于标准化区间变量张成的凸域及其扩展空间中和通过原点及凸域顶点的有限条超射线与失效面的某个交点处,从而使放弃计算量大的数值迭代搜寻法成为可能。提出了通过求解有限个一元方程确定可靠性指标的半解析方法,该方法准确高效,适用于所有类型的功能函数。

A Semi-analytical Approach for Calculating Index of Non-probabilistic Reliability Based on Interval Analysis

This paper draws a conclusion that index of non-probabilistic reliability of a generalized structure exists merely at one of the intersections where a hyper radical line intersects at failure surface of the generalized structure,which is proved in functional analysis theory.A semi-analytical approach for getting the index was developed.The approach is simple in its analysis procedure and efficient in its calculations because it needs only to do infinite one-place operations in the calculations.Examples of practical application validate the approach.