区间模型非概率可靠性全局最优解

考虑到实际工程中大量存在不确定性因素，将结构中不确定参数描述为凸集变量的一种特殊情况－区间变量，根据区间模型可靠性指标的定义，采用解析方法进行非概率可靠性全局分析。为避免可能失效点遗漏，解析分析从二、三维开始，对平面和空间进行区域划分，根据极限状态函数的形式，指出了可能失效点依赖于极限状态函数的极值点和根植点。通过简单的量值比较，即可确定最可能失效点，进一步可求得可靠性指标。将低维分析方法推广到n维情况，给出了n维空间中用于计算极值点和根植点方程的数量，能够有效避免发生可能失效点遗漏现象，对优化搜索具有指导意义。针对两类算例进行求解，并与已有结果比较，验证了本文解析方法的正确性。

Theoretical analysis about non-probabilistic reliability base on interval model

Considering the great amount of uncertainty factors existing in actually engineering, the uncertain parameters in the structure were described as one special case of convex variables, that is, the interval variables. According to the definition of reliability-index based on interval model, the non-probabilistic reliability analysis was carried out with analytical approach. In order to avoid the loss of the probable failure point, analytical model starts from 2-D plane and 3-D space. After division of domain within 2-D and 3-D, the probable failure points can only exist on the extreme points and the root points of the limit state function. after simple comparison directly, it is easy to find the most probable failure point and to acquire the reliability-index. Furthermore, the low-dimensional analytical scheme has been extended to high- dimensional case. The equation numbers used for calculating the extreme point and the root point has obtain, which can be useful to avoid the loss of the probable failure point and meaningful for optimizing searching in this researching field. Finally, two kinds of examples were presented and compared with existing computation. The agreement shows that the analytical approach in the paper is correct.