结构可靠度计算的Gauss-Hermite积分方法

高精度的可靠度计算方法是结构可靠度研究的基本内容之一,根据结构失效概率取决于失效面上验算点区域局部特性的特点,应用高效的Gauss-Hermite积分,研究了结构失效概率的计算问题,分析方法为在标准正态空间内对坐标轴进行旋转,使第n个坐标轴通过验算点且正交于极限状态曲面,然后在新的坐标系内布置Gauss-Hermite积分的节点并进行计算,由于Gauss-Hermite积分的高效性,一般情况下每一个坐标轴只需布3或5个点即能获得较好的计算结果,通过两个算例说明了上述方法的可行性,该方法既可用于精确计算结构的失效概率,也可用于其他各种可靠度近似方法计算结果的校核。

Gauss-Hermite Integration-Based Approach for Structural Reliability Analysis

An attempt was made to introduce the Gauss Hermite integration into the computation of reliability depending on the local characteristics of limit state function. To fulfill this, the orthogonal transformation of basic variables is necessary to make the n th coordinate axis being perpendicular to the limit state function surface and the abscissa 0 in Gauss Hermite integration coinciding with the design point at limit state surface. The validity of the proposed method was demonstrated by two numerical examples. The proposed method can be used in the situation that higher precision is requested or as a pseudo exact solution to calibrate the result of other approximate calculating methods.