响应面法在结构体系可靠度分析中的应用

一个失效模式由许多的失效单元构成,它是一个并联系统;而所有的失效模式构成一个串联系统.整个结构体系可看成是许多并联系统(失效模式)组成的一个串联系统.首先,利用基于响应面的随机有限元法来获得失效模式中各个单元的极限状态方程,这些方程都是二次多项式;第二步,利用结构可靠度分析中的几何法得到这些方程的等效线性化方程从而可逐步得到该失效模式的等效线性化方程;第三步,计算各失效模式间的相关系数;最后,由Ditlevsen界限法来计算结构的体系可靠度.算例表明,利用该方法来获得大型、复杂结构的体系可靠度具有高效、实用的特点.

APPLICATION OF RESPONSE SURFACE METHOD IN SYSTEM RELIABILITY ANALYSIS

A failure mode, which consists of failure elements, is considered as a parallel system. All failure modes form a series system. A structural system is modeled as a series system that consists of failure modes. In the first step, stochastic finite element method based on response surface is suggested to get a set of limit state functions of failure elements of a failure mode. All these functions are quadratic polynomial. In the second step, a set of equivalent linear equations for these functions is obtained by geometric method in structural reliability analysis and an equivalent linear equation of the failure mode is evaluated step by step. In the third step, the correlation coefficients between failure modes are evaluated., structural system reliability is computed by Ditlevsen bounds method. A numerical example shows that the suggested approach is efficient and applicable.