基于随机响应面法和弹性模量缩减法的结构可靠度分析

Structural Reliability Analysis Based on Stochastic Response Surface Method and Elastic Modulus Reduction Method

结合随机响应面法和弹性模量缩减法,提出了一种基于随机极限承载能力的结构可靠度分析方法.首先根据极限分析理论和广义屈服准则,建立了确定性极限承载能力分析的弹性模量缩减法;然后基于逐步回归分析和线性无关原则,提出了结构随机响应分析的新型随机响应面法;最后结合弹性模量缩减法和随机响应面法确定了随机极限承载能力的展开式,进而提出了基于随机极限承载能力的可靠度分析方法.算例分析表明,该方法直接建立随机极限承载能力和结构功能函数的展开式,在结构可靠度分析中具有较高的计算精度和效率.

Proposed in this paper is a reliability analysis method based on the stochastic ultimate bearing capacity, which combines the stochastic response surface method （SRSM） with the elastic modulus reduction method （EM- RM）. In the investigation, first, based on the limit analysis theory and the generalized yield criterion, an EMRM is developed to determine the ultimate bearing capacity. Then, an improved SRSM for stochastic response analysis is proposed based on the stepwise regression analysis and the linear independent criterion. Finally, a novel reliability analysis method is presented based on the expansion of the stochastic ultimate bearing capacity determined by the SRSM and the EMRM. Numerical example shows that the proposed method is of high accuracy and efficiency for structural reliability analysis because it helps to directly obtain the expansion of the stochastic ultimate bearing ca- pacity and the structural performance function.