基于弹性模量缩减法的随机极限承载力分析

为确定工程结构的随机极限承载力，结合弹性模量调整策略和摄动随机有限元法，提出一种基于弹性模量缩减法的随机极限承载力分析方法.首先利用摄动随机有限元法计算结构的随机响应量和单元可靠指标，并定义单元可靠指标均匀度和基准可靠指标，进而论证随机极限分析的比例加载条件及随机响应量的比例关系；然后通过有策略地缩减低可靠度单元的弹性模量，以模拟结构的失效演化历程，形成一系列静力容许应力场，进而根据塑性极限分析理论确定结构的失效模式及其对应的随机极限承载力.算例分析结果表明，该方法通常只需要迭代15步左右即可收敛，与蒙特卡洛法（抽样50万次）的相对误差在0.5%以内. 

Stochastic Ultimate Bearing Capacity Analysis Based on Elastic Modulus Reduction Method

To determine the stochastic ultimate bearing capacity of engineering structures, a novel method for stochastic ultimate bearing capacity analysis based on the elastic modulus reduction method (EMRM) was proposed by combining the elastic modulus adjustment procedure (EMAP) and the perturbation stochastic finite element method (PSFEM). The stochastic responses and reliability indices of structural elements were calculated by the PSFEM to define the uniformity of reliability indices and the reference reliability index. Meanwhile, the proportional loading conditions of stochastic limit analysis as well as the proportional relationship between the stochastic responses and the external loads were demonstrated theoretically. Finally, by adjusting the elastic moduli of elements with low reliability index the failure evolution was simulated to form a set of statically admissible stress fields, and further the structural failure mode and the corresponding stochastic ultimate bearing capacity were determined based on the plastic limit analysis theory. Numerical examples demonstrate that the proposed method is converged after 15 iterative steps or so, and compared with the Monte Carlo method for 500 000 samples, it has a relative error of less than 0.5%.