结构可靠度分析的有限单元数值逼近法  

Finite Element Numerical Approximation Method for Structure Reliability Analysis

作　　者：刘旭 Liu Xu(School of Energy Science and Engineering,Henan Polytechnic University,Jiaozuo 454000,China)

机构地区：[1]河南理工大学土木工程学院,焦作454000

出　　处：《特种结构》2022年第3期8-14,共7页Special Structures

摘　　要：结构可靠度分析中失效概率本质上是随机变量失效域的多维积分问题,针对蒙特卡洛法(MCS)处理小概率事件时工作量大、效率低且误差分析困难的不足,将有限单元法应用于该类问题,提出了结构可靠度计算的有限单元数值逼近法。该算法首先对计算结果预设误差限,在此误差限内利用随机分布的概率集中性,将基本变量的概率分布空间分为高概率区间和低概率区间。为提高计算效率,舍弃低概率区间保留高概率区间建立计算域。采用有限单元法将计算域均匀划分为有限个互不重叠的单元,经筛选、累加位于失效域内单元的概率计算近似失效概率。通过增加有限单元法划分精细度实现数值逼近的计算过程,得到满足预设误差范围的失效概率。使用MCS法做对照,验算了三个数值算例,结果表明:新算法在同精度下计算效率显著提高,且具有较强的鲁棒性;可获得计算结果的误差范围。The failure probability in the structural reliability analysis is essentially the multi-dimensional integration of random variables in failure domains.In this paper,a finite element numerical approximation method for structural reliability calculation is proposed,which aims at solving the disadvantages of Monte Carlo method(MCS) in dealing with small probability events,such as large workload,low efficiency and difficulty in error analysis.The algorithm first presets the error limit for the calculation result,and then divides the probability distribution space of basic variables into high probability intervals and low probability intervals within the error limit based on the probabilistic centrality of random distributions.To improve computational efficiency,the low probability interval is discarded,and the high probability interval is reserved to establish a calculation domain.The calculation domain is evenly divided into a limited number of independent units using the finite element method,and the approximate failure probability is calculated by screening and accumulating the probability of the units in the failure domain.By increasing the segment fineness of the finite element method,the calculation process of the numerical approximation is achieved,and the failure probability satisfying the preset error range is obtained.The MCS method is used as a comparison,and three numerical examples are checked.The results show that the new algorithm can significantly improve the computational efficiency and strong robustness under the same accuracy,and the error range of the calculation results can be obtained.

关 键 词：结构可靠度 有限单元法 失效概率 数值逼近 

分 类 号：TU311.2[建筑科学—结构工程]