随机载荷作用下的结构疲劳寿命区间分析

doi:10.13229/j.cnki.jdxbgxb20200502

摘要/Abstract

摘要：

传统的概率方法分析结构疲劳寿命时，需要大量的样本以确定随变量的概率密度分布，而且概率密度函数较小的误差将会引起结构疲劳寿命较大的误差。针对这种情况，提出了一种随机载荷作用下结构疲劳寿命的区间分析模型。将影响结构疲劳寿命的不确定因素视为区间变量，给出了随机载荷作用下结构疲劳寿命的降维表达式，结合区间数学方法，得到了结构疲劳寿命的上限和下限。数值算例表明，与Taylor方法相比，基于降维算法的结构疲劳寿命区间分析方法具有较高的精度。对于强度极限和疲劳参数而言，一阶降维算法和二阶Taylor方法精度相当；而对于疲劳载荷，当其变化范围较大时，Taylor方法已经不能满足精度要求，而二阶降维算法仍然具有较高的计算精度和稳定性，其计算精度在一定范围内和遗传算法大致相当，但计算效率却远高于遗传算法。

关键词: 工程力学, 疲劳寿命, 随机载荷, 区间分析, 降维算法, Taylor展开法

Abstract:

Traditional probabilistic methods require large number of samples to determine the probability density distribution of the dependent variable when analyzing the fatigue life of structures， and a small error in the probability density function will cause a large error in the fatigue life of the structure. To solve this problem， an interval analysis model for structural fatigue life under random loads were proposed. The uncertain factors that affect the fatigue life of the structure were regarded as interval variables. The dimensionality reduction expression of the fatigue life of the structure under random load was given. Combined with the interval mathematical method， the upper and lower limits of the fatigue life of the structure were obtained. Numerical examples show that compared with the Taylor method， the structural fatigue life interval analysis method based on dimensionality reduction algorithm proposed in this paper has higher accuracy. For the strength limit and fatigue parameters， the first-order dimensionality reduction algorithm has almost the same accuracy compared with the second-order Taylor method. For fatigue loads， when the variation range is large， the Taylor method cannot meet the accuracy requirements， but the second-order dimensionality reduction algorithm is still steady. It has high calculation accuracy and stability. Its calculation accuracy is roughly equivalent to genetic algorithm within a certain range， but the calculation efficiency is much higher than that of the genetic algorithm.

Key words: engineering mechanics, fatigue life, random load, interval analysis, dimensionality reduction algorithm, Taylor expansion

中图分类号:

TP202.1

孟广伟,任传鑫,李锋,魏彤辉. 随机载荷作用下的结构疲劳寿命区间分析[J]. 吉林大学学报(工学版), 2022, 52(1): 46-52.

Guang-wei MENG,Chuan-xin REN,Feng LI,Tong-hui WEI. Interval analysis of structural fatigue life under random load[J]. Journal of Jilin University(Engineering and Technology Edition), 2022, 52(1): 46-52.

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β_q	MCS	二阶降维算法		遗传算法
β_q	中值/10⁵	中值/10⁵	误差/%	中值/10⁵	误差/%
0.025	2.006	2.005	0.0	2.003	0.1
0.050	2.164	2.162	0.1	2.161	0.1
0.075	2.423	2.419	0.2	2.413	0.4
0.100	2.801	2.790	0.4	2.790	0.4
0.125	3.325	3.302	0.7	3.298	0.8
0.150	4.033	3.992	1.0	4.001	0.8
0.175	4.980	4.909	1.4	4.942	0.8
0.200	6.240	6.126	1.8	6.192	0.8