一种新的结构疲劳寿命分析的概率-模糊-区间混合模型
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摘要
为解决混合变量下的结构疲劳寿命分析问题,建立了同时含有概率、模糊、区间变量的结构疲劳寿命分析模型,采取对模型中的模糊变量取截集的方法,使模糊变量退化为相应的区间向量,相当于将问题化为仅含有随机变量和区间变量的结构疲劳寿命分析问题。依照概率和非概率寿命分析方法得到在截集水平α下的随机变量为自变量的疲劳寿命下限估计值表达式,采用数值积分的方式得到只含有随机变量的结构疲劳寿命上、下限值表达式,最后根据概率疲劳寿命分析方法可以得到一定置信度下的寿命上、下限值。算例结果表明:本文方法能够解决含概率-模糊-区间混合变量的结构疲劳寿命分析问题,不仅拓展了非概率在疲劳寿命分析中的应用范围,也是对非概率疲劳寿命分析方法的理论补充。
In this paper, a structural fatigue life analysis model with consideration of probability, fuzzy and interval variables is established to solve the structural fatigue life analysis problem under mixed variables. Taking the set of fuzzy variables in the model, the fuzzy variable is degraded to the corresponding interval vector. By making the fuzzy variables reduce to interval variables, the problem is transformed into structural fatigue life analysis with random variables and interval variables. According to the probabilistic and non-probabilistic life analysis method, the random variable under α-level is obtained as the independent variable fatigue life lower limit estimation expression, the upper and lower limit expressions of structural fatigue life with random variables are obtained by means of numerical integration. Finally, according to the probabilistic fatigue life analysis method, the upper and lower limits of life can be obtained under certain confidence. The experimental results show that this method can solve the problem of structural fatigue life analysis with probability-fuzzy-interval mixed variables, and this method not only extends the application of non-probabilities in fatigue life analysis, but also provides the theoretical supplement for the non-probabilistic fatigue life analysis.
In this paper, a structural fatigue life analysis model with consideration of probability, fuzzy and interval variables is established to solve the structural fatigue life analysis problem under mixed variables. Taking the set of fuzzy variables in the model, the fuzzy variable is degraded to the corresponding interval vector. By making the fuzzy variables reduce to interval variables, the problem is transformed into structural fatigue life analysis with random variables and interval variables. According to the probabilistic and non-probabilistic life analysis method, the random variable under α-level is obtained as the independent variable fatigue life lower limit estimation expression, the upper and lower limit expressions of structural fatigue life with random variables are obtained by means of numerical integration. Finally, according to the probabilistic fatigue life analysis method, the upper and lower limits of life can be obtained under certain confidence. The experimental results show that this method can solve the problem of structural fatigue life analysis with probability-fuzzy-interval mixed variables, and this method not only extends the application of non-probabilities in fatigue life analysis, but also provides the theoretical supplement for the non-probabilistic fatigue life analysis.
引文
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[11]陈小月,卿启湘,刘杰,等.基于概率-模糊-区间不确定量的结构混合可靠度泛灰求解方法[C]//第十五届全国非线性振动暨第十二届全国非线性动力学和运动稳定性学术会术会议摘要集.长沙:中国振动工程学会非线性专业委员会,2015.(CHEN Xiaoyue,QING Qixiang,LIU Jie,et al.Preparation of mixed-reliability gray-gray method based on probability-fuzzy-interval uncertainty[C]//Proceedings of the 15th National Conference on Nonlinear Vibration and the Twelfth National Conference on Nonlinear Dynamics and Motion Stability Abstructs.Changsha:China Society of Vibration Engineering Non-linear Professional Committee,2015(in Chinese)).
[12]NI Z,QIU Z.Hybrid probabilistic fuzzy and non-probabilistic model of structural reliability[J].Computers&industrial engineering,2010,58(3):463-467.
[2]钟全飞.概率疲劳寿命预测方法及可靠性分析[D].成都:电子科技大学,2013.(ZHONG Quanfei.Probability fatigue life prediction method and reliability analysis[D].Chengdu:University of Electronic Science and Technology,2013(in Chinese)).
[3]ELISHAKOFF I.Essay on uncertainties in elastic and viscoelastic structures:from A.M.Freudenthal’s criticisms to modern convex modeling[J].Computers&structures,1995,56(6):871-895.
[4]邱志平,王晓军.结构疲劳寿命的区间估计[J].力学学报,2005,37(5):653-657.(QIU Zhiping,WANG Xiaojun.Interval estimation of fatigue life of structures[J].Acta mechanica sinica,2005,37(5):653-657(in Chinese)).
[5]邱志平,王晓军,马智博.结构疲劳寿命估计的集合理论模型[J].固体力学学报,2006,27(1):91-97.(QIU Zhiping,WANG Xiaojun,MA Zhibo.A set theory model for fatigue life estimation of structures[J].Journal of Chinese society for solid mechanics,2006,27(1):91-97(in Chinese)).
[6]孙文彩,杨自春,李昆锋.结构疲劳寿命分析模糊凸集模型[J].固体力学学报,2013,34(2):200-204.(SUN Wencai,YANG Zichun,LI Kunfeng.Fuzzy convex set model for structural fatigue life analysis[J].Journal of solid mechanics,2013,34(2):200-204(in Chinese)).
[7]曹珊珊,雷俊卿.考虑区间不确定性的钢结构疲劳寿命分析[J].吉林大学学报(工学版),2016,46(3):166-187.(CAO Shanshan,LEI Junqing.Analysis of fatigue life of steel structures considering interval uncertainties[J].Journal of Jilin university(engineering edition and technology),2016,46(3):166-187(in Chinese)).
[8]魏宗平.结构疲劳裂纹扩展寿命的区间预测[J].机床与液压,2013,41(15):61-64.(WEI Zongping.Interval prediction of structure fatigue crack propagation life[J].Machine tool and hydraulics,2013,41(15):61-64(in Chinese)).
[9]孙文彩,杨自春.含裂纹压力容器混合变量下疲劳剩余寿命分析[J].压力容器,2010,27(1):17-20.(SUN Wencai,YANG Zichun.Analysis of fatigue residual life under mixed variable crack pressure vessel[J].Pressure vessel,2010,27(1):17-20(in Chinese)).
[10]宋利锋,邱志平.含模糊-区间变量的结构非概率可靠性优化设计[J].工程力学,2013,30(6):36-40.(SONG Lifeng,QIU Zhiping.Design of nonprobility reliability of structures with fuzzy-interval variables[J].Engineering mechanics,2013,30(6):36-40(in Chinese)).
[11]陈小月,卿启湘,刘杰,等.基于概率-模糊-区间不确定量的结构混合可靠度泛灰求解方法[C]//第十五届全国非线性振动暨第十二届全国非线性动力学和运动稳定性学术会术会议摘要集.长沙:中国振动工程学会非线性专业委员会,2015.(CHEN Xiaoyue,QING Qixiang,LIU Jie,et al.Preparation of mixed-reliability gray-gray method based on probability-fuzzy-interval uncertainty[C]//Proceedings of the 15th National Conference on Nonlinear Vibration and the Twelfth National Conference on Nonlinear Dynamics and Motion Stability Abstructs.Changsha:China Society of Vibration Engineering Non-linear Professional Committee,2015(in Chinese)).
[12]NI Z,QIU Z.Hybrid probabilistic fuzzy and non-probabilistic model of structural reliability[J].Computers&industrial engineering,2010,58(3):463-467.