【作者】 吕玺琳；

【导师】 吕恩琳；

【作者基本信息】 重庆大学 ， 固体力学， 2005， 硕士

【摘要】 复杂工程结构中模糊性和随机性常同时存在,常规可靠性分析模型已不能满足日益复杂的工程结构系统分析需要,且在某些问题上由于不恰当地使用常规可靠性理论使结果与实际不一致。本文系统地建立了结构构件模糊可靠性分析模型,对抗力、载荷分别为确定性量、随机性量、模糊性量、模糊随机性量的各种组合进行分析,并成功地将模糊可靠性模型推广到结构系统模糊可靠性分析中。首先研究模糊有限元和模糊随机有限元的求解,利用分解定理,取一系列λ水平截集,将模糊变量转换为一系列区间变量,利用区间有限元及区间运算法则,求出结构响应的区间解。研究表明将所得区间解代入模糊可靠性分析模型,求结构构件模糊可靠度各λ水平截集下的区间解是可行的。当结构的基本变量有模糊随机性时,得到的结构构件可靠度也是模糊的,这样的处理为结构系统可靠性分析保留了中间过程的模糊性。对结构灵敏度分析的研究表明可靠性分析中的模糊性是不能忽略的。对结构构件模糊可靠度的两种算法的研究表明:(1)直接积分法简单明了,适用于基本随机变量较少,概率分布模型简单时的情况,在某些情况下,应力和抗力具有随机性和模糊性时构件安全隶属函数可以直接构造;(2)通过变换,将模糊事件转换为普通事件的概率来求解更具有通用性,取模糊事件的一系列λ水平截集,得到各水平截集下对应的可靠度区间值,利用这些区间结果,既能估算构件模糊可靠度值,也能直接代入系统可靠度计算中;(3)当应力和抗力都是随机变量,而其均值和方差具有模糊性时,取其各λ水平截集,将得到的区间值代入一次二阶矩法计算,得到模糊可靠性指标β~ 各λ水平截集下对应的区间值,利用这些结果可以得到可靠度的估计值。　通过对结构系统模糊可靠度计算的研究,得出了结构系统模糊可靠度的一般计算表达式,串联、并联及混联系统的计算公式。在此基础上,进一步研究了基于β约界法的结构系统模糊可靠度计算。研究结果表明,将构件模糊可靠度计算得到的一系列λ水平截集下对应的区间解直接代入结构系统模糊可靠性分析模型是可行的,既保留了中间计算过程的模糊性,使分析结果更准确,又充分利用常规可靠性模型中已有的方法。具体算例表明,本文提出的模糊可靠度计算方法是正确可行、符合工程实际的,且计算量与常规情形大致相当。更多还原

【Abstract】 Due to the stochastic and fuzzy variables in structural system reliability analysis, itis difficult to use normal model to calculate the reliability, even in some cases, the resultobtained from normal model is false. In this paper, the properties of uncertain variablesare systematically analyzed, and a series of methods are represented to calculate thefuzzy reliability of structural component and system.Firstly, investigate the computation of fuzzy FEM(finite element method) andfuzzy stochastic FEM, utilize λcut, and use interval FEM and interval algorithm, aseries of interval answers obtained, and thenλcut fuzzy reliability obtained. Whenbasic variables are fuzzy stochastic numbers, the reliability of structural component isalso fuzzy number, this consideration holds the fuzzy character in midst process, andensures the accuracy of final result.The research of structural fuzzy sensitivity shows that the fuzzy characters can notbe neglected. The research of two methods shows: (1)The direct integral method issimple, safety subjective function could be constructed in some case, but it is onlysuitable for some simple circumstance; (2)Using counterchange, fuzzy affair changedinto normal affair, get λcut of fuzzy affair and fuzzy parameters, a series intervalnumbers obtained, these interval numbers could be used in the calculation of componentreliability, and also be used in estimating the reliability of system; (3)When stress andstrength are stochastic numbers ,but their means and variances are fuzzy numbers, gettheir λcut number,　take them into first order and second moment method, intervalnumber of fuzzy reliability index obtained, use these numbers,thereliability obtained.Common expression of structural system fuzzy reliability is educed in this paper,include serial structural system, parallel structural system and serial parallel structuralsystem, and an applicable method is represented which based onβ-Unzipping method.Result shows that to insert the λcut number result obtained from structural componentreliability analysis in the calculation of system reliability not only make the result moreaccurate, but also make the best of way in normal model. Example indicates the way putforward in this paper is rational, feasible, effective and suitable for engineering, and itscomputation almost equals to normal model.更多还原