基于仿射算法的不确定性结构区间非概率可靠性分析
发布时间：2019-04-20 09:33
【摘要】：在实际的工程应用中结构的性能受多方面的不确定性因素和误差的影响,如结构的材料参数、载荷或几何参数等不确定性。为了确保结构在规定的使用环境和使用条件下,在给定的使用寿命期间和环境下有效地承受载荷而正常工作,对其进行必要的可靠性分析显得尤为重要。为了建立合理的可靠性分析模型,确保可靠性分析结果的有效性,在结构分析的过程中必须采用合适的处理方法来处理这些不确定性因素。目前处理这类不确定性问题常用的方法可以分为概率可靠性分析与非概率可靠性分析,但是概率可靠性分析方法对于统计信息有较强的依赖,这与实际工程应用中可得数据的有限性矛盾,因此在一定程度上限制了该种方法的实际应用。而作为另一种分析方法,非概率可靠性分析方法恰好可以弥补这一不足。本学位论文首先以区间参数与未确知参数结构为研究对象,探索性研究了当结构参数和外载荷为区间变量或未确定变量时采用区间算法嵌入仿射算术的方法对结构进行非概率可靠性分析以及静力区间位移响应分析。其主要内容如下：(1)首先介绍了有关区间数学、区间有限元与仿射算法的基本理论,针对机械结构设计中关于不确定性参数统计较少的情况,将主要影响结构非概率可靠性分析的因素用区间变量来表达,建立一种新的结构分析的可靠性模型。(2)针对有限元分析求解过程中出现的区间扩张间题,分析了区间截断法、子区间摄动法、迭代法等几种求解区间有限元模型的方法,由于仿射算法具有限制区间扩张现象的优点,故在本文中最终采取将仿射算法引入到区间有限元中来求解有限元静力位移响应间题,并通过改变结构外载荷、材料参数的不确定度来确定结构所受外载荷以及材料参数不确定性对结构的可靠度的影响。(3)将仿射算术思想引入到非概率可靠性指标计算当中,并为了得到更高精度要求的结果,将区间逐步分离法与仿射算法相结合形成了基于仿射形式的区间逐步分离法,将该方法应用于工程算例,并将所得结果与采用其他方法所得结果对比分析验证了该方法的正确性,同时将本文提出的基于仿射形式的区间逐步分离法、区间算法、仿射算法分别应用于工程算例结果对比分析验证了该方法的优越性。
[Abstract]:In practical engineering applications, the performance of the structure is affected by many uncertainties and errors, such as the uncertainty of material parameters, loads or geometric parameters of the structure. In order to ensure the normal operation of the structure under the specified service environment and service conditions and under the given service life period and environment, it is very important to carry out the necessary reliability analysis of the structure. In order to establish a reasonable reliability analysis model and ensure the validity of reliability analysis results, it is necessary to adopt appropriate methods to deal with these uncertainties in the process of structural analysis. At present, the methods commonly used to deal with this kind of uncertainty can be divided into probabilistic reliability analysis and non-probabilistic reliability analysis, but the probabilistic reliability analysis method has a strong dependence on statistical information. This is in contradiction with the limitation of available data in practical engineering applications, so the practical application of this method is limited to a certain extent. As another analysis method, the non-probabilistic reliability analysis method can make up for this deficiency. Firstly, the structure of interval parameter and unascertained parameter is taken as the research object of this dissertation. The non-probabilistic reliability analysis and static interval displacement response analysis of the structure are studied by embedding affine arithmetic into the interval algorithm when the structural parameters and external loads are interval variables or uncertain variables. The main contents are as follows: (1) the basic theories of interval mathematics, interval finite element method and affine algorithm are introduced firstly. The main factors influencing structural non-probabilistic reliability analysis are expressed as interval variables, and a new reliability model of structural analysis is established. (2) aiming at the interval expansion problem in the process of finite element analysis and solving, a new reliability model of structural analysis is established. Several methods for solving interval finite element model, such as interval truncation method, subinterval perturbation method and iterative method, are analyzed. Because affine algorithm has the advantage of limiting interval expansion phenomenon, In this paper, the affine algorithm is finally introduced into the interval finite element method to solve the static displacement response problem of the finite element, and by changing the external load of the structure, the problem of the static displacement response of the finite element is solved. The uncertainty of the material parameters is used to determine the external load of the structure and the influence of the uncertainty of the material parameters on the reliability of the structure. (3) the affine arithmetic is introduced into the calculation of the non-probabilistic reliability index. In order to obtain the higher precision result, the interval stepwise separation method is combined with affine algorithm to form the interval stepwise separation method based on affine form, and the method is applied to engineering examples. The results obtained by this paper are compared with those obtained by other methods, and the correctness of the method is verified. At the same time, the interval step-by-step separation method and interval algorithm based on affine form are proposed in this paper. The advantages of the method are verified by comparing the results of the affine algorithm in engineering examples.
【学位授予单位】：西安电子科技大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TB114.3
本文编号：2461488
[Abstract]:In practical engineering applications, the performance of the structure is affected by many uncertainties and errors, such as the uncertainty of material parameters, loads or geometric parameters of the structure. In order to ensure the normal operation of the structure under the specified service environment and service conditions and under the given service life period and environment, it is very important to carry out the necessary reliability analysis of the structure. In order to establish a reasonable reliability analysis model and ensure the validity of reliability analysis results, it is necessary to adopt appropriate methods to deal with these uncertainties in the process of structural analysis. At present, the methods commonly used to deal with this kind of uncertainty can be divided into probabilistic reliability analysis and non-probabilistic reliability analysis, but the probabilistic reliability analysis method has a strong dependence on statistical information. This is in contradiction with the limitation of available data in practical engineering applications, so the practical application of this method is limited to a certain extent. As another analysis method, the non-probabilistic reliability analysis method can make up for this deficiency. Firstly, the structure of interval parameter and unascertained parameter is taken as the research object of this dissertation. The non-probabilistic reliability analysis and static interval displacement response analysis of the structure are studied by embedding affine arithmetic into the interval algorithm when the structural parameters and external loads are interval variables or uncertain variables. The main contents are as follows: (1) the basic theories of interval mathematics, interval finite element method and affine algorithm are introduced firstly. The main factors influencing structural non-probabilistic reliability analysis are expressed as interval variables, and a new reliability model of structural analysis is established. (2) aiming at the interval expansion problem in the process of finite element analysis and solving, a new reliability model of structural analysis is established. Several methods for solving interval finite element model, such as interval truncation method, subinterval perturbation method and iterative method, are analyzed. Because affine algorithm has the advantage of limiting interval expansion phenomenon, In this paper, the affine algorithm is finally introduced into the interval finite element method to solve the static displacement response problem of the finite element, and by changing the external load of the structure, the problem of the static displacement response of the finite element is solved. The uncertainty of the material parameters is used to determine the external load of the structure and the influence of the uncertainty of the material parameters on the reliability of the structure. (3) the affine arithmetic is introduced into the calculation of the non-probabilistic reliability index. In order to obtain the higher precision result, the interval stepwise separation method is combined with affine algorithm to form the interval stepwise separation method based on affine form, and the method is applied to engineering examples. The results obtained by this paper are compared with those obtained by other methods, and the correctness of the method is verified. At the same time, the interval step-by-step separation method and interval algorithm based on affine form are proposed in this paper. The advantages of the method are verified by comparing the results of the affine algorithm in engineering examples.
【学位授予单位】：西安电子科技大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TB114.3
【参考文献】
相关硕士学位论文 前1条
1 魏宗平;机械非概率可靠性分析与可靠性优化设计研究[D];西安电子科技大学;2006年
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