【摘要】：在實(shí)際的工程應(yīng)用中結(jié)構(gòu)的性能受多方面的不確定性因素和誤差的影響,如結(jié)構(gòu)的材料參數(shù)、載荷或幾何參數(shù)等不確定性。為了確保結(jié)構(gòu)在規(guī)定的使用環(huán)境和使用條件下,在給定的使用壽命期間和環(huán)境下有效地承受載荷而正常工作,對(duì)其進(jìn)行必要的可靠性分析顯得尤為重要。為了建立合理的可靠性分析模型,確�？煽啃苑治鼋Y(jié)果的有效性,在結(jié)構(gòu)分析的過(guò)程中必須采用合適的處理方法來(lái)處理這些不確定性因素。目前處理這類不確定性問(wèn)題常用的方法可以分為概率可靠性分析與非概率可靠性分析,但是概率可靠性分析方法對(duì)于統(tǒng)計(jì)信息有較強(qiáng)的依賴,這與實(shí)際工程應(yīng)用中可得數(shù)據(jù)的有限性矛盾,因此在一定程度上限制了該種方法的實(shí)際應(yīng)用。而作為另一種分析方法,非概率可靠性分析方法恰好可以彌補(bǔ)這一不足。本學(xué)位論文首先以區(qū)間參數(shù)與未確知參數(shù)結(jié)構(gòu)為研究對(duì)象,探索性研究了當(dāng)結(jié)構(gòu)參數(shù)和外載荷為區(qū)間變量或未確定變量時(shí)采用區(qū)間算法嵌入仿射算術(shù)的方法對(duì)結(jié)構(gòu)進(jìn)行非概率可靠性分析以及靜力區(qū)間位移響應(yīng)分析。其主要內(nèi)容如下：(1)首先介紹了有關(guān)區(qū)間數(shù)學(xué)、區(qū)間有限元與仿射算法的基本理論,針對(duì)機(jī)械結(jié)構(gòu)設(shè)計(jì)中關(guān)于不確定性參數(shù)統(tǒng)計(jì)較少的情況,將主要影響結(jié)構(gòu)非概率可靠性分析的因素用區(qū)間變量來(lái)表達(dá),建立一種新的結(jié)構(gòu)分析的可靠性模型。(2)針對(duì)有限元分析求解過(guò)程中出現(xiàn)的區(qū)間擴(kuò)張間題,分析了區(qū)間截?cái)喾ā⒆訁^(qū)間攝動(dòng)法、迭代法等幾種求解區(qū)間有限元模型的方法,由于仿射算法具有限制區(qū)間擴(kuò)張現(xiàn)象的優(yōu)點(diǎn),故在本文中最終采取將仿射算法引入到區(qū)間有限元中來(lái)求解有限元靜力位移響應(yīng)間題,并通過(guò)改變結(jié)構(gòu)外載荷、材料參數(shù)的不確定度來(lái)確定結(jié)構(gòu)所受外載荷以及材料參數(shù)不確定性對(duì)結(jié)構(gòu)的可靠度的影響。(3)將仿射算術(shù)思想引入到非概率可靠性指標(biāo)計(jì)算當(dāng)中,并為了得到更高精度要求的結(jié)果,將區(qū)間逐步分離法與仿射算法相結(jié)合形成了基于仿射形式的區(qū)間逐步分離法,將該方法應(yīng)用于工程算例,并將所得結(jié)果與采用其他方法所得結(jié)果對(duì)比分析驗(yàn)證了該方法的正確性,同時(shí)將本文提出的基于仿射形式的區(qū)間逐步分離法、區(qū)間算法、仿射算法分別應(yīng)用于工程算例結(jié)果對(duì)比分析驗(yàn)證了該方法的優(yōu)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.
【學(xué)位授予單位】：西安電子科技大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類號(hào)】：TB114.3

【參考文獻(xiàn)】

相關(guān)碩士學(xué)位論文 前1條

1 魏宗平;機(jī)械非概率可靠性分析與可靠性優(yōu)化設(shè)計(jì)研究[D];西安電子科技大學(xué);2006年

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本文編號(hào)：2461488