【摘要】：組成結(jié)構(gòu)系統(tǒng)的各構(gòu)件的可靠度稱為結(jié)構(gòu)系統(tǒng)中的構(gòu)件可靠度，簡(jiǎn)稱為結(jié)構(gòu)中構(gòu)件可靠度。本文主要研究結(jié)構(gòu)中的構(gòu)件功能函數(shù)不能夠表示為影響單元功能的基本隨機(jī)變量的顯式函數(shù)時(shí)構(gòu)件可靠度，又稱為結(jié)構(gòu)單元可靠度。傳統(tǒng)的一次二階矩方法計(jì)算可靠度時(shí)需要求解功能函數(shù)的偏導(dǎo)數(shù)，因此不能夠直接用于求解隱式功能函數(shù)結(jié)構(gòu)單元的可靠度。經(jīng)典可靠度計(jì)算方法中能夠處理隱式功能函數(shù)的方法主要包括蒙特卡洛法、響應(yīng)面法和矩方法。 目前有學(xué)者提出了基于有限元的嵌入式算法和分離式算法用于計(jì)算結(jié)構(gòu)單元可靠度。雖然說嵌入式算法和分離式算法在理論上是可行的，但是在實(shí)際運(yùn)用中存在很多困難，本文提出了基于有限元的蒙特卡洛法、響應(yīng)面法和矩方法。 基于有限元的蒙特卡洛法適用范圍廣泛，計(jì)算結(jié)果可靠，其結(jié)果可以作為近似的精確解。與蒙特卡洛法相比，，基于有限元的響應(yīng)面法和矩方法計(jì)算結(jié)果相對(duì)誤差均較小，能夠滿足工程可靠度計(jì)算的精度要求。蒙特卡洛法計(jì)算可靠指標(biāo)所需時(shí)間代價(jià)隨著桿件可靠指標(biāo)的增加而增加，求解時(shí)間依賴于可靠指標(biāo)結(jié)果。相對(duì)的，響應(yīng)面法和矩方法則不存在這一問題，與蒙特卡洛法相比具有明顯的計(jì)算效率。當(dāng)工程結(jié)構(gòu)復(fù)雜，桿件增多時(shí)，響應(yīng)面法需要對(duì)每個(gè)桿件構(gòu)造響應(yīng)面函數(shù)，計(jì)算變得更加復(fù)雜。與響應(yīng)面法相比，矩方法在求解可靠指標(biāo)的過程中時(shí)間代價(jià)更低，能夠一次性求解所有單元的可靠指標(biāo)�；谟邢拊木胤椒ㄊ亲顬楹�(jiǎn)便的方法，最適合于工程結(jié)構(gòu)的單元可靠度計(jì)算。 本文編寫了基于矩方法的結(jié)構(gòu)梁柱單元可靠度計(jì)算專用程序，該程序通用性較強(qiáng)，對(duì)于不同工程結(jié)構(gòu)僅需對(duì)程序稍加改動(dòng)即可用于計(jì)算結(jié)構(gòu)單元可靠指標(biāo)。利用以上程序計(jì)算了鋼框架結(jié)構(gòu)梁柱單元的可靠指標(biāo)。
[Abstract]:The reliability of each component in a structural system is called the reliability of the component in a structural system, which is referred to as the reliability of a component in a structure. In this paper, the component function in the structure can not be expressed as an explicit function of the basic random variable that affects the function of the element, and the reliability of the component is also called the reliability of the structural element. The traditional first-order second-moment method needs to solve the partial derivative of the function, so it can not be directly used to solve the reliability of the implicit functional function structural element. The classical reliability calculation methods can deal with implicit function mainly including Monte Carlo method, response surface method and moment method. At present, some scholars put forward the embedded algorithm based on finite element and the separate algorithm to calculate the reliability of structural element. Although embedded algorithm and split algorithm are feasible in theory, there are many difficulties in practical application. In this paper, Monte Carlo method, response surface method and moment method based on finite element are proposed. The Monte Carlo method based on finite element method has a wide range of applications and reliable calculation results, which can be used as approximate exact solutions. Compared with Monte Carlo method, the response surface method based on finite element method and the moment method have smaller relative errors, which can meet the accuracy requirements of engineering reliability calculation. The time cost of calculating reliability index by Monte Carlo method increases with the increase of reliability index of member, and the solution time depends on the result of reliability index. On the other hand, the response surface method and the moment method do not have this problem, and have obvious computational efficiency compared with the Monte Carlo method. When the engineering structure is complex and the number of bars increases, the response surface method needs to construct a response surface function for each member, and the calculation becomes more complicated. Compared with the response surface method, the time cost of the moment method is lower than that of the response surface method, and it can solve the reliability index of all the elements at one time. The moment method based on finite element is the most convenient method and is most suitable for the element reliability calculation of engineering structures. In this paper, a special program for calculating the reliability of structure Liang Zhu element based on moment method is developed. The program has strong generality, and it can be used to calculate the reliability index of structure unit only with minor modification of the program for different engineering structures. The reliability index of Liang Zhu element of steel frame structure is calculated by using the above program.
【學(xué)位授予單位】：重慶大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類號(hào)】：TU311.2

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本文編號(hào)：2201039