结构中的构件可靠度分析方法研究
发布时间：2018-08-24 14:00
【摘要】：组成结构系统的各构件的可靠度称为结构系统中的构件可靠度，简称为结构中构件可靠度。本文主要研究结构中的构件功能函数不能够表示为影响单元功能的基本随机变量的显式函数时构件可靠度，又称为结构单元可靠度。传统的一次二阶矩方法计算可靠度时需要求解功能函数的偏导数，因此不能够直接用于求解隐式功能函数结构单元的可靠度。经典可靠度计算方法中能够处理隐式功能函数的方法主要包括蒙特卡洛法、响应面法和矩方法。 目前有学者提出了基于有限元的嵌入式算法和分离式算法用于计算结构单元可靠度。虽然说嵌入式算法和分离式算法在理论上是可行的，但是在实际运用中存在很多困难，本文提出了基于有限元的蒙特卡洛法、响应面法和矩方法。 基于有限元的蒙特卡洛法适用范围广泛，计算结果可靠，其结果可以作为近似的精确解。与蒙特卡洛法相比，，基于有限元的响应面法和矩方法计算结果相对误差均较小，能够满足工程可靠度计算的精度要求。蒙特卡洛法计算可靠指标所需时间代价随着杆件可靠指标的增加而增加，求解时间依赖于可靠指标结果。相对的，响应面法和矩方法则不存在这一问题，与蒙特卡洛法相比具有明显的计算效率。当工程结构复杂，杆件增多时，响应面法需要对每个杆件构造响应面函数，计算变得更加复杂。与响应面法相比，矩方法在求解可靠指标的过程中时间代价更低，能够一次性求解所有单元的可靠指标。基于有限元的矩方法是最为简便的方法，最适合于工程结构的单元可靠度计算。 本文编写了基于矩方法的结构梁柱单元可靠度计算专用程序，该程序通用性较强，对于不同工程结构仅需对程序稍加改动即可用于计算结构单元可靠指标。利用以上程序计算了钢框架结构梁柱单元的可靠指标。
[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.
【学位授予单位】：重庆大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TU311.2
本文编号：2201039
[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.
【学位授予单位】：重庆大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TU311.2
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本文编号：2201039
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