随机桁架结构可靠性分析的完全概率方法

Analysis of reliability of stochastic truss structure based on full-probability

提出了一种求解随机参数桁架结构在随机荷载作用下反应的概率密度函数和结构精确可靠度的方法。通过对随机参数桁架结构在随机荷载作用下的有限元分析方法的研究,考虑了结构的物理参数,构件的几何尺寸和作用荷载幅值等的随机性。应用随机向量函数的概率分布函数表达式,通过确定积分区间、变量替换、交换积分顺序等一系列数学上的处理,获得所求结构反应的概率密度函数。由干涉理论得到了结构位移和应力的可靠度。通过算例的结果与Monte-Car-lo模拟法结果比较,表明该方法具有较高的精度及良好的实用性。

The present paper aims to propose a new method for analyzing statics and reliability of the stochastic truss structural response under random loading based on the analysis of full-probability. As is known, it is necessary to take into full account all the stochastic factors of the structural physical parameters along with the geometrical dimensions and the stochastic loads applied on such structure in the study of the truss structural response analysis. The probability density function for the stochastic truss structural responses can only be obtained by determining the limits of integration as well as substitution of the variables, Then a precise reliability analysis for the displacement and stress has been done. In the end of the paper, two examples are to be illustrated to explain the present method. A comparison of its results gained by the new method with the results given by the Monte-Carlo method shows that the proposed method is of high accuracy and feasibility, regardless of the different distribution types. Therefore, it can be pointed out that： （1） when the physical parameters and the loading are all in normal random variables, the structural responses obtained by our method will be a normal variable too. However, if the physical parameters and the loading are not in normal random variables, the structural responses obtained shall never be any more normal again. In this case, the mean and the variance of the responses can not characterize the probability distribution for the responses, and we can not get accurate structural reliability by using the First Order Square method or Hasofer-Lind method or Rackwitz-Fiesser method. It is necessary to do more accurate calculation so as to get an accurate structural reliability. （2） Our method is only directed against reliability of a node or an element in the structure, therefore, the method based on full-probability for calculating the whole structure reliability is worth further study.