应力极值分布、强度威布尔分布的可靠性

Reliability of Extreme Value Distributed Stress and Weibull Distributed Strength

本文运用应力—强度干涉理论,推导了应力为Ⅰ型极小值分布,强度为威布尔分布的可靠度计算公式,并对冗长的计算公式进行简化,在简化公式的基础上,运用一定的数学技巧,改变积分公式中的积分变量和上下限。将被积函数化成在某一区域内的可积函数。采用de Boor编制的一种严谨的自适应Romberg外推格式的FORTRAN程序进行数值积分。对应予不同的组合参数,给出应力服从Ⅰ型极小值分布,强度服从威布尔分布的可靠度数值。本文最后讨论了服从这两种分布的组合参数的变化对可算度数值变化的影响。

In this paper the interference theory of stress-strength is applied to drive the reliability computation equation for type I minimum distributed stress and Weibull distributed strength. The lengthy equation is then simplified. On the basis of it, a paticular mathematical technique is used to change the integrated variable of the integrand and its upper and lo-wer bounds. The integrand is changed into a regional integrable function, which may be calculated with a FORTRAN program written by de Boor. This is a strict and automatical fit Romberg numerical integration method. For different values of the parameters, numerical relibilities are given to the type I minimum distributed stress and the Weibull distributed strength. At the end of this paper, the effect of numerical changes of relibility is discussed that obeys the change of the combined parameters of the two distributions.