用摄动法研究几何尺寸为随机量时轮盘的可靠性

PERTURBATION TECHNIQUE FOR RELIABILITY ANALYSIS OF A ROTATING DISK WITH UNCERTAIN GEOMETRY

几何尺寸和材料性质等的随机性都影响结构的可靠性。本文提出用建立在二阶摄动法基础上的概率有限元来分析轮盘的几何形状不确定时的随机应力场和可靠性，研究用摄动方法处理问题的基本思路，推导随机应力场和可靠度的计算公式，用简单算例分析讨论了几何尺寸对可靠性的影响规律，算例结果与ＭｏｎｔｅＣａｒｌｏ模拟结果的对比表明本文的方法有效，理论正确。

Design methods for the aerospace technology are,in general,based on deterministic parameters.In paractice there always exist random deviations of parameters,such as material properties and geometry,forces,and boundary conditions.In most situations the random deviations are small,but their overall effect can have a strong impact on behaviours of critical components,particularly in failure and reliablility analysis.For this reason a probabilistic finite element method based on second order perturbation technique is used to analyze the reliabilty and the random stresses of a rotating disk with uncertain geometery,the elementary perturbation approach to this problem has been studied and formulas for the random stress and the reliability have been deduced.The effect of uncertain geometery on the reliability is considered by a simple numerical example.The accuracy and efficiency of the method is demonstrated by its application to a rotating disk with uncertain geometery.The reliability calculated by this method compares favorably with that obtained from Monte Carlo simulation.