二维弹性随机边界元与可靠性分析

本文利用对随机变量求偏导数的方法，推导了二维弹性随机边界积分方程及其相应的公式，考虑了随机边界条件、材料性能参数随机量以及几何尺寸随机因素等。本文还将所发展的方法用于结构静强度的可靠性分析。算例分析表明，本文数值结果与ＭｏｎｔｅＣａｒｌｏ模拟和理论解相比是十分满意的。

2-D Elastic Stochastic Boundary Element Methods and the Analysis of Reliability

The integral equations of stochastic boundary element methods(SBEM)for 2-D elastic problemsand the corresponding for mula are de rived in this paper with the help of the partial derivative tech-niques to fundamental stochastic variables,including stochastic boundary conditions,stochastic geo-metric dimensions,stochastic elastic modulus and poisson ratios,The method developed in this paper isalso used to analyze the reliability of the safety strength of com ponents,and the corresponding for mu-las are derived. The effects of the discrete distributions of stochastic loads or stochastic elastic modulusas well as poisson ratias on the parameters of failure points and the reliability are discussed separately.Compared with Monte Carlo and theoretical results,those in this paper are satisfactory.