中文摘要：

基于随机有限元的思想，提出了一种求解缺口根部最大应力概率分布的方法。该方法通过对应力表达式的Taylor展开，将影响应力分布的因素分为载荷和材料性能参数两部分，且材料性能参数部分可近似等效为一个正态随机变量，从而缺口根部最大应力的分布可表示为外载荷分布和材料性能参数分布的线性组合，容易计算得到最大应力的分布函数。完成了中心孔和椭圆边缺口根部最大应力分布的算例分析，结果表明这种近似比较精确和有效。

英文摘要：

A method for the probability distribution of the maximum stress at notch root is proposed in this paper based on stochastic finite element method. Firstly the maximum stress at notch root was expressed in finite element method format, then the factors which affect the stress distribution were separated into two parts, the loads and the material, with Taylor expansion of the stress expression, and lastly the distribution of the maximum stress at notch root was expressed as a linear combination of the distri- bution of loads and the one of the performances of material, in which performances of material were equivalent to be normal random variables approximately. Thus the distribution function of the maximum stress can be easily obtained. Two examples of center hole and elliptical edge notch were accomplished and the results demonstrate that this approximation is accurate and effective.