薄板统计分析的随机边界元法

本文建立了分析含随机材料参数的薄板弯曲问题的随机边界元法。基于Ｔａｙｌｏｒ级数展开技术，分别得到了位移的均值和一阶偏差的边界积分方程，发现材料参数的随机性可作为一个等效的随机荷载处理，从而得到边界位移或边界力的均值和协方差，并进一步求出内点位移和力矩的均值和协方差，最后用本文方法计算了两个算例，并对结果进行了必要的分析。

THE STOCHASTIC BOUNDARY ELEMENT METHOD IN STATISTICAL ANALYSIS OF THIN PLATES

In this paper, to analyze the bending problems of thin plates with random material parameters a stochastic boundary element method is developed. Basing on the Taylor series expansion, the boundary integral equations concerning the mean displacement and the deviations of the displacements are also derived respectively. It is found that the randomness of the material parameters is equivalent to a random load. Thus, the mean and covariance matrices of unknown boundary displacements and tractions may be obtained. Furthermore, the mean and covariance of displacements and moments at inner points can also be obtained. Two numerical examples are presented in this paper and with necessary discussions.