中厚板统计分析的随机边界元法

Stochastic boundary element method in statistical analysis of moderately thick plates

本文建立了分析含随机材料参数并具厚度不均匀性的中厚板问题的随机边界元法。基于Taylor级数展开技术 ,分析得到广义位移的均值和一阶偏差的积分方程 ,其中将材料参数的随机性和厚度的不均匀性作为等效荷载处理 ,从而得到广义边界位移或面力的均值和协方差 ,并进一步求出内部点广义位移和内力的均值和协方差。最后用本文方法计算了两个数例 ,并对所得结果进行了分析、探讨。

The stochastic boundary element method is developed to analyse moderately thick plate problems with random material parameters and random thickness. Based on the Taylor series expansion, the boundary integration equations concerning the mean and deviation of the generalized displacements are derived, respectively. It is found that the randomness of material parameters is equivalent to a random load, so the mean and covariance matrices of unknown generalized boundary displacements and tractions can be obtained. Furthermore, the mean and covariance of the generalized displacements and forces at inner points can also be obtained. Two numerical examples are worked out with the presented method in this paper and necessary analysis is made for the results.