基于分解法的最大熵随机有限元法

摘要：提出了一种新的基于分解法的最大熵随机有限元方法，利用单变量分解将多维随机响应函数表述为单维随机响应函数的组合形式，从而将求解随机结构响应统计矩的多维积分表达式转化为单维积分式，对单维积分采用高斯-埃尔米特积分格式求解。在获得结构响应的统计矩之后，利用最大熵原理求得结构响应的概率密度函数解析表达式。该法不涉及求导运算，对于非线性随机问题非常适用。算例结果表明，本文方法具有较好的精度与计算效率。

Maximum entropy stochastic finite element method based on dimension-reduction method

A new maximum entropy stochastic finite element method was proposed on the basis of the dimension-re- duction method. In this method, the multi-dimensional random response functions were decomposed into the combination of one-dimensional response functions with the univariate dimension-reduction method, so the multi-dimensional integra- tion which was employed to calculate statistical moments of response of stochastic structures was transformed into one-di- mensional integration, and the one-dimensional integration was calculated using the Gauss-Hermite integration. After get- ting the statistical moments of structure response, the explicit expression of probability density function of response of structures was obtained using the maximum entropy principle(MEP). The proposed method doesn't involve the calculation of partial derivatives of response and is suitable for nonlinear stochastic problems. The examples illustrated that the pro- posed method has good accuracy and computational efficiency.