In this paper, a stochastic meshless method which can take care of random fields with lognormal distribution characteristics is developed. The method devised incorporates random fields associated with both material properties and external forces. This method is a modification of the improved response function method originally developed for normal random fields. In this method, the random displacement vector is decomposed into a deterministic component and an improved response function which is a function of discretized set of random variables. A second order Taylor series expansion at the mean values of random variables is used to model both the stiffness matrix, and the force vector. The homogeneous lognormal field is expressed as exponential function of homogeneous normal field. The probabilistic characteristics of response are evaluated by performing simulations on the response. From the numerical examples solved, it is found that the method developed can produce comparable results with those obtained from direct Monte Carlo simulation of system of equations using lesser computational time. Results of proposed method are found to be superior to those obtained from perturbation method. Further, the proposed method is found to be suitable for structural reliability estimation.

中文翻译：

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一种改进的响应函数方法，用于具有对数正态变化输入随机场的结构的随机无网格分析

本文提出了一种随机无网格方法，可以处理具有对数正态分布特征的随机场。设计的方法结合了与材料特性和外力相关的随机场。该方法是最初针对正态随机场开发的改进响应函数方法的修改。在该方法中，随机位移矢量被分解为确定性分量和改进的响应函数，该响应函数是离散随机变量集的函数。使用随机变量平均值的二阶泰勒级数展开来对刚度矩阵和力矢量建模。齐次对数正态场表示为齐次正态场的指数函数。通过对响应进行模拟来评估响应的概率特征。从求解的数值例子可以看出，所开发的方法可以使用更少的计算时间产生与直接蒙特卡罗模拟方程组所获得的结果相当的结果。发现所提出的方法的结果优于扰动方法获得的结果。此外，发现所提出的方法适用于结构可靠性估计。