一种新的蒙特卡罗随机有限元方法

来源期刊：中南大学学报(自然科学版)2006年第5期

论文作者：邓建 边利 彭怀生

文章页码：997 - 1001

关键词：蒙特卡罗模拟;随机有限元;径向基网络;岩土工程

Key words：Monte-Carlo simulation; stochastic finite element method; radial basis function network; geotechnical engineering

摘    要：针对岩土工程可靠性分析的功能函数是隐式函数或高次非线性函数的特点,提出并从理论上论证隐式功能函数和高次非线性功能函数可靠性问题的新解法,即基于径向基网络的蒙特卡罗随机有限元方法;给出计算框图和计算步骤。以钢筋混凝土浅基础和某矿山矿柱为例,说明其在岩土与采矿工程中的应用。研究结果表明,采用蒙特卡罗随机有限元方法可直接使用确定性有限元分析程序而无需任何改动,对于极限状态函数不能用显式表达和高次非线性的可靠性问题都适用。

Abstract: Based on the fact that the performance functions in reliability analysis of geotechnical engineering are usually implicit or higher order nonlinear in terms of basic random variables, a new Monte-Carlo stochastic finite element method using radial basis function neural network was put forward to deal with reliability problems in geotechnical engineering. The flowchart and computational procedure were presented. Examples on a reinforced concrete foundation and a mining pillar are presented to illustrate the applicability of the new method. The new method directly employs deterministic finite element analysis to establish a radial basis function neural network to approximate implicit and/or higher order nonlinear performance functions.