随机有限元法在砖石古建数值模拟中的应用

Application of Stochastic Finite Element Method in the Numerical Simulation of Historical Masonry Buildings

砖石古建确定性有限元数值模拟中材料参数取值较难,并且分析结果只能定性地反映结构响应的分布规律。针对这些局限性,把计算中涉及到一些材料参数视为服从某种概率分布形式的随机输入变量,采用基于拉丁超立方抽样的蒙特卡洛随机有限元法的基本原理,运用有限元软件ANSYS中的概率设计模块(PDS),以开封市延庆观玉皇阁为例进行了随机有限元分析,得到了相应随机输出变量的统计特征,并详细探讨了随机输入变量和结构的应力分布规律以及随机输出变量间的关系。结果表明,该方法能更合理、更清楚地反映结构在某一工况下的力学性能,其为砖石古建的数值模拟提供了一种新分析思路。

In order to deal with the problem of determining the material parameters in the numerical simulation process of historical masonry buildings,some important parameters to be random variables described by appropriate probability distribution are presented.Based on the theory of Monte Carlo stochastic finite element method using Latin hypercube sampling,the Jade Emperor Pavilion of Yanqing Taoist Temple in Kaifeng city is analyzed by stochastic finite element method applying finite element software ANSYS.The results show that this method can obtain a better understanding of the structural behavior under a certain load case,and it may be beneficial to the protection of historical masonry buildings.