具有随机弹性模量的平面弹性模型的双线性有限元解法

Stochastic bilinear finite element method for plane elasticity equations with stochastic modulus

本文针对随机平面线弹性问题,采用Neumann级数展开构造随机有限元方法.首先利用Karhunen-Loève展开对随机系数进行有限维逼近,把随机模型转换为确定性参数的问题.其次,在空间上采用矩形剖分的双线性有限元来离散位移.最后,文章给出了收敛性分析,并通过数值算例验证了理论结果.

The bilinear finite element with Neumann expansion is used for the model of stochastic plane elasticity. By using the Karhunen-Loeve expansion to approximate the elasticity modulus, the original model changes into a deterministic parametric problem. In the space direction,the bilinear finite element is used to approximate the displacement. Convergence is analyzed. Numerical experiments are done to confirm the theoretical results.