CAJ | 학술논문

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。
본문침대수궤평면선탄성문제，채용Neumann급수전개구조수궤유한원방법。수선이용Karhunen-Loève전개대수궤계수진행유한유핍근，파수궤모형전환위학정성삼수적문제。기차，재공간상채용구형부분적쌍선성유한원래리산위이。최후，문장급출료수렴성분석，병통과수치산례험증료이론결과。
The bilinear finite element with Neumann expansion is used for the model of stochastic plane elasticity .By using the Karhunen-Loève 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 .