【作者】 景鹏；

【导师】 黄淑萍；

【作者基本信息】 上海交通大学 ， 结构工程， 2011， 硕士

【摘要】 基于配点法的谱随机有限元法(CSFEM)方法实现了随机分析和有限元分析的解耦,使确定性有限元分析可用作“黑箱”,一般需要的样本计算比蒙特卡罗法少。但CSFEM在处理高维问题时,其样本(配点)是基于张量积法的,配点数会随着维数增长呈几何级数增加,有时甚至比蒙特卡罗法所需的配点数还要多。稀疏网格法提供了在多维空间中采用最少的点来构造插值函数的方法,而且这种方法的插值误差非常接近张量积法。本文研究了随机配点法的各种配点选取方法,详细介绍了稀疏网格法的基本原理和配点选取方法。并将稀疏网格法与CSFEM方法相结合,可以大量地减少高维问题所需的配点数,克服了配点数随维数呈几何级数增长的问题,使得CSFEM方法能够更好的处理高维问题。本文以混凝土框架结构以及单桩沉降随机响应为例,研究了CSFEM方法在结构工程和岩土工程中的应用。其中单桩沉降分析中用稀疏网格法来选取配点,并与采用张量积法选取配点得到的结果进行对比。结果表明,利用稀疏网格法来选取配点,只需要较之普通CSFEM方法少很多的配点就可以得到与其相接近的计算精度。更多还原

【Abstract】 Collocation based stochastic finite element method (CSFEM) can uncouple the finite element analysis with stochastic analysis, which means the finite element code can be treated as a black box. It needs much fewer samples than the Monte Carlo method does. But when CSFEM is dealing with problems with high dimension, the number of collocation points will grow very fast, sometimes even more than Monte Carlo’s.Sparse grid method uses fewer points to construct multidimensional interpretation functions with very small error. Several methods for selecting collocation points are introduced. The sparse grid method is illustrated in length. Combining CSFEM with the sparse grid method can reduce the number of collocation points in high dimension. It extends the applicability of CSFEM to problems with high dimension. Numerical examples involving a concrete frame and a single pile are studied. The sparse grid method is applied to the analysis of the settlement of single pile. Compared to the tensor product method for the collocation selection, the sparse grid method is more efficient. Results show that the sparse grid method save a lot of computational effort.更多还原