Collocation Based Stochastic Finite Element Method And The Applications

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.