  This paper presents a new stochastic finite element method for computing
structural stochastic responses. The method provides a new expansion of
stochastic response and decouples the stochastic response into a combination of
a series of deterministic responses with random variable coefficients. A
dedicated iterative algorithm is proposed to determine the deterministic
responses and corresponding random variable coefficients one by one. The
algorithm computes the deterministic responses and corresponding random
variable coefficients in their individual space and is insensitive to
stochastic dimensions, thus it can be applied to high dimensional stochastic
problems readily without extra difficulties. More importantly, the
deterministic responses can be computed efficiently by use of existing Finite
Element Method (FEM) solvers, thus the proposed method can be easy to embed
into existing FEM structural analysis softwares. Three practical examples,
including low-dimensional and high-dimensional stochastic problems, are given
to demonstrate the accuracy and effectiveness of the proposed method.

Numerical Analysis;Numerical Analysis