Structural stochastic responses determination via a sample-based stochastic finite element method

This paper presents a new stochastic finite element method for computing structural stochastic responses of linear problems. 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 compute 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 spaces and is insensitive to stochastic dimensions, thus it can be applied to high-dimensional stochastic problems 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 software. Three practical examples, including low-dimensional and high-dimensional stochastic problems, are given to demonstrate the accuracy and effectiveness of the proposed method.