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

TL;DR

This paper introduces a novel sample-based stochastic finite element method that efficiently computes structural responses by decoupling stochastic and deterministic components, suitable for high-dimensional problems and easy to integrate with existing FEM software.

Contribution

The paper proposes a new stochastic finite element approach with an iterative algorithm that is dimension-insensitive and compatible with existing FEM tools, enhancing efficiency and applicability.

Findings

Accurately computes stochastic responses in structural analysis.

Effective for both low- and high-dimensional stochastic problems.

Demonstrated robustness and efficiency through practical examples.

Abstract

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.