Stochastic finite element with material uncertainties: Implementation in a general purpose simulation program

Authors:
Shen Shang;Gun Jin Yun
Affiliations:
Department of Civil Engineering, The University of Akron, Akron, OH 44325, USA;Department of Civil Engineering, The University of Akron, Akron, OH 44325, USA
Venue:
Finite Elements in Analysis and Design
Year:
2013

Citing 2
Cited 2

Concepts and Applications of Finite Element Analysis

Concepts and Applications of Finite Element Analysis
On using deterministic FEA software to solve problems in stochastic structural mechanics

Computers and Structures

Stochastic stability analysis of steel tubes with random initial imperfections

Finite Elements in Analysis and Design
Transformed perturbation stochastic finite element method for static response analysis of stochastic structures

Finite Elements in Analysis and Design

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Abstract

This paper presents a stochastic finite element (SFE) within a general purpose finite element analysis program ABAQUS to simulate the probabilistic structural response of stochastic materials. Discretization and quantification of random fields associated with material uncertainties are accomplished through Karhunen-Loeve (KL) expansion in order to simulate the stochastic response of structures under material uncertainties. Although SFE is one of the most widely accepted approaches, its integrations into general-purpose finite element software are rare in literatures due to difficulties in its intrusive formulation and managing two different meshes for discretizing the physical and random field domains subjected to different meshing criteria. Therefore, issues on the separation of RF mesh from FE mesh have been addressed along with its efficient implementations. The proposed method can significantly reduce dimensionality of the stochastic domain and efficiently predict probability density functions of the structural response under material uncertainties through Monte Carlo simulations combined with the Latin hypercube sampling technique.