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

• Published in: Finite elements in analysis and design 2013-02, Vol.64, p.65-78
• Main Authors: Shang, Shen, Yun, Gun Jin
• Format: Article
• Language: English
• Subjects: Abaqus uel; Computer simulation; Discretization; Finite element method; Karhunen–Loève expansion; Material uncertainty; Mathematical analysis; Meshing; Monte Carlo methods; Monte Carlo simulation; Probabilistic analysis; Stochastic finite element; Stochasticity; Uncertainty
• ISSN: 0168-874X; 1872-6925
• DOI: 10.1016/j.finel.2012.10.001

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–Loève (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. ► A general mapping–interpolation method for separating RF mesh and FE mesh is developed. ► Large scale engineering problems are solved to show the capacity and fidelity of the proposed SFEM. ► The proposed method has various applications in stochastic nonlinear solid mechanics problems.