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Practical application of the stochastic finite element method. (English) Zbl 1348.65160

Summary: The stochastic finite element method is an extension of the FEM that considers the uncertainty of a system that arises through variations in initial conditions, materials or geometry. Systems which display a measurable degree of disorder can be studied efficiently using a probabilistic approach. Different scenarios can be randomly generated with the SFEM to study the behaviour of systems that take into account prior knowledge of the differing variations in properties. This review paper introduces the most commonly used techniques: direct Monte Carlo simulation, the perturbation method and the spectral stochastic finite element method. It then looks at the currently available software for the SFEM and provides examples from the disciplines of materials science, biomechanics and engineering to illustrate different procedures by which the SFEM is practically used. The aim of the paper is to help scientists and engineers quickly assess how they might apply SFEM to their own research and guide them towards key publications.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N75 Probabilistic methods, particle methods, etc. for boundary value problems involving PDEs
65C05 Monte Carlo methods
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