Articlegold2015

A Modified Computational Scheme for the Stochastic Perturbation Finite Element Method

27 citations0/0 files storedLatin American Journal of Solids and Structures

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Abstract

A modified computational scheme of the stochastic perturbation finite element method (SPFEM) is developed for structures with low-level uncertainties. The proposed scheme can provide second-order estimates of the mean and variance without differentiating the system matrices with respect to the random variables. When the proposed scheme is used, it involves finite analyses of deterministic systems. In the case of one random variable with a symmetric probability density function, the proposed computational scheme can even provide a result with fifth-order accuracy. Compared with the traditional computational scheme of SPFEM, the proposed scheme is more convenient for numerical implementation. Four numerical examples demonstrate that the proposed scheme can be used in linear or nonlinear structures with correlated or uncorrelated random variables.

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References

2002The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations 2008The stochastic finite element method: Past, present and future 1986Random field finite elements 2001Solution of stochastic partial differential equations using Galerkin finite element techniques 2007Sparse grid collocation schemes for stochastic natural convection problems 1993The stochastic finite element method: basic perturbation technique and computer implementation 2004Probability density evolution method for dynamic response analysis of structures with uncertain parameters 2013The Stochastic Perturbation Method for Computational Mechanics

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