Fourier representation of random media fields in stochastic finite element modelling

Abstract

Purpose

To provide an explicit representation for wide‐sense stationary stochastic fields which can be used in stochastic finite element modelling to describe random material properties.

Design/methodology/approach

This method represents wide‐sense stationary stochastic fields in terms of multiple Fourier series and a vector of mutually uncorrelated random variables, which are obtained by minimizing the mean‐squared error of a characteristic equation and solving a standard algebraic eigenvalue problem. The result can be treated as a semi‐analytic solution of the Karhunen‐Loève expansion.

Findings

According to the Karhunen‐Loève theorem, a second‐order stochastic field can be decomposed into a random part and a deterministic part. Owing to the harmonic essence of wide‐sense stationary stochastic fields, the decomposition can be effectively obtained with the assistance of multiple Fourier series.

Practical implications

The proposed explicit representation of wide‐sense stationary stochastic fields is accurate, efficient and independent of the real shape of the random structure in consideration. Therefore, it can be readily applied in a variety of stochastic finite element formulations to describe random material properties.

Originality/value

This paper discloses the connection between the spectral representation theory of wide‐sense stationary stochastic fields and the Karhunen‐Loève theorem of general second‐order stochastic fields, and obtains a Fourier‐Karhunen‐Loève representation for the former stochastic fields.

Citation

Li, C.F., Feng, Y.T., Owen, D.R.J. and Davies, I.M. (2006), "Fourier representation of random media fields in stochastic finite element modelling", Engineering Computations, Vol. 23 No. 7, pp. 794-817. https://doi.org/10.1108/02644400610689901