Fourier representation of random media fields in stochastic finite element modelling

摘要

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-Loeve expansion. Findings - According to the Karhunen-Loeve 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-Loeve theorem of general second-order stochastic fields, and obtains a Fourier-Karhunen-Loeve representation for the former stochastic fields.