Abstract:

An arbitrary 8-node element with curved sides is proposed for the discretization of 2D random fields, and the formulations of second-order stochastic characteristics are presented for the local averages of the random field based on the proposed element. Explicit matrix expressions of the relation between the covariance matrix of the local averages and the covariance matrix of the random variables at Gaussian points are then established by means of coordinate transformation and Gaussian numerical integral. The proposed element is found suitable for the discretization of random fields with curved edges, with straightforward and practical calculation of the stochastic characteristics for local averages. Moreover, the thin-plate bending, the plane stress and the plane strain problems are taken as examples to reveal the effects of correlation structure and correlation length on the displacement deviation via the proposed discretization method and the Monte-Carlo method, the choice of Gaussian points being finally considered.

Key words: random field, discretization, local average, curved-side element