Stochastic Finite Elements of Discretely Parametrized Random Systems on Domains with Boundary Uncertainty

A Kundu, S Adhikari & MI Friswell (Swansea University)

International Journal for Numerical Methods in Engineering, Vol. 100, No. 3, 19 October 2014, pp. 183-221

Abstract

The problem of representing random fields describing the material and boundary properties of the physical system at discrete points of the spatial domain is studied in the context of linear stochastic finite element method. A randomly parametrized diffusion system with a set of independent identically distributed stochastic variables is considered. The discretized parametric fields are interpolated within each element with multidimensional Lagrange polynomials and integrated into the weak formulation. The proposed discretized random field representation has been utilized to express the random fluctuations of the domain boundary with nodal position coordinates and a set of random variables. The description of the boundary perturbation has been incorporated into the weak stochastic finite element formulation using a stochastic isoparametric mapping of the random domain to a deterministic master domain. A method for obtaining the linear system of equations under the proposed mapping using generic high order finite elements and the stochastic spectral Galerkin framework is studied in detail. The treatment presents a unified way of handling the parametric uncertainty and random boundary fluctuations for dynamic systems. The convergence behavior of the proposed methodologies has been demonstrated with numerical examples to establish the validity of the numerical scheme.

Paper Availability

This material has been published in the International Journal for Numerical Methods in Engineering, Vol. 100, No. 3, 19 October 2014, pp. 183-221. Unfortunately the copyright agreement with Wiley InterScience does not allow for the PDF file of the paper to be available on this website. However the paper is available from the Wiley website - see the link below.


Link to paper using doi:10.1002/nme.4733

International Journal for Numerical Methods in Engineering on Wiley InterScience