Reduction techniques for the discretisation of random fields involved in stochastic finite element models

摘要

Random fields are generally used to model the spatial variability of the material properties in uncertain structuralrnmodels. In order to be used in the framework of the stochastic finite element method (SFEM), theserncontinuous models require a discretisation that should allow for an accurate representation of the continuousrnfield and should involve the smallest number of random variables. This paper presents the performances of twornreduction techniques. In the first technique, the finite element mesh is used for the random field discretisationrn(midpoint method or Karhunen-Loeve decomposition) and a reduced set of stochastic basic components is identified.rnIn the second technique, a specific mesh, usually coarser than the FEM mesh, is used for the random fieldrndiscretisation. Both reduction techniques are numerically tested in the framework of the perturbation SFEMrnfor the time-harmonic stochastic analysis of a plate whose Young modulus is modelled as a random field. Thernstudy of the performances of both methods in terms of accuracy and computational cost show that they arernglobally equivalent. Finally, some practical guidelines for the simultaneous use of both techniques are given.