A new stochastic isogeometric analysis method based on reduced basis vectors for engineering structures with random field uncertainties

Abstract

A new stochastic isogeometric analysis method based on reduced basis vectors (SRBIGA) is proposed for engineering structures with random field material properties and external loads. Based on the Galerkin isogeometric functions, the proposed SRBIGA applies the Karhunen–Loève expansion to discretize the random field uncertainties. Inspired by the stochastic Krylov subspace theory, the structural responses of linear elasticity structures with random field uncertainties are represented based on the reduced basis vectors. The tremendous advantage of SRBIGA over the spectral stochastic isogeometric analysis (SSIGA) in terms of the computational efficiency is disclosed through the comparison analysis in theoretical aspects. Three illustrative examples demonstrate that the proposed SRBIGA has not only significantly higher efficiency but also higher accuracy and better robustness than the SSIGA and that it can provide a novel and expedient stochastic structural analysis method for practical large-scale complex engineering structures when both material properties and external loads are spatially random.