A reduced-order stochastic finite element analysis for structures with uncertainties

This work examines the effects of uncertain material and geometry properties on the dynamic characteristics of a simply supported plate. The forced responses of the plate are predicted using the polynomial chaos expansion method. The stochastic system equations are transformed to a set of deterministic equations using Galerkin projection. In order to improve the computational efficiency when attempting to examine the structure with many degrees of freedom, the Arnoldi-based Krylov subspace technique is implemented to reduce the number of degrees of freedom in the finite element model, before the polynomial chaos expansion is applied. The combined stochastic finite element analysis and model order reduction technique is shown to provide accurate results with significantly reduced computational effort.