On the performance evaluation of stochastic finite elements in linear and nonlinear problems

Abstract

Due to the inherent uncertainties in various systems, deterministic approaches may not be able to satisfactorily characterize their response. In such cases, stochastic approaches that can systematically consider uncertainties have to be employed. In the past, many stochastic finite element analysis (SFEA) methods have been developed for uncertainty quantification (UQ), among which the perturbation methods, intrusive and non-intrusive polynomial chaos expansion (IPCE/NIPCE) methods and stochastic collocation (SC) methods have received considerable attention. However, in mechanics, most of the applications of these methods are confined to relatively simple problems, and the applicability and performance of these methods to complex nonlinear mechanics problems are not clear. To this end, this study carried out an investigation on the performance of different SFEA methods in linear and nonlinear problems. Numerical studies show that the NIPCE and SC methods are superior in terms of accuracy among other methods in the linear elastic case. The NIPCE method is also used for UQ in stochastic models with plasticity and nonlocal elastoplastic damage. The results demonstrate that the stochastic averages can be significantly different from the deterministic results, which indicates the necessity of considering UQ for improving response predictions.