Generalization of spectral stochastic finite element method for analysis of structures with elastoplastic materials

The significance of the influence of uncertainty and stochastic approach-related problems on engineering system analysis is now evident and irrefutable. On the other hand, considering the factors that apply these uncertainties in the findings should need a significant amount of computing cost and effort, which is why researchers are always looking for approaches that combine high calculation accuracy with speed. One of the most useful tools for analyzing systems with uncertainty in computational stochastic mechanics is the spectral stochastic finite element method. In the present paper, by applying uncertainty to the applied loads and elastic modulus, this method has been developed to analyze the structures with nonlinear materials, and a method called the nonlinear spectral stochastic finite element method (NLSSFEM) has been proposed. The results obtained from the used method have been compared with the results obtained from the Monte Carlo simulation method. The accuracy of calculations and the speed of access to the solution of the proposed method are evaluated as desirable.