| A technique is developed for the finite element method to analyze systems exhibiting uncertainties and to determine the effect of these uncertainties on the system's response. The uncertainties are classified based on their causes and are modelled as Random fields for consistent mathematical manipulation. There are two broad approaches to analyze systems with uncertainties. One is the more expensive statistical approach while the other is a non statistical approach. The merits and demerits of both these approaches are discussed. The First/Second order, second moment technique, a non-statistical approach, is chosen for implementation in the finite element method. This modified finite element method is referred to as the Stochastic Finite Element method. The computational aspect of the Stochastic finite element, as compared to the conventional deterministic finite element, is discussed. The stochastic finite element code was validated using the Monte Carlo technique of random sampling. Finally the application of Stochastic finite elements is demonstrated through two case studies, one for sensitivity analysis and the other for optimal experimental design. |
