Probabilistic analysis of structures using stochastic finite elements (2015)
Most of the published literature in the area of uncertainty quantification of structural systems via probabilistic methods, is concerned with the representation of uncertain quantities as random fields. These types of models allow a robust representation of the random nature of different kinds of structural parameters, provided there exists sufficient information about their random fluctuations. The inclusion of this probabilistic variation into the physical model affects directly the overall behavior of the structural system, which is generally simulated using the finite element method. Therefore, an instinctive way of proceeding is to extend the classical finite element approach for the solution of stochastic problems involving random structural properties, constituting the so-called stochastic finite element method. This technique has received a considerable attention over the last decade, due to its versatility in dealing with a broad range of stochastic problems. The fundamental idea of this thesis is to present a review of the stochastic finite element method, and to develop a collection of programs that allow a better understanding of this technique. Initially, a general overview of common methods used for the representation of random fields is carried out; special attention is made to the Karhunen-Loève and polynomial chaos expansions, since they are key concepts in the construction of the spectral stochastic finite element method. Secondly, the stochastic finite element is introduced by making a general description of its variants; where the spectral approach using the projection on the homogeneous chaos and the Monte Carlo simulation method are particularly revisited. Finally, the performance of the implemented methodologies is evaluated using several numerical experiments.