ABSTRACT
One of the main shortcomings of current fuzzy and interval finite element procedures is that mutual dependency between multiple uncertain model parameters cannot be included in the analysis. This limit is posed by the classical interval concept, where multi-dimensional interval quantities are generally treated as hypercubes, thus ignoring all possible dependency between vector components. For this reason, most literature on this subject focuses on one-dimensional output quantities.
In order to cope with this problem, this work discusses the application of the concept of interval fields for static analysis of uncertain mechanical structures in the context of fuzzy finite element analysis. The theoretic background of the concept is explained, and it is shown how it can be applied to represent dependency between parametric uncertainties.
Further, the paper concentrates on the calculation of interval fields resulting from static structural analysis. A procedure that enables the calculation of a joint representation of multiple output quantities of a single interval finite element problem while preserving the mutual dependency between the components of the output vector is introduced. This procedure is based on a projection of the original problem on the space composed by the classical static deformation patterns. This paper in particular introduces a novel projection in which the space of the classical deformation patterns is augmented with deviatoric parts. This novel projection leads to a better approximation of the results without a significant increase in computation time.
Finally, a numerical case study illustrates the procedure and validates the improved accuracy of the results obtained with the novel projection technique.
Keywords: Fuzzy finite elements, Fuzzy analysis, Interval analysis, Interval fields.
