Reanalysis-based FEM for fuzzy uncertainty treatment in static structural analysis

Uncertainty modeling applied at different stages of the virtual prototyping process enhances the quality of the of the design in terms of physical validity. The Fuzzy FEM is a widely accepted numerical simulation tool to model imprecise data in early design stages. The Interval FEM, which forms the basis of the Fuzzy FEM, is based on the interval arithmetic approach or on black-box approaches such as global optimisation or vertex sampling. The limitation of the interval arithmetics applied in general IFE analysis is the large overestimation of the interval results. In order to make black-box approaches computationally less expensive, a novel reanalysis-based finite element method (ReFEM) is applied. This paper presents the ReFEM method for static structural analysis. By supplying analytical gradients, this approach is explicitly suited for optimisation-based black-box techniques. The computational benefits and general applicability in the context of Fuzzy FE analysis of the new approach is illustrated on a mid-sized plate problem.