Fuzzy Finite Element Analysis using the Transformation Method

A promising approach to the problem of obtaining upper and lower bounds on the frequency response functions (FRFs) for structures whose parameters are not fully known has recently been published. The technique makes use of the modal superposition procedure in conjunction with a hybrid optimisation/interval arithmetic framework. One of the problems with this approach is that there is no self-validation capability available within interval arithmetic and so it is necessary to provide a suitable benchmark. The benchmark which is proposed in this paper is based around the transformation method which is a deterministic approach that returns sensitivity information that is unavailable through a MonteCarlo approach whilst in many situations returning better estimates of the true bounds on model output parameters. The approach is demonstrated using a dynamic analysis of a relatively simple structure with geometric and material uncertainties.