Enhanced uncertain structural analysis with time- and spatial-dependent (functional) fuzzy results

Abstract Uncertain structural analysis is the computation of uncertain structural response for uncertain input quantities. In terms of structural analysis, the result quantities (e.g. displacements, stresses, damages, …) are time- and spatial-dependent ( τ and θ respectively), such that x u ↦ z u ( τ , θ ) needs to be solved. The usual procedure is to a priori select a small amount of Quantities of Interest (QoI), e.g. for a specific time and spatial location. For this small amount, the uncertainty analysis is performed, but these results do not represent the structural behaviour; they are just an excerpt based on a priori knowledge (in general not available). The consideration of time- and spatial-dependent results yields a high amount of uncertain result quantities. The main goal of this contribution is the formulation of time and spatial dependency based on the continuous space, which allows the general application to structural analysis. Furthermore, the computation of a large amount of fuzzy result quantities is addressed. Therefore, a fuzzy analysis on the basis of a specific fuzzy sampling is introduced. The third aspect discussed is the enhanced fuzzy structural analysis, an approach to compute, visualise and evaluate functional fuzzy results. The necessity and usefulness of these procedures, in terms of identifying failure modes and weak points, is discussed by two examples.