An approach to the Sandia workshop static frame challenge problem: A combination of elementary probabilistic, fuzzy set, and worst scenario tools

A model static frame problem with uncertain input data is considered. The Young modulus of the frame material is known only through a limited number of measurements of its local and effective values. In the loaded frame, the displacement w   at a given point is to be predicted. To tackle the uncertainty in the displacement magnitude, a set FF of conservative Young modulus behavior (YMB) models is constituted and the mean and the variance of w   are inferred for each YMB model belonging to FF. Moreover, the degree of possibility of each YMB model is assessed by a weight (membership) function ν derived from measured data. The probability of w exceeding a given tolerance is inferred in each YMB model and then weighted by ν. To address the prediction problem in accordance with the worst scenario approach, the maximum is identified in the weighted probabilities. The analysis is based on elementary probabilistic tools as well as on the exploitation of computer algebra and numerical methods. The results are presented in numerous graphs.