ESSAY ON UNCERTAINTIES IN ELASTIC AND VISCOELASTIC STRUCTURES - FROM FREUDENTHAL,A.M. CRITICISMS TO MODERN CONVEX MODELING

Stochastic approach and non-stochastic, convex modeling of uncertainty are critically contrasted. First some drawbacks of the probabilistic methods are discussed, attributable to lack of sufficiently accurate data; then the effect of human error in constructing a probabilistic model for input quantities is elucidated. Extensive quotations from pertinent works of Freudenthal, who is rightfully considered as an architect of modern reliability theory, are utilized to explain some doubts he himself experienced about probabilistic methods. His hints are realized in modern convex modeling of uncertainty, which the writer is advocating and advancing. A set-theoretical, convex description of uncertainty is discussed in detail. Uncertainty is described as a set of constraints unlike the classical probabilistic approach. Moreover, instead of conventional optimization studies, where the minimum possible responses are sought, here an uncertainty modeling is developed as an ''anti-optimization'' problem of finding the least favorable response under the constraints within the set-theoretical description. The question of how the output quantities of such an anti-optimization process vary when the global knowledge on the uncertainties increases is considered in detail. Response variability of viscoelastic structures is evaluated. Combined probabilistic-convex modeling is proposed for situations where the input quantities should be modeled as stochastic ones, but some of their probabilistic characteristics are unknown but bounded.