Mechanical and Civil Engineering Seminar
"Current and Future Challenges in Probabilistic Mechanics"
The discipline of Probabilistic Mechanics has made major advances since Alfred M. Freudenthal established it in the 1950's. In his seminal 1956 paper "Safety and the Probability of Structural Failure," Freudenthal clearly identifies the importance of uncertainties in both applied loads and material properties, and then defines two problems: determining the probability of unserviceability and the probability of failure of a structure. Historically, the uncertainties in the applied loads were examined first, both at the serviceability and failure levels. The material property uncertainties were examined later, as that problem is in general more complex. However, the majority of research work involving the so-called "system uncertainty" has been performed so far at the serviceability level. Although the methodologies currently used to model system uncertainties are quite sophisticated (material and geometric properties are routinely modeled today as non-Gaussian, non-homogeneous stochastic vector fields), the problems examined are primarily serviceability ones: in the elastic range or just having entered the inelastic range. Consequently, in the vast majority of such cases, the degree of system (input) uncertainty is hardly changed in the response (output) uncertainty. In contrast, system uncertainty can have a truly dramatic effect on the response uncertainty in problems well into the inelastic range and/or involving failure. Small levels of input uncertainty can result in very large levels of output uncertainty. Classical examples include, among others, buckling, soil liquefaction, and failure of brittle/composite materials. Future research in probabilistic mechanics should focus along these lines as the practical consequences of small system uncertainties can be catastrophic and research has yet to fully resolve several important issues. Of particular interest are problems where the input system uncertainty is changing the fundamental nature of the stochastic response. A number of examples of current research will be provided together with suggestions about future research.
Contact: Sonya Lincoln at 626-395-3385 firstname.lastname@example.org