Formulation of Fuzzy Finite-Element Methods for Solid Mechanics Problems - Muhanna, Rafi L.; Mullen, Robert L. (Computer-aided civil and infrastructure engineering, 1999)
Accounting for uncertainties in mechanics problems has been accomplished previously by probabilistic methods that may require highly repetitive and time‐consuming computations to analyze the behavior of mathematical models. In addition to the repetitions, knowledge of the probability distribution of state variables is often incomplete. This article introduces a new treatment of uncertainties in continuum mechanics based on fuzzy set theory. Uncertainties or fuzzy numbers herein are viewed through the concept of presumption level of the uncertainty (α‐cut), α∈[0, 1]$, which gives an interval of confidence Aα = [a1(a), a2(α]. This treatment is included in a new fuzzy finite‐element formulation. The fuzzy approach to treating uncertainties in continuum mechanics is applied to load, geometric, and material uncertainties in a number of examples. Results demonstrate sharp inclusion of the fuzzy solutions in comparison with the exact solutions.