Development of interval based methods for fuzziness in continuum-mechanics

Accounting for uncertainties in mechanics problems has previously been accomplished by probabilistic methods. Such methods can require highly repetitive computations to analyze the behavior of mathematical models. In addition, knowledge of the probability distribution of state variables is often incomplete. In this paper, a new treatment of uncertainties in continuum mechanics, based on fuzzy set theory, is introduced. Uncertainties or fuzzy numbers here-in are viewed through the concept of presumption level of the uncertainty α, α∈[0, 1], which gives an interval of confidence A_α =[a₁^(α), a₂^(α) ]. The interval approach of treating uncertainties in continuum mechanics is applied to both geometric and material uncertainties in number of examples. Results demonstrate sharp inclusion of the interval solution in comparison with the exact solutions