Fundamental issues of the methodology, convex modelling of uncertainty, dedicated to unified treatment of geometric and material characteristics, are put forward in this research. Instead of classical probabilistic methods, no probabilistic treatment is utilized, but the new set-theoretical description of the uncertain variables and functions is presented. In addition, instead of usual optimization problems, where the minimum possible responses or least favorable shapes of the structures are sought, here an uncertainty modelling is developed as an anti-optimization problem of finding the least favorable responses due to shape or material uncertainty. Special emphases are placed on vibration and dynamic buckling of viscoelastic structures. The novel dynamic stability criterion based on Lyapunov exponents is introduced for viscoelastic structures. New treatment of uncertainty is especially attractive from the design point of view-since extrenal responses can be used for valid design of structures, with scant experimental data needed for their substantiation.
