Antioptimization of structures with large uncertain-but-non-random parameters via interval analysis

Non-probabilistic, interval modeling of uncertain-but-non-random parameters for structures is developed in this paper for antioptimization analysis, consisting in determining the least favorable responses. The uncertain-but-non-random parameter is considered to be a deterministic variable belonging to a set modeled as an interval. The least favorable static displacement bound estimation for structures with uncertain-but-non-random parameters is transformed into solving interval linear equations. For small interval parameters (the width of interval being small), the uncertainties of interval parameters are treated as the perturbed quantities around the midpoint of interval parameters, by means of the interval matrix central notation and the natural interval extension. Interval perturbation method for estimating the static displacement bound of structures with interval parameters was presented in the recent study by Qiu et al. [1]. For large interval parameters, a subinterval perturbation method for estimating the static displacement bound of structures with interval parameters is put forward in the study. The numerical results show that a subinterval perturbation method yields tighter bounds than those yielded by the interval perturbation method.