A new interval finite element method for the analysis of structures with interval uncertainties

This paper deals with the analysis of linear-elastic structures with uncertain material properties subjected to deterministic static loads. Under the assumption that available information is insufficient to pursue a probabilistic approach, the uncertain properties are modeled as interval variables characterized by a lower bound and an upper bound. A novel Interval Finite Element Method is formulated in the framework of the improved interval analysis, recently proposed to limit the overestimation affecting the classical interval analysis. Then, approximate explicit expressions of the lower bound and upper bound of the interval response are derived by applying the so-called interval rational series expansion for evaluating the inverse of the interval stiffness matrix. The accuracy of the proposed approach is demonstrated by appropriate comparison with the exact solution provided by a computationally intensive combinatorial procedure.