Static analysis of FE discretized structures with bounded uncertainties via interval method

The uncertainty presents in many engineering analysis is usually modeled by probabilistic approach. It is now largely recognized that the probabilistic approach often cannot be applied to describe structural uncertainty; indeed, it requires a wealth of data, often unavailable, to define the probability density function of the uncertainties. Alternatively nonprobabilistic method can be adopted. In this framework, the interval model seems today the most suitable analytical tool. The interval model is derived from the interval analysis, in which the number is treated as an interval variable with lower and upper bounds. However, the application of the interval analysis in classical form can result in a severe overestimation of the uncertainty of this output. In this paper the limit of interval analysis is overcome by deriving an alternative solution, in the framework of linear static analysis of finite element modeled structures with uncertain-but-bounded parameters. The proposed procedure is based on the factorization of the elemental stiffness matrix following the unimodal components concept, which allows a non conventional assembly of the global stiffness matrix, and on the inversion of the assembled stiffness matrix by an interval-valued Sherman-Morrison formula. Numerical results on truss structures evidence the great accuracy of the proposed approach.