Explicit Solutions for the Static and Dynamic Analysis of Discretized Structures with Uncertain Parameters

In this review paper, a novel approach to derive in explicit form both the static and the dynamic frequency domain responses of linear discretized structures with uncertain stiffness parameters is described. This approach is based on the following main steps: i) the decomposition of the deviation (with respect to its nominal value) of the stiffness matrix as a sum of rank-one matrices; ii) the use of an innovative series expansion, herein referred to as rational series expansion, to evaluate in approximate, but explicit form, the inverse of the stiffness matrix as well as the frequency response function of the structural system. By applying this procedure, very accurate explicit expressions of both the static and the frequency domain responses of structural systems with uncertain parameters are obtained. Furthermore, the described approach is applied in conjunction with the so-called improved interval analysis to evaluate in explicit form the bounds of the response of structures with uncertain-but-bounded parameters.