Analysis of structural systems with interval uncertainties under deterministic and stochastic excitations

This PhD thesis deals with the static and dynamic analyses of structural systems, with uncertain parameters modelled as interval variables, subjected to deterministic or stationary stochastic Gaussian actions. The PhD thesis is subdivided into six chapters. After the Introduction (Chapter 1), in Chapter 2, the interval model of uncertainties has been described and particular attention has been paid to strategies aimed to limit the overestimation of the resulting interval bounds due to the dependency phenomenon affecting the Classical Interval Analysis. In Chapter 3, the static analysis of structural systems with uncertain axial stiffnesses within the interval framework has been addressed. Approximate closed-form expressions of the bounds of the interval displacements and interval axial forces have been first derived. Then, with the purpose of investigating the influence of the uncertainty model on the static response, the uncertain axial stiffnesses have also been modelled as independent random variables with uniform and truncated Gaussian distributions. The comparison between the confidence interval of the response evaluated adopting the random model of uncertainties with the corresponding interval response region, showed that the interval model of uncertainties generally turns out to be more conservative than the probabilistic one, especially, when the number of uncertain parameters taken into account increases. In Chapter 4, first different strategies in evaluating approximate closed-form expressions of the bounds of the interval static responses of finite element discretized structures with uncertain Young moduli have been examined. It has been also shown that very accurate interval bounds of the response can be efficiently obtained, with a reduced computational burden, by adopting a sensitivity-based approach. Then, in order to examine the influence of the uncertainty model on the static response, the uncertain Young’s moduli have also been modelled as random variables described by uniform distribution. The confidence interval of random displacements and rotations have been compared with the corresponding interval regions, showing once again that the interval model of uncertainties generally turns out to be more conservative than the probabilistic one. In Chapter 5 the evaluation of the bounds of the response of linear-elastic structures with interval uncertain parameters subjected to deterministic dynamic excitations has been addressed. The proposed method has been developed in the context of the classical modal analysis by extending sensitivity-based procedures to dynamics. It consists essentially of two deterministic modal analysis (corresponding to the most common combinations of uncertain parameters). It can be easily implemented by taking advantages of commercial standard finite element codes. The feasibility and accuracy of the presented method have been demonstrated by numerical results regarding different structural typologies, even in the presence of relatively large degrees of uncertainty. Chapter 6 is devoted to failure analysis in terms of reliability function and fatigue life of truss structures with uncertain axial stiffness modelled as interval variables, subjected to multi-correlated stationary stochastic Gaussian loads. The mathematical models, performing failure analyses, have been developed by extending to the interval framework the classical formulations given in the framework of stochastic dynamics. In particular, the proposed method allows one to evaluate the bounds of the interval reliability function, as well the ones of the interval expected fatigue life, by performing only two stochastic analyses, corresponding to two combinations of the endpoints of the interval parameters identified by applying a novel sensitivity-based approach. Finally, a conclusive chapter summarizes meaningful results and highlights the main novelties introduced in the literature.