Static and Dynamic Analysis of Non-Linear Uncertain Structures

The procedures usually adopted in the evaluation of the stochastic response of structures with uncertain parameters, the so-called stochastic structures, are affected by some limits. Namely, the major drawbacks are: the conspicuous computational time required for the analysis of many degree of freedom systems and the loss of accuracy in the case of large uncertainty in the parameters. A method able to reduce the previous inconveniences was recently introduced in the study of statically loaded linear structures. The method, named improved perturbation method, was also extended to the field of linear dynamics. In both cases, the improved perturbation method provides a good approximation, even in the case of moderately large deviation of the uncertain parameters, and the computational time required is comparable to conventional first order perturbation. The present paper intends to apply the improved perturbation method in the second order analysis of geometrically non-linear uncertain systems subjected to static and dynamic deterministic forces.