Random variables transformation for the response evaluation of structures

The present PhD thesis deals with the use of the Probability Transformation Method (PTM) and of some of its extensions for solving mechanical and structural systems for which the response is modeled as random fields or variables that cannot be well approximated as Gaussian. In particular, besides the study of stochastic systems, whose geometric and material properties are random, structural systems in which uncertainties in the model designed could arise, have been investigated. In the contexts of stochastic systems, the exact probabilistic solution of redundant stochastic beams, when the flexural deformability is random has been formulated. Moreover, a study was conducted for the stochastic analysis of cracked Euler Bernoulli beams when the cracks are modeled as a rotational internal spring with random amplitude and positions. Then, the concept of the local and nonlocal randomness in stochastic mechanics have been investigated through three research works in which a link between the statistical properties of random field and the local and non-local randomness in stochastic mechanics have been found. Finally, the dynamic stochastic analyses of linear structural systems excited by non-Gaussian excitations have been considered. In any case, this PhD thesis collects several research works with the main goal of gathering all the typologies of stochastic structural analyses in which the PTM can be advantageously applied, both in terms of accuracy and efficiency.