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On stochastic modelling and reliability of systems with moving cracked material

2015

In many industrial processes, such as printing paper, a material travels through a series of rollers unsupported and under longitudinal tension. The value of the tension has an important role in the system behaviour, such as fracture and me- chanical stability. This thesis develops stochastic models for a system in which an elastic, isotropic cracked material travels through a series of spans and studies the probabilities of fracture and instability of the material. The models focus on describing tension variations and initial cracks in the material. Time-dependent tension fluctuations are modelled by the stationary Ornstein-Uhlenbeck process, and the occurrence and lengths of the cracks are…