Application of probabilistic thermomechanical models to large and/or complex structures

Abstract

Abstract An affine probabilistic model is used to show how the cumulative and local probabilities of fracture of yielding can be determined in complex and/or large structures. The theory of probabilistic strength of materials supplies an expression allowing the cumulative probability of fracture, or yielding of a large and/or complex structure to be computed, taking into account the knowledge of the said probabilities in a material similarly manufactured but smaller, using an affine transformation. The result is independent of the stress field and of the analytical form of Weibull's specific risk function. The system must be loaded gradually, and if there is some thermal shock then the time in which the thermal perturbation is dissipated into the structure must be greater than the time occupied by the elastic wave in going through the structure, such that the assumption of gradual loading still holds. Costs in terms of time and money are reduced by using smaller models and by considering a time-transformation that allows the testing of structures subjected to thermal stresses to be speeded up.