The manner in which a mechanical structure responds to loading depends on the type and magnitude of the applied loading, on the random character of material properties and on structural stiffness. In practice, some design parameters and their evolution in time are not completely mastered. For instance, in the case of assembling elements of composite structures or metallic materials by adhesive, the variability in joint thickness or the presence of possible defects can‘t be ignored. Thus, in order to improve the service life, those phenomena must be taken into account. Whether the response is considered satisfactory depends on the requirements which must be satisfied. These includes safety of the structure against collapse, damage, deflection or other criteria (termed by a limit state). As industrial applications are concerned, the structural response is, in general, non-linear. So a robust non-linear finite element analysis must be performed to model this response. The use of non-linear finite element analysis is nowadays widely recognized as the most effective method to assess the response of industrial-type structures. Its combination with time-variant reliability methods is thus a way to optimize their maintainability. In practice strongly non-linear time-dependent problems have to be solved in order to model this kind of issues, leading to important computational costs. To limit numerical costs, finite element model has to be optimized.

 If we focus attention on the study of the structural reliability, we notice that the assessment of risks stemming from these phenomena is an essential issue in predicting the service life. Time-independent reliability does not provide sufficiently relevant and realistic information. In fact loads and material properties can evolve in time. It is thus necessary to use the theory of time-dependent reliability to take into account the time dependence of the phenomena and the loadings. The coupling of the structural reliability software evaluation with a non-linear finite element analysis requires robust mechanical models to ensure the quality of durability of a structure in time.

This work introduces a time variant reliability approach based on the estimation of the durability of a T-bonded structure. This widely used structure (construction, naval field, aeronautical field...) can have various material behaviours, it can also evolve in an environment characterised by severe conditions. Loads can also be time dependent and can have random character. If we want to model correctly the structural response all these aspects must be taken into account. For this work, two studies will be introduced. The first study is based on an analytical elastic model of the T. For the second part of the work cohesive zone elements are used to model the adhesive in order to simplify the numerical study of the adhesively bonded assembly and limit the numerical cost. The cumulative probability of failure is computed and two methods are compared. An example showing the differences between the two methods is presented in the sequel.