Keywords: time-variant reliability, finite element model, non-linear simulations, ageing structures.

Reliability assessment of an ageing structure needs to focus attention on the temporal and random character of the data relating to environmental conditions and loads. Improving the accuracy of this reliability assessment allows better optimisation of planning inspection and maintenance. As a consequence, this improves safety during an extended service life. A promising way to deal with engineering problems relies on coupling time-variant reliability methods with finite element analysis.

As far as design of naval structures is concerned, the complexity of loading histories to be represented implies dealing with the non-linear aspect of the mechanical behaviour of the material. Furthermore, as structural properties can evolve in time due to ageing or corrosion, irreversible damage can appear in the most stressed parts, for example fatigue cracks. To model these kinds of issues, strongly non-linear time-dependent problems have to be solved, leading to important computational costs.

In addition, coupling of structural reliability methods with non-linear finite element analyses requires robust mechanical models to ensure accurate results [1]. The following study presents a time-variant reliability approach based on coupling the PHI2 method [2] with a non-linear finite element analysis. The originality of this approach is that only time-invariant reliability tools are needed to evaluate the cumulative probability of failure. Moreover, in order to limit the computational cost of simulations, appropriate mechanical models have to be developed.

The possibilities and validation of the propounded approach are presented through numerical examples. On one hand, the time-variant reliability analysis of a corroded elasto-plastic plate submitted to a stochastic load is presented. A usual finite element way to analyze the influence of the time-space evolution of the corrosion on a structure relies on using re-meshing strategies to deal with the local or global decrease of the safe thickness; but such mechanical strategies can strongly decrease the convergence speed of reliability analysis. Thus the proposed two-dimensional mechanical approach modelling continuously decreases of the safe thickness (corrosion effects) permits the avoidance of these re-meshing strategies. And on the other hand, a reliability approach of adhesively-bonded assemblies is presented. We use cohesive-zone models taking into account initial defects, damage evolutions. Moreover interface elements strongly limit the mesh dependence for crack propagation. This approach is well suited for bonded joints as the possible degradation zone is well defined.

This paper emphasizes the feasibility of the coupling of time-variant reliability methods with non-linear finite element analysis, highlighting the necessary effort to compute the cumulative probability of failure in terms of accuracy and computational cost.

1

Cazuguel M., Andrieu-Renaud C., Cognard, J.Y., "Time-variant reliability of non-linear structures: Application to a representative part of a plate floor", Quality and Reliability Engineering, Vol. 22, pp. 101-118, 2005.

2

Andrieu-Renaud C., Sudret B., Lemaire M., "The PHI2 method: A way to compute time-variant reliability", Reliability Engineering and System Safety, Vol. 84, pp. 75-86, 2004. doi:10.1016/j.ress.2003.10.005

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