Abstract
Classical approaches to inverse reliability analysis, and to reliability-based design optimization, require evaluation of limit state gradients. This can be an issue for highly non-linear time-variant reliability problems. Stochastic fracture mechanics, for instance, involves non-linear crack propagation and millions of load cycles; also hundreds to millions of random variables. Gradient computation becomes highly unstable at the end of fatigue life, as does the crack growth process. In this paper, a hybrid approach is proposed for solving this type of problem: it explores and combines the best of Monte Carlo Simulation (MCS), First-Order Reliability Method (FORM) and a root-finding method. The non-linear crack propagation phase of the problem is handled by MCS; the final fracture problem is handled by FORM; and the allowable crack size, required to impose a minimum lifetime reliability, is obtained by simple root-finding, among the set of initial crack size samples. Efficiency is achieved: (a) by classifying initial crack size samples, and computing only those terms effectively contributing non-zero probabilities to the integral; and (b) by solving the optimization problem using the information acquired from a single Monte Carlo run. The proposed hybrid approach is employed in the solution of typical crack propagation problems: it is shown that it gains efficiency when the target reliability and the number of load cycles are large, as expected in practical problems of this kind. It is also shown that it converges to the reference solutions, being them exact, when available, or usual MC-based solutions, while taking only a fraction of the computational time required by the latter.
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Acknowledgements
This work was sponsored by PETROBRAS through Cooperation Term 5900.0112628.19.9: “Innovation for acceptability of flaws in rigid risers using probabilistic fracture mechanics”. This work is also supported by the National Council for Technological and Scientific Development (CNPq) via grants 302489/2017-7 and 309107/2020-2.
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Gomes, W.J.S., Garmbis, A.G. & Beck, A.T. Hybrid MCS-FORM approach to solve inverse fracture mechanics reliability problems. Struct Multidisc Optim 65, 77 (2022). https://doi.org/10.1007/s00158-022-03182-4
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DOI: https://doi.org/10.1007/s00158-022-03182-4