Fatigue analyses of flexible pipes through the application of long-term response statistics, when considering bimodal seas, is particularly challenging due to the excessive computational costs involved, since it requires, generally, to solve numerically a four-dimensional integral associated with time-domain finite-element-based analyses of the flexible pipe. Thus, the search for effective approaches to solve this integral is the target of this paper, which investigates the efficacy of some Dimension-reduction methods (DRMs), which had never been applied to the problem posted, according to the authors' knowledge, as an option to compute the fatigue damage of these structures. The performance of the DRMs is compared with the Monte Carlo simulation method (MCSM). Two case studies are presented: a 4in, and a 7in, flexible riser connected to a Semi-submersible, and a spread-moored FPSO platform, respectively. The studies demonstrate that some DRMs presented very accurate results, exhibiting high efficacy with errors below 3% and that the Bivariate dimension-reduction method (BDRM) required only 18% of the computational cost compared to the Standard Gauss-Hermite Quadrature (SGHQ) in R^4 or much less when compared to the MCSM.

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