Structural Reliability Analysis of Container Ships under Combined Wave and Whipping Loads

A practical methodology for structural reliability assessment of ultra large container ships is proposed in the article. The commonly used limit state function for structural reliability analysis of oil tankers and bulk carriers was extended to take into account the whipping response due to the bow flare slamming. The ultimate vertical bending moment capacity of hull girder was considered as a fundamental safety variable in the limit state function, whereas the stochastic model of the loads consists of static still-water bending moments (SWBMs), low-frequency rigid body vertical wave bending moments and high-frequency whipping bending moments. The stochastic model of SWBM for one of the studied ships was obtained from actual bending moments recorded by the onboard loading computer in 2 years of operation. Linear vertical wave bending moment was calculated by a 3D panel seakeeping code, using International Association of Classification Societies (IACS) recommendation No. 34 for the computation of extreme global wave loads. The nonlinear correction of linear wave bending moment was obtained from the recent IACS Unified Requirement S11A for longitudinal strength of container ships. Impulsive loading was modeled by von Karman added mass variation method, whereas transient dynamic hull girder response was analyzed by Timoshenko beam finite elements. Load combinations between extreme still-water and vertical wave bending moments, and between extreme low- and high-frequency vertical wave bending moments are considered. The structural reliability analysis of two container ships of different sizes was performed using the first-order reliability method, to observe differences in safety levels due to different ship sizes. Safety indices are compared with the International Maritime Organization recommendations for double-hull oil tankers to have credible basis for assessing the obtained results. An extensive sensitivity and parametric study was performed, accounting for various operational, environmental, and modeling uncertainties, as well as for corrosion degradation. The presented study may be useful for classification societies in further development of recently introduced IACS Unified Requirements for longitudinal strength of container ships.