Analysis Method of Ultimate Strength of Ship Hull Girder Under Combined Loads: Application to an Existing Container Ship

A ship hull is regarded as a box girder structure consisting of plates and stiffeners. When the ship hull is subjected to excessive longitudinal bending moment, buckling and yielding of plates and stiffeners take place progressively and the ultimate strength of the cross-section is attained. The ultimate longitudinal bending strength is one of the most fundamental strength of a ship hull girder. Finite element method (FEM) analysis using fine-mesh hold models has been increasingly applied to the ultimate longitudinal strength analysis of ship hull girder. However, the cost and elapsed time necessary for FEM analysis including finite element modelling are still large for the design stage. Therefore, the so-called Smith’s method [1] has been widely employed for the progressive collapse analysis of a ship hull girder under bending. Recently, there is a growing demand for a container ship, which is characterized as a hull girder with large open decks. This type of ship has a relatively small torsional stiffness compared to the ships with closed cross-section and the effect of torsion on the ultimate longitudinal strength may be significant. However, the Smith’s method above mentioned cannot consider the influence of torsion. Therefore, some of the authors developed a simplified method of the ultimate strength analysis of a hull girder under torsion as well as bending [2–4]. In this method, a hull girder is modeled by linear beam elements in the longitudinal direction, and the warping as well as bending deformation is included in the formulation. The cross-section of a beam element is divided into plate elements by the same way as the Smith’s method. Therefore, the shift of instantaneous neutral axis and shear center can be automatically considered by introducing the axial degree of freedom as well as the bending ones into the beam elements, and keeping the zero axial load condition. In this study, the average stress-average strain relationship of each element is calculated using the formulae of the Common Structural Rules (CSR) [5] and HULLST proposed by Yao et al. [6, 7] considering the effect of shear stress due to torsion on the yield strength. There had been a lot of papers [8] which discuss the importance of strength assessment to large container ships under torsion. However, there are few papers which discuss the influence of torsion on the ultimate hull girder strength. In this paper, the proposed simplified method is applied to the existing Post-Panamax class container ship. First, a torsional moment is applied to the beam model for the ship within the elastic range. Then, the ultimate bending strength of cross-sections is calculated applying the Smith’s method to a beam element considering the warping and shear stresses. On the other hand, nonlinear explicit FEM are adopted for the progressive collapse analysis of the ship by using LS-DYNA. The effectiveness of present simplified analysis method of ultimate hull girder strength under combined loads is discussed compared with the LS-DYNA analysis.