The high demand for container transportation has resulted in an increase in ship size and capacity. Ultra Large Containerships (ULCS) are highly flexible in nature due to their high slenderness ratio and long hull. When encountered by ocean waves, flexible structures vibrate in longitudinal, vertical, horizontal, and torsional modes. In such cases, there is a mutual interaction among inertial, hydrodynamic, and elastic (structural) forces. This phenomenon is known as hydro elasticity. ULCS are also susceptible to nonlinear responses due to their low block coefficients and pronounced bow flares. High speeds and severe sea states complicate the problem and result in larger structural loads. This can be either due to slamming that results in a vibration response, called whipping, or due to the resonating phenomenon when encountering frequency moving closer to the structural natural frequency, called springing. Moreover, the slamming loads may increase with speed, even though the ship travels in a lower sea state. The wave-induced load acting on flexible hulls is influenced by structural vibration and vice versa [Bishop et al. (1979b)][1]. The extreme bending moment increases due to elastic responses, affecting the hull’s longitudinal strength, which decreases the structure’s life. Apart from the vertical and horizontal structural loads, containerships are also highly susceptible to torsional and warping loads because of the open hull. Horizontal and torsional vibrations are usually coupled due to the asymmetry of the ship cross-section with respect to the horizontal axis, as well as eccentricity between the centroid of the section and the shear deformation centre [2]. This results in challenges associated with torsion in the structural design of container ships. Therefore, it is essential to consider the hydroelastic effects while estimating the wave-induced bending moments of flexible hulls. Furthermore, long-term simulations are required for fatigue load assessment of the hull. The 3D RANS-based CFD tools can give accurate results; however, they are computationally intense methods that are still far from practical seakeeping calculations.
Many numerical studies have been conducted on the effect of hydroelasticity on the vertical bending moment of containerships in head seas. However, very limited studies have been conducted on the symmetric and anti-symmetric responses of containerships in oblique seas. Most researchers focused on the vertical bending of large floating structures in head seas. Still, the vertical, horizontal, and torsional bending of large container ships in oblique waves representing high sea states has rarely been studied. Therefore, computationally less intensive tools that account for the major sources of non-linearity are desirable for practical ship design. This current research study proposes a 2D time-domain method (TD) based on a body nonlinear approach. The method can generate long-term time series simulations of hydroelastic responses in high-sea states with minimal computational time. Ships tend to cruise at lower speeds during extreme conditions, and the proposed TD method efficiently estimates the longitudinal strength of large, slender structures like ULCS in such scenarios. The proposed numerical method captures vertical elastic responses even in extreme oblique sea states, which is an aspect that has yet to be explored in existing studies. The bending moment under various sea states, heading conditions, and different speeds of the vessel are investigated and compared with the existing experimental results available in the literature. The hydroelastic effect on the total response of the hull is quantified. Moreover, it is essential to note the hydroelastic characteristics of coupled horizontal and torsional vibrations that occur when containerships encounter oblique waves due to large deck openings. Incorporating these coupled vibrations into the numerical method and investigating its effects on structural loads is a major part of my research objectives.

Keywords: ULCS, Hydroelasticity, Springing, Whipping, slamming, Torsion, Horizontal bending, Vertical bending, 2D method, 3D, RANS, CFD, Seakeeping, Time domain(TD), Body nonlinear.