Objectives In the context of the continuous development of modern ships towards large sizes and high speeds, along with the application of high-strength steel, the hydroelastic vibration problem of ships has become more prominent due to the decrease of hull natural frequencies. The loads of springing and whipping significantly contribute to the wave loads of large ships. However, existing research on ship wave loads and hydroelasticity mainly focuses on the symmetric responses of ships sailing in head regular waves. In realistic sea conditions, ships encounter waves from various directions. Due to the complexity of solving ship asymmetric responses, research on wave loads and hydroelasticity of ships in oblique waves remains limited. It is of great significance to accurately predict the asymmetric wave loads and structural responses of ships under extreme wave conditions. The objective of this study is to establish a ship hydroelasticity method based on the CFD-FEM two-way fluid-structure coupling, which can predict the motions and wave loads of ships in oblique regular waves considering the influences of asymmetric loads, structural responses, and nonlinear load effects. This method can provide a new approach for evaluating the hydrodynamic and structural load performance of ships in oblique sea conditions, and help to understand the effect of hydroelastic on ships.

Methods The methodology employed in this research involves several steps. Firstly, a computational domain for oblique regular waves is established within the CFD software. The three-dimensional N-S equations are solved in the fluid domain to calculate the nonlinear wave loads on the ship in model scale. The numerical wave tank's computational domain includes a background region and an overset region. The Euler Overlay method is used to generate fifth-order Stokes waves. Secondly, a finite element model integrating the hull beam and the ship hull is developed. The massless hull surface is modeled with shell elements while the backbone beam is modeled using 3D uniform beam elements. The total mass and moment of inertia of roll motion of the ship model are similar to the full-scale ship. To ensure the longitudinal weight distribution and moment of inertia of the roll motion of the FE model to be consistent with the experimental model, concentrated mass and moment of inertia of the roll motion are added to the reference points in two stages. Finally, a two-way fluid-structure coupling analysis is carried out. Both the motions and structural deformations of flexible structure derived from the FEA will be fed back to the CFD solver to update the hydrodynamic grid data. The fluid loads on the deformed structure calculated by CFD, which is realized with the help of morphing grid technique, will be then applied to the structural FE model for the subsequent FEA.

Results The results show that the numerical method is proved to be effective by conducting the CFD grid and time step sensitivity analysis and the free roll decay comparison. It can accurately predict the trends and amplitudes of pitch motion, vertical bending moment (VBM), and torsional moment (TM) when compared with experimental results. For instance, in the motion response analysis of a ship in oblique waves, the numerical simulation results of heave, pitch, and roll are generally consistent with the experimental results, with the pitch peak error within 8%. In terms of load analysis, the VBM and TM calculated by the numerical method show good agreement with the experimental trends, although there are some difference. In extreme sea conditions, the high-frequency components caused by slamming become the main components of the total bending moments. The wave frequency horizontal bending moment (HBM) and TM increase linearly with the wave height, while the high frequency components exhibit significant nonlinear growth. Under typical extreme sea conditions, the HBM at typical sections is comparable to the VBM loads.

Conclusions In conclusion, the established CFD-FEM method can accurately predict the motion and load responses of ship under asymmetric waves. It serves as a novel approach for evaluating the hydrodynamic and structural load performance of ships in oblique sea conditions. The research also reveals that the ship hydroelastic effect has a significant impact on VBM, HBM, and TM under severe sea conditions. This study provides valuable insights into ship design and performance evaluation in complex sea environments, and promotes the development of ship hydroelasticity research.