A benchmark study of 10 different numerical methods for ship motion and load assessment is presented. Pitch motions and midship vertical bending moments are compared to model test results for a containership at zero speed in head regular waves. The wave steepness is varied from 2.1% to 10.5%. The model tests show that pitch and the vertical bending moment (VBM) display nonlinear behavior even for low-steepness waves. It is demonstrated that computational fluid dynamics (CFD) methods can reproduce the ship responses with good accuracy, even in very steep waves, involving green water and parts of the ship going in and out of water. Weakly nonlinear potential-theory methods tend to overestimate the pitch motions and the sagging moments as the wave steepness increases. For the vertical bending moment in steep waves, the 3D panel methods did not give significantly better results than those obtained with the nonlinear strip theories.

Accurate prediction of nonlinear vertical bending moment (VBM) in large regular waves remains challenging, especially when wave steepness increases and strong free-surface nonlinearity and local impact loads become relevant. This study investigates the influence of wave steepness and boundary treatment on VBM predictions using a GPU-accelerated smoothed particle hydrodynamics (SPH) solver. A segmented-hull approach is adopted to compute the time history of VBM from integrated hydrodynamic forces, and the numerical results are assessed against benchmark data and reference solutions. A series of simulations are conducted for a range of wave steepness from 2.1% to 10.5%, and sensitivity analyses are performed with different particle resolutions. Particular attention is paid to the comparison between the dynamic boundary condition (DBC) and the dummy particle condition (DPC). The results show that boundary treatment has a dominant impact on the prediction of VBM. DPC consistently provides improved agreement with the reference data, while DBC exhibits larger deviations in terms of hogging, sagging and waveform in time history data. Concerning the peak-to-peak VBM, both SPH models with the two boundary conditions show similar accuracy, comparable to the experimental data, the weakly nonlinear boundary element method, and the FVM-based CFD solver. These findings highlight the necessity of carefully selecting and validating boundary treatments when applying GPU-SPH to nonlinear VBM predictions.