Numerical Method to Compute the Wave-Induced Rigid Body and Elastic Response of Ships at Forward Speed
Throughout the ship’s operating life, the structural components of the ship hull have to withstand wave-induced loads. For the design of the steel structure, wave-induced global sectional loads, such as the vertical and horizontal bending moment or the torsional moment, play an important role. In some situations, resonant wave-induced hull girder vibrations, so-called springing, can occur, which is an important issue when addressing fatigue damage of the steel structure. The present work introduces a new numerical method that combines numerical efficiency with an accurate prediction of the global hydroelastic behaviour of ships in waves and is also able to predict higher order springing induced vibrations. Structural dynamics were computed based on a new beam element approach that considers vertical and horizontal bending as well as nonuniform torsion. The mass and stiffness matrices accounted for coupling effects between hull girder bending and torsion. A weakly-nonlinear time domain approach based on Rankine sources was developed to compute the ship’s hydrodynamic properties and wave-induced forces and moments. The hydrodynamic solver coupled the fully nonlinear stationary forward speed flow problem with the oscillatory flow problem in waves and considered geometrical nonlinearities caused by the changing wetted surface due to the incident waves, ship motions and elastic deformation. New free surface and body boundary conditions were developed to account for elastic deformations of the ship structure. The new numerical method was systematically validated against model test data and CFD results of four different types of ships at forward speed in head and oblique waves. It was shown that the new numerical method is able to compute wave-induced hydrodynamic forces, wave-induced rigid body motions, the wave added resistance and wave-induced sectional loads of an elastic ship as well as higher order springing-induced vibrations with a good agreement to the model test and CFD results. Furthermore, it was shown that forward speed effects (the stationary wave system and dynamic trim and sinkage) and the wave steepness influences the hydroelastic response of ships in waves strongly.