Hydro-elastic response of ship structures to slamming induced whipping

Slamming induced whipping can significantly increase the structural loading of ships. Although this is well-known, the whipping contribution to the structural loading is rarely taken into account when computing the structural loading. An exception are the "dynamic loading" factors found in Classification Societies rules. Currently there are no commercial tools available to compute the seakeeping response including slamming induced whipping. This is the main reason for not accounting for the effects of whipping. Extensive research has been done on the subject of slamming impact and whipping response but an integral and computationally efficient method is not yet available for ship structure designers. This is the starting point for this research presented in this thesis. The objective of this thesis is: "The development of a practical method to calculate the global and local response of the ship structure due to the seakeeping loading including the slamming loading. This method should contain the full hydro-elastic coupling." This method is developed by combining well-known components and new tools. The concept of generalised modes is used to solve the hydro-elastic seakeeping problem. All degrees of freedom of the ship structure are described by mode shapes using this approach, even the rigid-body modes. The number of degrees of freedom may be arbitrary selected by the user. The flexible mode shapes of the structure are obtained from either a 3D-FEM analysis or a 1D-FEM analysis using a beam model of the ship structure. The seakeeping response of all modes, rigid and flexible, is solved simultaneously which ensures a full account for the hydro-elastic coupling. The seakeeping response is solved in the time domain using a 3D surface integration method. The time domain allows one to include non-linear load components and to calculate the transient response with relative ease. The non-linear Froude-Krylov and non-linear hydrostatic loads are taken into account to improve the seakeeping and internal load predictions. The diffraction and radiation loads are kept linear to allow for reasonably fast computations. The linear diffraction and radiation coefficients are solved in the frequency domain using a 3D boundary element method. This hydro-elastic approach allows one to compute the transient whipping response. The springing response can only be partially predicted because springing is often caused by additional non-linear load components which are not included in the presented theory. Since fast and robust, non-empirical 3D methods are not yet available for the calculation of the slamming loads, the slamming loads are solved using 2D methods. The first of the two used methods is the Generalised Wagner Model (GWM). This is the most accurate of the two methods. The second method is the Modified Logvinovich Model (MLM) which is much faster compared to the GWM. The drawback of using these 2D methods is that the slamming loading can only be computed accurately for head seas and near head sea conditions. The computation of the slamming loads is directly integrated into the time domain seakeeping calculation. At every time step the slamming loads are computed based on the actual relative motions, and the computed slamming loads are taken into account for the solution of the resulting motions. Insight into the global response of the ship structure is obtained by using the modal approach for computing the seakeeping response. However, it is difficult to compute the local structural response of a ship structure using the modal method. Therefore, the local structural response is computed by transferring the seakeeping loads to the 3D-FEM model of the structure and solving the response using the FEM method. The method used ensures that the hydrodynamic loads at the structural model are well balanced by the applied nodal acceleration loads, thus ensuring a consistent FEM solution. These nodal acceleration loads allow one to include the effect of whipping even when a quasi-static FEM approach is used. The developed methodology is verified and validated using different ships, results of model experiments and the results of one full-scale sea trial. All verifications show that the developed approach gives the expected results and that the presented theory is consistent. The slamming forces are verified using model experiments of a container ship and an aluminium model. This validation shows that it is necessary to take into account the static bow wave generated by the blunt bow of the container ship when computing the slamming loads to a reasonable accuracy. The validations using experiments with the aluminium model show that the contribution of the added mass on the natural frequency is well predicted, even for conditions with forward speed. The calculated slamming loads and resulting whipping response compare well with the experimental results of the aluminium model. Stresses measured during a sea trial of the M-Frigate of the Royal Netherlands Navy are also used to validate the developed methodology. The computed spectral energy of the wave frequency and the whipping response are close to the spectra measured. The Weibull fits of the extremes of the calculated and measured stresses shows very good agreement, the hog/sag ratio is also well predicted. The stresses are slightly overpredicted for the highest speed. Two ultra large container ships are used for a case study. Design values such as the expected ultimate bending moment and fatigue loading are calculated based on the computed bending moment or stress history. It is shown that the seakeeping response should be calculated for at least 750 wave encounters in order to accurately compute the design values. The developed seakeeping method is fast and robust enough to compute the design values for all cells of a scatter diagram. The expected ultimate bending moment and fatigue damage are calculated based on a life-time of thirty years with both North Atlantic and World wide scatter diagrams. It is shown that the slamming induced whipping and the computed springing response reduce the predicted fatigue lifetime by about forty percent and increase the expected ultimate bending moment by about twenty percent. This shows the importance of accounting for these effects when computing the design values for such flexible ships. It can be concluded that a practical method to calculate the global and local response of the ship structure due to the seakeeping loading including the slamming loading and whipping has been developed. It is shown that the developed method can be applied to calculate the design values for a complete scatter diagram. The validations shows that the predictions are reasonably accurate.