On Dynamic effects of Bulbous Bow Crushing

For evaluation of the consequences of ship-ship collisions, and ship collisions against offshore installations and bridges, it is important to know the force-displacement relation and the energy absorption caused by crushing of complex bulbous bow structures. This paper presents a method to calculate the dynamic bow crushing forces using simplified analytical procedures taking into account the variation of the crushing velocity during impact. Firstly, a non-linear finite element method is applied to simulate the dynamic as well as the quasi-static crushing process of the large scale quasi-static bow crushing experiments performed by Yamada and Endo (2005). The dynamic crushing force-displacement relations, the strain rates and the energy absorption of the bow models are evaluated. An empirical relation is derived between the actual crushing velocity and the strain rates in the bow structure. For different ship impact velocities and impact masses, the dynamic impact results are compared with the experimental static crushing results. It is observed that for realistic velocities and masses the crushing forces and energy absorption of the bulbous bow structure is increased significantly due to the dynamic effects. Secondly, an analytical procedure is presented which is based on a quasi-static simplified calculation method modified by the derived relation between actual deformation velocity and the strain-rates. The varying crushing velocity is determined by an energy based procedure to give consistent estimates of the dynamic bow crushing forces. Finally, the simulated numerical non-linear finite element dynamic and static crushing responses are compared with the results of the presented simplified analytical method.