The evaluation of extreme bending moment corresponding to a 25 years return period requires very long simulations on a large number of sea states. This long term analysis is easy to do with a linear model of the ship response, but is impractical when using a time consuming model including non linear and slamming loads. In that case some simplified methods need to be applied. These methods are often based on Equivalent Design Waves (EDW) which are calibrated on the extreme linear value.

The general practice is to define the EDW as a regular wave. A very simple method is to compute the non linear bending moment applying the pressure correction on the hull without recomputing the ship motions. A better method is to recompute in time domain the non linear ship response on this Design Wave. It is even possible to define a more realistic Design Wave, taking into account the frequency and directional content of the sea states used in the long term analysis: those waves are called Response Conditioned Wave and Directional Response Conditioned Waves.

The different methods are applied to an Ultra Large Container Ship (ULCS). Hydro-structure calculations are carried out on a severe design sea state, taking into account Froude-Krylov pressure correction, slamming forces and whipping response. Results of a very long computation are compared to the results of the Design Wave approaches.

Another method is proposed to compute very rare events. It is based on an artificial increase of the significant wave height of the sea state, and the assumption of the independence of the non linear effects to the significant wave height. Using this method it is possible, with a simulation of only a few hours, to predict a very rare short term event, corresponding to a very long return period. The results are compared to the Design Wave results and appear to be much more precise.

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