A time domain code based on strip theory is applied to calculate the probability distributions of relative motions and bending moments of a cruise ship in a set of extreme seas. The code includes two levels of complexity. The simpler one combines linear radiation and diffraction forces with nonlinear Froude-Krylov forces, hydrostatic forces and shipping of green water on the bow. Cummins formulation is used to represent the radiation forces. The second approach is a generalization of the first one and, although the formulation is based on the linear assumption (of the radiation forces), the effects of body nonlinearity are considered by a simplified method: the memory functions, infinite frequency added masses and the radiation restoring coefficients are assessed at each time instant as function of the instantaneous wetted surface. A similar procedure is used to calculate the diffraction forces.
The code is used to analyze the responses of a cruise ship in a set of extreme sea conditions. The nonlinear radiation and diffraction effects on the responses are analyzed by comparing the “fully nonlinear” results with the numerical predictions assuming linear radiation and diffraction forces. The short term nonlinear responses are represented by empirical probability distributions, obtained from time domain simulations, and the quality of the predictions is assessed by comparing with model tests experimental data.