Evaluation of time step in the retardation function considering a statistical approach for offshore platforms.*

In irregular wave excitation, correct evaluation of time step is extremely important for the accurate prediction of motions of the semi-submersible platform namely surge, heave and pitch which are predominant. The retardation function in the Cummins equation plays a major role in the evaluation of system damping. In the coupled equation of motion, the convolution integral involving the retardation function is very important for correct prediction of the responses. In this study, the probable time step for the calculation of retardation function has been found out using statistical outlier approach. The wave spectrum used was a JONSWAP spectra with a significant wave height 6.0 m and spectral peak period of 11.2 sec. The wave forces based on diffraction theory were calculated using the boundary element method. In the time domain simulation, numerical integration for the damping has been carried out using trapezoidal rule and to calculate the platform motions predictor-corrector rule has been applied. At last, comparing frequency domain analysis, the motion time history has been verified with power spectral density.