Accelerated second-order hydrodynamic load calculation on semi-submersible floaters

A rapid method for calculation of second-order hydrodynamic wave loads on semi-submersible platforms is developed and validated against radiation–diffraction theory. The method is based on slender-body theory and builds on modal truncation of the quadratic transfer function (QTF). The semi-submersible floater is split into individual members and the existing theory for vertical cylindrical columns is extended to include the heave force. Further expressions for the surge, heave and pitch load on the horizontal pontoons are derived and implemented. The accuracy of the method is assessed by comparison to radiation–diffraction results using the Pinkster approximation. We find that the slender-body approximation for the column surge force is most accurate for small values of the diameter-to-draft ratio. For the three sea states considered, this error is below 10% for diameter-to-draft ratios less than 0.2. Error analysis is provided for the column heave and pitch and the pontoon loads. For all members, application of 128 modes in the QTF approximation is found sufficient to accurately represent the full slender-body QTF solution. Next, the first- and second-order loads on the full floater under different sea state conditions are compared to radiation–diffraction theory. With 128 modes, the second-order loads are obtained 2500 times faster than with conventional approaches with error levels of 22% for surge, 10% for pitch and zero error for heave. The surge error is discussed and linked to the small draft of the columns. The numerical efficiency of the method allows the consideration of second-order loads in the first stages of the design and optimisation of semi-submersible floaters.