Abstract: In one or more embodiments, a method is disclosed for performing fatigue analysis for a given process and utility piping geometry having one or more restraint locations disposed about a floating vessel. The method can include the steps of generating one or more bending moment polynomials from bending moment data associated with the floating vessel; generating a slope polynomial from each of the bending moment polynomials by integrating each of the one or more bending moment polynomials; generating a displacement polynomial from each of the slope polynomials by integrating each of the one or more slope polynomials; solving the slope polynomial integration constants; and solving the displacement polynomial integration constants to provide slope and displacement polynomials representing the floating vessel response to excitations while at sea.