| A set of fully non-linear equations of motion for a single-tendon tension leg platform are developed. Many of the simplifying assumptions used by prior researchers have been eliminated. The equations of motion consist of a partial differential equation describing the surge response of the hull and tendon, coupled with an ordinary differential equation for the pitch response of the rigid hull. The tendon is modelled as a nonlinear elastic beam undergoing time dependent tension. This extension of the tendon is due to the ocean forces on both the tendon and the hull, and the increase in the hull's buoyancy due to setdown. The full derivation with assumptions is presented. The dynamic response, analyzed for stochastic ocean wave and current loading, is presented with a planar motion assumption. The response is calculated numerically in the time domain by implementing a finite difference scheme. Forces on the tendon have been neglected in much of the literature. Case studies include a tension leg platform with a 415 m tendon and 67.5 m hull, a similar platform with a 1415 m tendon, and a comparison of platforms with large and small hull/mass ratios. The responses presented in this work show that the inclusion of forces on the tendon will result in both a greater amplitude and offset position. This offset position, which is the surge displacement from the vertical position, is significant in the operation of an offshore oil and gas production platform. Monte Carlo simulations are performed on the drag and inertia coeffcients in Morison's equation. The analytical model presented in this dissertation would be useful to researchers to analyze the relative importance of the terms in these equations of motion. Designers of tension leg platforms will find that this model can assist in determining the overall dynamic response characteristics. The structural and fluid parameters may be varied to determine their effects. |
