Formulation of consistent nonlinear restoring stiffness for dynamic analysis of tension leg platform and its influence on response

Shortcomings of the traditionally used nonlinear restoring stiffness of TLPs, i.e. unrealistically high stiffness of horizontal motions, their uncoupling and secant formulation are pointed out. Therefore, new consistent restoring stiffness is derived. The platform is considered as a rigid body moored by flexible pretensioned tendons. Global horizontal low frequency motions (surge, sway and yaw) with large amplitudes as a result of dominant second order wave excitation and small stiffness, and vertical local motions (heave, roll and pitch) of higher frequency and small amplitudes excited by the first order wave forces, are distinguished. Hence, horizontal displacements represent position parameters in analysis of vertical motions. First, the linear restoring stiffness, which consists of the tendon conventional axial stiffness, the tendon geometric stiffness and the platform hydrostatic stiffness, is established. Then it is extended to large displacements resulting in new secant restoring stiffness. It depends on surge, sway and yaw displacements and is the same in any horizontal direction. Also, the tangent stiffness, which gives more accurate results, is derived. Heave is defined as vertical projection of axial tendon vibrations and platform tangential oscillations, which are analyzed in their natural moving coordinate system. Inertia force due to setdown, as a slave d.o.f. of the master horizontal motions, is taken into account in the dynamic equilibrium equations. As a result the complete tangential stiffness matrix of horizontal and vertical motions includes 7 d.o.f. The known secant restoring stiffness matrices are compared with the new one and noticed differences are discussed. All theoretical contributions are illustrated by relatively simple numerical example.