For a towed tether, one tether end is attached to a nominal structure with three spring stiffnesses in the translational directions, which are assumed to represent a soft mooring line stiffness between the tether and its attached structure. As shown in Figure 10.1: Tether Element Axes and Nodal Displacement (a), those three stiffnesses are denoted as , , and .

For an installed tether, between the vessel end of the tether and its corresponding vessel attachment point, three spring stiffnesses (, , and ) are defined as the inline stiffness and two rotational stiffnesses about the TEA y- and z-axes respectively. These are used to determine the relative translational displacement in the TEA x-direction and rotations about the TEA y- and z-axes between the vessel end of the tether and the vessel attachment point. The relative translational displacements in the TEA y- and z-axial directions are set to be zero at the vessel attachment point.

Similar to the vessel end of an installed tether, three spring stiffnesses ( , , and ), between the anchor end of the tether and the corresponding fixed point on the sea bed, are defined as the inline stiffness and two rotational stiffnesses about the TEA y- and z-axes. The relative translational displacements in the TEA y- and z-directions are set to be zero at the anchor point.

As a special case, if the anchor inline stiffness is positive but small, the tether can be considered to be free-hanging. In this case, a tether lower stop distance can be introduced to define a stop point below the anchor end. The anchor end of the tether is restricted to be no lower than this point.

Several other constraints at the specified tether element nodes can be defined, such as the tether fixed lateral constraint, the tether fixed rotational constraint, the tether rotational vessel constraint (representing an encastre condition on the vessel) and the tether lateral vessel constraint. It should be noted that the two above-mentioned rotational constraints are rarely used, as they will cause large bending moments at the attachment points. A tether lateral vessel constraint defines a gap to represent an opening on the vessel that is wider than the tether. This is assumed to be a frictionless circular gap in the structure, below the vessel end of the tether along the TEA x-axis direction. If the total lateral movement relative to the center of the gap is greater than the specified gap distance, it is assumed that the tether node at the gap is constrained laterally by the structure.