Constant tensions/forces (see Winch Line and Force Line) or thruster forces (see External Static Forces) acting at specified locations on a structure can be defined as necessary.

Additional structure stiffness forces can also be defined as necessary with respect to the fixed reference axes:

(13–10)

where is the additional structure stiffness matrix of the structure system, is the equilibrium position of the origin of GXYZ of each structure, and is the force at the equilibrium position.

External forces can also be defined in a time domain analysis by importing a time history record of those forces, and/or by an external force dynamic link library named user_force.dll.

The time history record of any additional external forces and moments acting at the center of gravity or the combined COG of a structure (expressed in the local structure axes (LSA) of that structure) can be stored in a file and imported for an Aqwa time domain analysis. The times defined in this imported record of external forces do not need to match the time steps of the time domain analysis, as Aqwa will interpolate the forces when necessary (using a cubic spline interpolation technique). However, when periods of constant forces are included in the record, an adequate number of data points must be provided to satisfy the interpolation method.

The dummy variables of user_force.dll consist of a series of constant integer and real parameters that you input, as well as the current time and time interval , the position and orientation array , and the velocity array , for each structure at that time in the fixed reference axes (FRA). The additional external force matrix in the fixed reference axes can be defined as a function of the known structure positions and velocities, such as

(13–11)

where and are sets of user-defined constant integer and real parameters.

Alternatively, if the external forces in the structure local axis system (LSA) are defined as a function of the velocities,

(13–12)

where , is the Euler transformation matrix between the local structure axes (LSA) and the fixed reference axis (FRA) (as given by Equation 1–7), and is therefore the structure velocity in the LSA.

The external force matrix in the FRA is then:

(13–13)

The external forces, which are linearly proportional to the structure acceleration, can be defined via the additional added mass matrix, as the accelerations are unknown variables. Similar to the external force definitions in Equation 13–11 through Equation 13–13, the additional added mass matrix in the global axes can be expressed in a general form:

(13–14)

Equation 13–11 through Equation 13–14 can be employed in both the prediction and correction stages of the predictor-corrector numerical time integration scheme.