Time Domain Analysis |
 
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Time Domain Analysis |
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Each floating body is modelled as a rigid body with six degrees of freedom that are included amongst the solution variables. The hydrostatic stiffness contribution associated with the floating body is included in the global stiffness matrix at the location of the floating body Centre of Buoyancy (CoB). The (frequency independent) mass and inertia of the floating body is included in the global mass matrix at the location corresponding to the floating body Centre of Gravity (CoG). Mechanical loads from connected structures (such as mooring lines, risers, transfer lines etc.) are automatically transmitted to the floating body by means of its inclusion in the finite element model.
During time domain dynamic analyses, static, low frequency and wave frequency loads on the floating body are computed and accumulated at the appropriate location in the global force vector. Further details are provided in Applied Loading.
The position of the floating body is solved for at each timestep, subject to the full range of environmental loading and mechanical loads from connected structures.
Hydrodynamic coupling between pairs of floating bodies is specified by means of defining co-influence added mass and radiation damping matrices for the two floating bodies. In the case of time domain dynamic analyses, the off-diagonal terms of the co-influence matrices give rise to additional off-diagonal retardation functions in the matrix of retardation functions, and additional off-diagonal terms in the frequency-independent added mass matrix.
As discussed in Wave Radiation Loads, frequency-dependent radiation damping forces are computed via a convolution integral of velocity time history and retardation functions. This would be the standard modelling procedure for random sea analyses in the time domain. However, there are certain circumstances where a different approach is adopted. For example, Flexcom does not generally compute the damping forces in this manner if the wave loading consists of a single regular wave only, even if frequency-dependent radiation damping data has been specified. Typically the program finds a (constant) radiation damping matrix (by interpolation if necessary) corresponding to the single regular wave frequency, and adds this matrix at an appropriate location on the left-hand side of the equations of motion. However, you have the option to override this default behaviour, and compel Flexcom to perform the convolution calculation, in which case the radiation damping becomes a force on the right-hand side of the equations of motion as before.