Dynamic Calculation Parameters

The following parameters are available:

The simulation time step should be chosen such that important dynamic effects are captured in the structural analysis. This time step should be chosen based on the loading rates, finite element length, dynamic response, and iteration procedure. Simulations considering contact problems generally require a short time step.

The following parameters are available:

Time series of waves, wind, and/or first or second order wave loads (or linear support vessel motions) are required during the dynamic simulation. These time series should be generated such that they are at least as long as the full dynamic simulation and correctly represent the desired frequencies. That is, the time series length should be greater than or equal to the simulation length (to avoid repetition), and the time increment for time series generation should be appropriate for the given process. The time increment for time series generation should also be an integer multiple of the simulation time step.

The wave seed is used to generate random phase angles for each wave frequency component, giving different realizations of the selected wave spectrum for different seeds.

If stochastic amplitudes are not selected, deterministic amplitudes are used (this is the default option). All realizations will have the same spectrum with sampled or interpolated values from the specified wave spectrum.

If stochastic amplitudes are selected, the amplitude of each wave component will have a scatter around the values given by the wave spectrum. The realizations will have different spectra and the significant wave height will vary between realizations. Multiple, long wave realizations should therefore be simulated if stochastic waves amplitudes are selected.

As shown below, the time series (wave/wind/load/motion) are generated by discretizing the variance spectrum into a finite number of harmonic components with uniformly distributed phases using FFT. The phase angles are generated using a pseudo-random number generator with the seed given as user input. Choosing a different seed will give a different time series realization which in turn will yield different simulation results when wave loads or support vessel motions are included in the simulation.

The time increment, frequency increment and maximum duration (without repetition) are interrelated when the addition of the harmonic components is performed by FFT:

\(\Delta \omega = \frac{2\pi}{N_t \Delta t} = \frac{2\pi}{T_{rep}}\)

where \(\Delta \omega\) is the frequency increment, \(N_t\) is the number of time steps (in practice, this will be increased such that \(N_t = 2^N\)), \(\Delta t\) is the time increment, and \(T_{rep}\) is the length of the generated time series.

This section includes options for the generated wave and motion timeseries:

If wave forces are included on RIFLEX elements (Wave forces present) the Wave kinematics specification section will be available.

SIMA allows the user to control the application of wave kinematics at nodes. The nodes for calculation of wave kinematics should be chosen such that important wave loads are captured. Reducing the number of nodes for kinematics calculation improves the simulation efficiency.

The main input is:

Wave kinematics may be pre-generated using FFT or calculated during the simulation as a sum of cosine terms. Pre-generation is much more efficient than calculating kinematics during the dynamic simulation.

Kinematics can be pre-generated at the static positions of the selected kinematics nodes.
Alternatively, kinematics can be calculated at the dynamic position of the selected kinematics nodes by summing cosine terms at each generation time step.

The kinematics at a generation time step are calculated using the dynamic position at the previous generation time step. Kinematics at simulation time steps (between the generated time steps) are found using linear interpolation. The generation time step should be small enough that the change in dynamic position between generation steps is negligible and that the highest frequency wave components with significant contributions are well represented. Om the other hand, a short generation time step will lead to frequent calculation of kinematics, which will make a time-consuming simulation.

Selecting kinematics calculated during the simulation for a linear time domain simulation with Wilson’s integration method will result in the calculation of kinematics at two generation time steps each time a new generation time step is reached.

The option Kinematics at static position calculated during simulation should give the same results as Kinematics at static position, but take several times longer. It is primarily implemented for for testing.

The option Kinematics at fixed static position (linearized) results in the same kinematics as the default option Kinematics at static position. The difference is that in Kinematics at fixed static position (linearized), a node remains wet or dry depending on its static position. Thus, a node that has a static position 10 cm below the surface will continue to have wave loads even if it is lifted well above the surface in a dynamic simulation. The option may be useful when investigating differences between nonlinear and linear analysis.

The possible combinations are described below.

Second-order Stokes wave theory for finite water depth may be used to calculate fluid velocities and accelerations below the water surface if the second order wave kinematics option is chosen. The first order wave elevation and mean water depth are input to the calculation. A second order, non-linear contribution to the wave elevation is calculated and added to the first order elevation. The second order contribution grows with increasing wave steepness, leading to a flattening of troughs and sharpening of crests. Fluid velocities and accelerations are calculated from the velocity potential, up to and including second order. Currently, second order wave kinematics are only available for long-crested sea-states.

Wave kinematics theory manual

To be able to see the results from within SIMA, the user must choose the Binary Format storage.