Ashes offers the possibility to run simulations using a linear or a non-linear algorithm. This can be changed in the  Analysis  tab of the  Analysis parameters  dialog.

When a linear simulation is carried out, the external forces  (also called excitation forces , such as aerodynamic or hydrodynamic loads) are calculated on the initial position of the system: the deflections that occur during the simulation will not be taken into account when computing the forces. In addition, the mass , damping and stiffness properties   of the system are time-independent, so they are based on the initial position of the structure. This is typically accurate enough when the structure experiences small deflections. Consider the following examples:

• A floating wind turbine will drift over time and move away from its initial position. If a linear analysis was carried out on a floating wind turbine, the wave loads would be computed as if the floater was still at its initial position, which will produce inaccurate wave loads. In that case, a non-linear  analysis is required.
• A bottom-fixed wind turbine with a parked rotor will experience small deflections, and will therefore remain close to its initial position. In such a situation, it a linear  analysis typically gives results similar to a nonlinear analysis.

In the following paragraph, we compare simulation results for a linear and a non-linear analysis for a bottom-fixed wind turbine with locked main shaft under turbulent wind (with an average wind speed of 20 m.s ^-1 ) and irregular seas (with H _S = 6 m and T _P = 10 s). Figures 1 and 2 show the bending moment at the lowest element of the monopile and the displacement at the top of the tower, respectively, for a simulation carried out with the nonlinear and the linear algorithm. For both output, the extreme values of the linear solution lie within 10% of the non-linear solution. Note that these conditions do not corrrespond to a realistic situation, as a locked rotor will generally have its blades pitched and therefore reduce the thrust load.

Figure 1 Bending moment at the sea bottom

Figure 2 Tower top displacement

It is possible to set the elements of the support structure as Small deflection elements  in the Advanced  tab of the Analysis  section in the  Analysis parameters . If this option is not selected, the elements are co-rotational elements.

This is generally recommended for onshore and bottom-fixed offshore models since

• the displacements experienced by the support structure are small
• Rayleigh damping can be applied to small deflection elements

However, using this option implies that you will miss out on some non-linear responses, such as the P-delta effect (see  https://en.wikipedia.org/wiki/P-delta_effect ). For the default offshore template at the rated speed, selecting small deflection elements produces a decrease in the maximum overturning moment at the seabottom of about 2.7%.

Another effect is that the effective natural periods of the model will be slightly shorter than with co-rotational elements. The image below shows the shear forces at the bottom of the tubular tower for the default offshore template, with no waves and a wind speed of 19 m.s ^-1 . While there is no significant difference in the shear force in the wind direction (see bottom plot), the side-to-side eigenperiod is about 2% shorter with the small deflection elements.