**floating wind turbines**as those models experience large displacements from their initial position and that could lead to inaccurate results. For bottom-fixed wind turbines with rotating rotors, it is not recommended to run linear analysis for the same reason. A linear analysis can be carried out on bottom-fixed turbines whose main shaft is locked (see Main shaft)

# Linear analysis

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.Note: in Ashes, it is not possible to run linear solution on

## 1 Small deflection elements

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

**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.