# Analysis

This section enables you to define the analysis parameters. The parameters affecting the finite element algorithm are defined in the Theory Manual, in the FEM code section. In particular, that section defines Linear analysis and the Time domain simulation.

Convergence parameters are only relevant for Analysis mode: Nonlinear (for Linear anlaysis they are NOT used).

This section contains the following parameters.

## General

### Analysis mode

The finite element analysis can be performed linearly or nonlinearly. Note: This parameter is set to Nonlinear and disabled for floaters, since floaters always should be analyzed nonlinearly.

Nonlinear analysis

- a nonlinear analysis algorithm is used - particularly Newton-Rhapson iterations

- Euler-Bernoulli beam elements with a corotated coordinate system are used for all elements

- works well (is accurate) for unlimited deformations/deflections (both translations and rotations)

- ALWAYS use nonlinear analysis for a (rotating) rotor where the blades are flexible (the parameter Rotor model set to Flexible)

- ALWAYS use nonlinear analysis for floaters

Linear analysis

- a linear analysis algorithm is used

- normal Euler-Bernoulli beam elements are used for the support structure whereas Euler-Bernoulli beam elements with a corotated coordinate system are still used for blades and main shaft (unless Stiff blades are used, in which case the baldes are not modelled with finite elements)

- stiffness properties are constant (not changed/updated)

- typically faster than nonlinear analysis

- will be inaccurate for large translations or rotations. Thus, should only be used for small deflections/deformations.

- works well for a simulation with a rotation rotor only if the blades are stiff - the parameter Rotor model set to Stiff (i.e. not modelled with finte elements)

- NEVER use linear analysis for floaters

- Note: A rotor modelled flexible can give trustworthy results if it is not rotating (i.e. stopped) and the deformations are small. This should be accomplished by turning on the Bearings locked parameter in the Main shaft.

References:

Euler-Bernoulli beam theory in Wikipedia

Options:

Nonlinear (default):

The solver is nonlinear and the elements are corotational. This is the recommended alternative.

Linear:

The solver is linear and the elements are linear. This is typically faster than nonlinear.

### Numerical integration method

The numerical method used to solve the dynamic system.

The Hughes Hilbert Taylor method is a modification of the Newmark-beta method that enables the use of numerical damping. More information about the numerical methods is given in the theory manual, in the Time domain simulation section.

Options:

HHT-alpha (default):

The Hughes Hilbert Taylor modified Newmark-beta method is used

Newmark-beta:

The Newmark beta method is used.

### HHT-alpha factor

The numerical damping factor used in the HHT numerical integration method. The value must be negative, or zero.

Setting this factor to 0 implies no numerical damping. This is discouraged since it often leads to numerical problems (non-convergence).

The min value -0.333 gives maximum damping. The damping of a natural mode shape increases for increasing natural frequencises.

This parameter is not relevant and thus hidden if the Numerical integration method is Newmark-beta (see Damping).

Note: In addition to numerical damping there can be material damping.

• Default value: -0.025
• Unit:
• Range: -0.333 — 0

### Beta factor

The beta factor in the Newmark-beta numerical integration method.

This factor is hidden if the Numerical integration method is HHT-alpha, since it is calculated from the alpha factor and cannot be set directly.

• Default value: 0.25
• Unit:
• Range: 0 — 1

### Gamma factor

The gamma factor in the Newmark-beta numerical integration method.

This factor is hidden if the Numerical integration method is HHT-alpha, since it is calculated from the alpha factor and cannot be set directly.

• Default value: 0.5
• Unit:
• Range: 0 — 1

### Default element type

Sets the default type of beam elements to use. Some parts of the model might override this setting, and use a different type. The type of each element can be seen by right-clicking it, or in the Information pane one the part.

Options:

Euler-Bernoulli (default):

Ordinary Euler-Bernoulli beam elements. Also called engineer's beam or classical beam.

Timoshenko:

Timoshenko beam elements. The Timoshenko element accounts for shear deformations, which are of importance for short beams.

### Mass formulation

The mass formulation for elements.

Options:

Lumped, no inertia (default):

Lumped nodal mass. Half of the element's mass is lumped to each of the two nodes. No rotational inertia.

Consistent:

Consistent mass formulation.

Lumped, with inertia:

Lumped nodal mass with lumped inertia. Half of the element's mass is lumped to each of the two nodes. Rotational inertia is set to m*L^2*alpha, where alpha is a parameter.

### Inertia factor inverse

One divided by this value is multiplied by element mass times length squared to get the lumped rotational inertia on each node.

• Default value: 78
• Unit:
• Range: 0 — 1e+07

### Inner solver

Experimental feature

Changes the inner equation solver type.

Options:

Gaussian elimination (default):

Gaussian elimination

Gauss-Seidel (experimental):

Gauss-Seidel (experimental)

### Solution acceleration factor

Accelerates (or decelerates) the solution process by multiplying the predicted displacement increment by this factor.

• Default value: 1
• Unit:
• Range: -∞ — ∞

## Damping (structural)

### Structural damping mode

Choice of structural damping.

Note: In addition to the structural damping there can be numerical damping (depending on the value of the HHT-alpha parameter)

Options:

None (default):

There is no structural damping

Rayleigh:

Sum of stiffness proportional and mass proportional damping.

Stiffness proportional:

The damping is proportional to the stiffness

Mass proportional:

The damping is proportional to the mass

### Damping input

The way structural damping is defined.

Damping can be set by damping coefficients explicitly, or implicitly by setting damping ratio for one or two periods (or frequencies). Usually, natural periods of the system is used, but this does not have to be the case.

If Damping ratio(s) is chosen, then Damping ratio 1 and possibly Damping ratio 2, as well as Period 1 and possibly Period 2 are shown. The damping coefficients are calculated from these inputs, see the Info window.

Options:

Damping ratio(s) (default):

Damping ratio(s) for one or two periods is used to define the damping

Explicit coefficient(s):

The mass and/or stiffness coefficient(s) is/are given as input directly

### Mass coefficient

The factor that is multiplied with the mass properties of the element to get the damping effect of the mass

This coefficients is used both for Rayleigh damping and for mass proportional damping.

The Period 1 parameter is also shown, but it is not used in the simulations. It is only used to calculate the corresponding damping ratio and these are presented in the Info window.

• Default value: 0.05
• Unit: ${\text{rad}} \over {\text{s}}$
• Range: 0 — 10

### Stiffness coefficient

The factor that is multiplied with the stiffness properties of the element to get the damping effect of the stiffness

This coefficients is used both for Rayleigh damping and for stiffness proportional damping.

The Period 1 parameter is also shown, but it is not used in the simulations. It is only used to calculate the corresponding damping ratio and these are presented in the Info window.

• Default value: 0.05
• Unit: ${\text{s}} \over {\text{rad}}$
• Range: 0 — 10

### Damping ratio 1

The damping ratio (in percent) at the first period for which the damping is tuned.

100% damping means that the damping is equal to the critical damping.

• Default value: 1
• Unit: $\text{%}$
• Range: 0 — 100

### Period 1

The period for which the first damping ratio (ksi 1) is given.

This period must be greater than the second Rayleigh period to be used.

Note: If the Damping input is Explicit coefficient(s) then this parameter is NOT used in the simulations, but only to calculate the corresponding damping ratio presented in the Info window.

• Default value: 3
• Unit: $\text{s}$
• Range: 0.001 — 1000

### Damping ratio 2

The damping ratio (in percent) at the second period for which the damping is tuned.

100% damping means that the damping is equal to the critical damping.

• Default value: 2
• Unit: $\text{%}$
• Range: 0 — 100

### Period 2

The period for which the second damping ratio (ksi 2) is given.

Note: If the Damping input is Explicit coefficient(s) then this parameter is NOT used in the simulations, but only to calculate the corresponding damping ratio presented in the Info window.

• Default value: 0.3
• Unit: $\text{s}$
• Range: 0.001 — 1000

## Convergence

### Energy tolerance (absolute)

The exponent of the tolerance of residual energy allowed when continuing nonlinear equilbrium iterations. This value is the exponent, and gives an absolute tolerance (E = 10^value) of the total residual energy required for equilibrium.

This is explained more in details in the Time simulation section of theory manual

• Default value: -6
• Unit:
• Range: -1000 — 1000

### Energy tolerance for static solver (absolute)

The exponent of the tolerance of residual energy allowed when continuing nonlinear equilbrium iterations. This value is the exponent, and gives an absolute tolerance (E = 10^value) of the total residual energy required for equilibrium.

This is explained more in details in the Time simulation section of theory manual

• Default value: -1
• Unit:
• Range: -1000 — 1000

### On non-convergence

If the nonlinear equilibrium iterations do not converge within the specified tolerances, Ashes can either abort the simulation or ignore the convergence problem and continue the simulation. Use the "Continue" option with caution!

Options:

Stop simulation (default):

If the nonlinear equilibrium iterations do not converge within the specified tolerances, Ashes stops the simulation.

Continue:

If the nonlinear equilibrium iterations do not converge within the specified tolerances, Ashes continues the simulation. Use this option with caution!

### Maximum iterations

The maximum number of nonlinear iterations performed without achieving the specified tolerances before stopping the simulation.

• Default value: 1000
• Unit:
• Range: 0 — 1e+09

## Statics

### Mass scale factor for static solve

Determines the amount of mass/inertia that is included when finding a static equilibrium before starting the dynamic analysis.

If this scale factor is 0, a pure static nonlinear analysis is performed. A value greater than 0 will scale all mass/inertia with this factor, and a quasi-static analysis will be performed. If a fully static solution doesn't converge, this value should be set to a small value, such as 10-6.

• Default value: 0
• Unit:
• Range: 0 — 1

• Unit: $\text{s}$