Analysis
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
Loads ramp-up
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
Special events
One prescribed load
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
Load categories on/off
Misc.
Statistics start time
The time from which on statistics for sensor data should be calculated and viewed.- Default value: 0
- Unit: $\text{s}$
- Range: 0 — 1e+06