1D beam modelling

[kevinarden]

I would not expect any damping unless you defined it in the material property section. It certainly looks like a damped response.
The way you started it is interesting, with the initial displacement of the entire model 0.1
then with the boundary condition you bring back node 1 to zero.
Elmer does not output step zero.

[raback]

Hi,

Have you varied the timestep? I would guess you need easily ~20 steps for full cycle to get reasonable results. How does the damping depend on the this? The damping should be eliminated when timestep goes to zero. Time integration schemes tend to have some damping. In fact it is difficult to have a stable algorithm without any.

-Peter

[mika]

Both these cases are free vibrations and were supposed to vibrate forever with a magnitude of the initial displacement as there was no damping

First, it might be good to mention that while this is expected for an analytic solution, computational time integration methods often have numerical damping, sometimes even by design to help in treating high-frequency numerical noise. The Bossak method applied here with the default values set by Elmer has such dissipation, so the numerical solution will eventually be damped, but this shouldn't happen too quickly for modes for which the time integration method has chances to be accurate. What is seen as a high-frequency component by the numerical method is related to a chosen time step size. The user can also try to change the amount of numerical damping by changing the solver parameter Bossak Alpha (the default value is -0.05).

To select a time step size for time-accurate simulation, one must identify the highest frequency of interest in the response of a structure. I think that if you create an initial condition as done now by setting one of the displacement components to a constant value expect for an end point, a large number of eigenmodes is required to represent the initial condition accurately. The associated frequencies can thus be high and the choice of time step size for accurate simulation so that none of the component modes is dampened strongly can be demanding.

To see whether there is a clear mistake somewhere, I did the following test. First I computed some of the lowest eigenmodes of the beam of a cross section 0.2x0.2 and then picked the lowest mode to create an initial condition for time history analysis. That is, I set the initial displacement to be according to the first eigenmode. Now I know the frequency f=1/T for the expected response and I can calculate a time step size from the period as dt = T/20 (this is considered to be the largest time step possible). The displacement components U 1 and U 2 at the free end are then plotted for the first five periods as

download/file.php?mode=view&id=7547

so the response seem to be reasonable. If the simulation is continued for fifty periods we start to see numerical damping as illustrated here

download/file.php?mode=view&id=7548

If this level of damping is not accepted, one could try to reduce the time step size and possibly to adjust the alpha parameter. This is the result for the larger Bossak alpha value -0.01 as compared with the default solution

download/file.php?mode=view&id=7549

so we see less dissipation.

To sum up, considering the issue of damping, I don't see a clear mistake in the response when the model is created such that time accurate simulation from the initial state is realistic. I nevertheless observed in the code a mistake when the polar moment of inertia for torsional motion was calculated from the second moments of area. This is correted in the devel branch as

https://github.com/ElmerCSC/elmerfem/co ... 1b6d59bd17

[kevinarden]

I decided to go back to this damping test and repeat it using the 1d beam model and the initial displacement method
viewtopic.php?p=20818&hilit=abaqus+damping#p20818

3D.PNG

(220.43 KiB) Not downloaded yet

1dbeam.PNG

(170.41 KiB) Not downloaded yet

beam.zip

(1.91 KiB) Downloaded 56 times

The 1D beam element results look reasonable

[kevinarden]

and if I add some damping to the 1D beam
Rayleigh Damping = Logical True
Rayleigh Damping Alpha = Real 100.2836
Rayleigh Damping Beta = Real 5.38E-5

I don't get any

1ddamped.PNG (92.42 KiB) Viewed 695 times

[mika]

The beam solver doesn't yet understand the Rayleigh damping parameters, but adding the Rayleigh damping would be an easy modification

[kevinarden]

It would be nice to add, but at least a message to tell the user it is not supported would help cut down on confusion.

[mika]

I made a small change to the devel branch so that mass-proportional damping (Rayleigh Damping Alpha) for translational motions can now be given for the beam solver, whereas giving Rayleigh Damping Beta = ... causes a warning message.

[kevinarden]

Great, thanks.