Time History units and methods

[davideng13]

Have spent some time on reading related topics but still having a hard time with units. 

http://forums.autodesk.com/t5/Robot-Structural-Analysis/Time-History-Analysis/td-p/4782985

http://forums.autodesk.com/t5/Robot-Structural-Analysis/great-work/td-p/3729078

If newmark method (acceleration) is selected and "Direction X" is specified robot assumes the units are m/s2 not g's? what should the factor to be if working in US customary units. 

What is the difference between the newmark method and newmark "acceleration" methods?

If you select a case with associated loads on your structure, the function you define in your  force vs. time will scale relative to your defined loads? so no factors are necessary to account for units.

How do you place an acceleration vs. time at a single node rather than the whole system as you do when by specifying "Direction X or Y or Z"? Also what should the factor be for US customary units?

any help in the right direction will be much appreciated. 

Thank You

[Pawel.Pulak · Accepted solution]

Hello,

below my explanations to your questions:

If newmark method (acceleration) is selected and "Direction X" is specified robot assumes the units are m/s2 not g's? what should the factor to be if working in US customary units.

It depends in what units is the accelerogram used by you.

• If it is unitless (it means in g's) then the factor should be equal to gravity acceleration expressed in m/s2 so 9.80665 m/s2
• If it is in ft/s2 then the factor should consider conversion from ft to m. Such conversion factors can be easily obtained from Robot - see the screen capture below. So it will be 0.3048

What is the difference between the newmark method and newmark "acceleration" methods?

Newmark "acceleration" method was implemented in Robot later than Newmark method and it is more versatile because:

1/ it suports not only linear time history but also non-linear time history

2/ it supports kinematic excitations in supports expressed in velocities or accelerations:

If you select a case with associated loads on your structure, the function you define in your  force vs. time will scale relative to your defined loads? so no factors are necessary to account for units.

Yes

How do you place an acceleration vs. time at a single node rather than the whole system as you do when by specifying "Direction X or Y or Z"? Also what should the factor be for US customary units?

You can do it on a single node using imposed displacements of supports expressed in accelerations ("imposed accelerations") - see the screen capture above. In this case (contrary to  "Direction X or Y or Z") the forcing function is unitless - units are taken from Imposed displacements - for the screen capture above it will be in/s2.

Additional note:

"Base-line correction" is not implemented in Robot so when using "imposed accelerations" you can obtain in response not only oscillating accelerations, velocities and displacements but additionally constant speed of whole structure and linearly changing displacements of whole structure. It means that as a results you obtain the superposition of oscillations and rigid-body movement of whole structure with constant speed. It does not influence reactions, internal forces and moments. But it makes analysis of deflections and deformations more difficult because it is necessary to subtract this translation component from total displacements.

Analogous effect for "imposed velocities" - but here it is additional rigid body movement of constant displacement (not constant speed as above)

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Best regards,

[davideng13]

Thank you for your reply, it was very helpful as always on here. 

To get started on a pilot study, I am trying to model a steel bracket attached to a large pipe that supports a smaller vibrating pipe, I am trying to determine maximum stresses in the bracket. At the end of the bracket there is an 80lbs mass which I added as a nodal mass in two locations for all cases.  I have been provided accelerating data in units of g's. For simplicity I am assuming the bracket is rigidly attached to the larger pipe. 

In the model included two THA cases

3. THA " Direction X" -  used collected acceleration data and  use a  factor of 32.2 to covert g's to ft/s2 

4. THA - Nodal Acc - used same data but applied to node (imposed displacement), assigned a unit load and used a factor of 32.2x12 = 386.4 to covert ft/sec2 to in/sec2 .

Could you take a look at the attached model to see if I have my units correct. Also, i'm open for any general modeling recommendations or best practices. 

Thank You!

[davideng13]

opps fogot to attached files. see attached. (I have delted the mesh to shrink file size)

[davideng13]

Any way you could still confirm I have the right factors/units for this? 

[Pawel.Pulak]

I have some questions related to time function "4Z_acc" defined in your model:

1/ is the maximum value of 15.13 defined in it corresponding to 15.13g?

2/ why is it not starting from 0 acceleration but from 1 and moreover keeping it constant until t=3.75s? Robot treats it as sudden application of acceleration from 0 to 1 at t=0s, resulting in additional transient oscillations. Have you tried to model some constant load (gravity?) this way?

Regards,

[davideng13]

See my responses below in blue. 

I have some questions related to time function "4Z_acc" defined in your model:

1/ is the maximum value of 15.13 defined in it corresponding to 15.13g? That is correct, but I need to contact the company that provided me the Data. I anticipate it isn't realistic but will be in the 3 g range.   

2/ why is it not starting from 0 acceleration but from 1 and moreover keeping it constant until t=3.75s? Robot treats it as sudden application of acceleration from 0 to 1 at t=0s, resulting in additional transient oscillations. Have you tried to model some constant load (gravity?) this way? I took a quick clip in the middle of a vibration data clip. Right now I only have the acceleration data in terms of rms. So I am trying to get the raw data to use as my acceleration forcing curve.

For now I guess I would like to make sure my units are correct and I can then update the data. I am unsure why I requested acceleration data and they provided the rms averages ? Good idea I can  model constant gravity and check it that way. 

Thank you for your time.

[Pawel.Pulak]

Hi David,

So here are my more detailed observations related to your models.

You have attached 2 files - both using Newmark acceleration method, one with acceleration excitation using "Direction X", another with analogous nodal accelerations. They were expected to give similar results but they didn't.

First as concerns the model with "Direction X" excitation:

1/ In Message 2 of this forum topic I have written "the factor should be equal to gravity acceleration expressed in m/s2 so 9.80665 m/s2". It is independent from units used in the project - I know it is unexpected, especially for someone using imperial units 😞  So it was necessary to change the factor from 32.2 (corresponding to ft/s2) to 9.80665 (corresponding to m/s2)

Then as concerns the model with nodal acceleration excitation:

2/ Load case 1, used in this excitation, contained not only imposed nodal acceleration but also the self-weight load. In such case the self-weight load was also multiplied by the forcing function "4Z_acc". It was necessary to delete the self-weight load from load case 1 to avoid this effect.

3/ The imposed nodal acceleration load in load case 1 was applied to nodes where added masses were defined. Any imposed acceleration, velocity or displacement loads should be applied to supported nodes (and moreover to fixed directions in these supports) - in opposite case they do not work. It was necessary to replace the loaded nodes by nodes where supports were defined by you.

Now as concerns more general remarks related to both models:

4/ You have defined damping as 0.05 for Alpha. In case of Newmark acceleration, Newmark or HHT methods damping matrix is defined as the linear combination of mass matrix and stiffness matrix with Alpha and Beta coefficients respectively. So Alpha=0.05 does not correspond to 0.05 relative damping (5%) which you probably indended. Alpha and Beta corresponding to such damping can be calculated using the "calculator" available in the bottom part of Rayleigh Damping window - necessary to specify relative damping values for some represenattive pulsations omega (frequencies expressed in radian/s instead of Hz - multiplied by 2*PI). To avoid doubts I have specified no damping.

5/ As I have noticed before your forcing function contained not only the acceleration impulse but also some constant acceleration before the impulse (from t=0 seconds) and after it. It corresponds to applying some constant load to the unsupported structure resulting in rigid body movement with constant acceleration - so not resulting in any internal forces (except of transient effects when applying such load at t=0s). That is why I modified the forcing function leaving only the acceleration impulse and "moving" it close to t=0s.

6/ The acceleration impulse in the forcing function is also very "artificial" because it contains only positive acceleration. In your last answer you have mentioned RMS values of accelerations - time history analysis expects excitation defined in the time (not frequency) domain without any statistical processing - it should be physical values.

According to above points I have modified your model. I have also defined the 3rd one - using "Direction X" excitement and Modal Decomposition method (this one also without damping).

Then I have run analysis of them and checked some results - reaction in one of supported nodes and von Mises stress in the center of one of finite elements.

Results in all 3 models are very close - see the screen captures below.

I have also attached the models - without results to reduce the size.

When checking displacements in the model with imposed nodal acceleration you can see that it is a superposition of displacements resulting from deformations caused by vibrations and displacements (much bigger than the first ones) caused by rigid body movement of all structure. The acceleration impulse contains only posititive accelerations so after ending it the non-zero velocity of structure remains. As I have mentioned before the "Base-line correction" is not implemented in Robot so it is not possible to separate in it this rigid body movement and deformations.

I hope these too long explanations will be useful:)

Regards,