direct transient analysis using nastran - kfourmetricsdirecttransientanalysisusingnastran.pdf ·...

February, 2012 www.kfourmetrics.com

Direct Transient Analysis using Nastran

Casting the BlameThere's a lot that can be improved with very many of the commercial FE preprocessors, but not all the blame lies with them.

One way to reflect on this is to use programming equivalents. The FE solver provides you with keywords, much the same way that software provides you with APIs. The pre-processor tries to make things easier, much the same way that an IDE knits together the various steps. An IDE can't do very much if the API is poor. FE pre-processors are similarly constrained, unfortunately.

The Story BeginsI've taken a simple enough problem – a rectangular plate supported on 4 springs. Logically, you can replace the plate with pretty much any structure, but the obvious motivation is a vehicle that rests on 4 wheels.

The springs I've used are uni-dimensional: they have a stiffness only in the “vertical” direction. Nothing prevents you from adding lateral stiffness, though you'll have to think a bit about Nastran's CELAS elements. They're not pretty.

My story ignores birth and early childhood. Use your preprocessor to create the mesh you want, together with material properties and section properties (shell element thickness and spring stiffness, in this case) and save that in a text file. We'll use that file by either copying and pasting it (as I do here, for clarity) or by “including” it (as you should if it's a large mesh).

Make sure you have ready access to the Nastran user-manual (the Quick Ref Guide, is adequate) for the keywords listed below. You don't need to understand them before you start reading this article, but should know they exist. Once you've gone through this article, the user-manual descriptions should make perfect sense, and you'll be able to use them correctly.

• SPC (Case control)• DLOAD (Case control)• TSTEP (Case control)• SPC1 (Bulk)• SPCD (Bulk)• TLOAD1 (Bulk)• TABLED1 (Bulk)

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• TSTEP (Bulk)• PARAM/G • PARAM/W3

The Plot ThickensYou've a lot to worry about with dynamic analyses: what time step to use, how to obtain damping data, what output's to be recorded, how to understand the output, and so on.

We bypass all that here, but it's important to understand why. Getting data is important, but that's only a part of the story. How do you know where to put the data you have? It's this mystery we're looking at here.

Probably due to reasons that I'll criticize elsewhere, Nastran uses different approaches depending on whether the time-dependent force (the “excitation”) is a displacement / acceleration / velocity or a force. The first 3 are often lumped together as “enforced motion”. This used to require the much-reviled “large mass” method, which meant that any enforced motion was “converted” to an applied force. That's no longer required – the large mass method can be ignored now.

Both enforced motion and applied forces are sometimes referred to as “loads”, though they really aren't. Forces are on the right-hand side of the matrix equation [K]{u} = {f}, while enforced motions are on the left.

It's more correct to refer to them as “excitations”, though I'd vote for “BCs” myself. (There is an argument against “BCs”, to be fair: what if you have a body load that's time dependent?)

Howdunnit and WheredunnitTime dependent excitations (frequency dependent too, though we're not going into that here) consist of two things: where they're applied and how they vary with time.

This is what the Nastran manuals say. Where = spatial variation, how = time variation.

Nastran doesn't quiet support that point of view in practice. I believe the logic behind Nastran's implementation is better viewed as separating the excitation into time-dependent and time-independent parts of the excitation, and not into spatial variation and time variation.

The SPC1 and SPCD cards take care of the time independent parts – where the excitation is to be applied, and the amplitude of the excitation. Remember that if we think of the excitation as G(t) = A*g(t), the A is independent of time – and is what we mean by the “amplitude”.

The time variation is taken care of by the TABLED1 (or other TABLEDi keywords).

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Both these are cobbled together by the TLOAD card.

Next, the time-integration aspect is taken care of by the TSTEP keyword. This allows us to say what time-step-size we want to use, how many of these (and therefore the total time we're simulating for) and how often we want output.

So far so good.

Now comes the twist in the tail. Or is it the tale? Or does it matter?

WhydunnitThe executive-control vs. case-control vs. bulk-data sections of an input file are awful. They're almost as bad as IBM's JCL. Still, they're a fact of life. And they beat the hell out of a GUI, so accept them.

The keywords we just saw come in the “bulk” section of the input. What we must also do is create a “CASE CONTROL” section. Here we have to create a loadcase and tell the solver what loads etc. are to be used.

We can also specify output here, but in the examples below we'll skip that by using a brute-force method – we'll output everything. Unlike the earlier simplification (where we bypassed time-step size etc.) this is not something I recommend. But including things like sets will detract from our story, so I'm leaving it out. Be warned though: even for this small problem (just 40 nodes),you can drown in the flood of output.

So here's the file. The explanations for each keyword follow. Note that if you want to try this yourself, you can copy the entire file and paste it in a text-editor.

SOL 109CENDTITLE = Hand edited - CVECHO = NONESUBCASE 1 TITLE=Ground excitation SPC = 1 DLOAD = 4 TSTEP = 7 DISPLACEMENT(SORT1,REAL)=ALL ACCELERATION(SORT1,REAL)=ALL SPCFORCES(SORT1,REAL)=ALL STRESS(SORT1,REAL,VONMISES,BILIN)=ALLBEGIN BULK

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PARAM POST 0PARAM G .02PSHELL 1 1 13. 1 1CQUAD4 1 1 1 2 8 7CQUAD4 2 1 2 3 9 8CQUAD4 3 1 3 4 10 9CQUAD4 4 1 4 5 11 10CQUAD4 5 1 5 6 12 11CQUAD4 6 1 7 8 14 13CQUAD4 7 1 8 9 15 14CQUAD4 8 1 9 10 16 15CQUAD4 9 1 10 11 17 16CQUAD4 10 1 11 12 18 17CQUAD4 11 1 13 14 20 19CQUAD4 12 1 14 15 21 20CQUAD4 13 1 15 16 22 21CQUAD4 14 1 16 17 23 22CQUAD4 15 1 17 18 24 23CQUAD4 16 1 19 20 26 25CQUAD4 17 1 20 21 27 26CQUAD4 18 1 21 22 28 27CQUAD4 19 1 22 23 29 28CQUAD4 20 1 23 24 30 29CQUAD4 21 1 25 26 32 31CQUAD4 22 1 26 27 33 32CQUAD4 23 1 27 28 34 33CQUAD4 24 1 28 29 35 34CQUAD4 25 1 29 30 36 35PELAS 2 100000.CELAS1 26 2 29 2 37 2CELAS1 27 2 11 2 38 2CELAS1 28 2 8 2 39 2CELAS1 29 2 26 2 40 2MAT1 1 2.07+8 .3 7.83-6GRID 1 370. 0. 230.GRID 2 296. 0. 230.GRID 3 222. 0. 230.GRID 4 148. 0. 230.GRID 5 74. 0. 230.GRID 6 0. 0. 230.GRID 7 370. 0. 184.GRID 8 296. 0. 184.GRID 9 222. 0. 184.GRID 10 148. 0. 184.GRID 11 74. 0. 184.GRID 12 0. 0. 184.GRID 13 370. 0. 138.GRID 14 296. 0. 138.GRID 15 222. 0. 138.GRID 16 148. 0. 138.

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GRID 17 74. 0. 138.GRID 18 0. 0. 138.GRID 19 370. 0. 92.GRID 20 296. 0. 92.GRID 21 222. 0. 92.GRID 22 148. 0. 92.GRID 23 74. 0. 92.GRID 24 0. 0. 92.GRID 25 370. 0. 46.GRID 26 296. 0. 46.GRID 27 222. 0. 46.GRID 28 148. 0. 46.GRID 29 74. 0. 46.GRID 30 0. 0. 46.GRID 31 370. 0. 0.GRID 32 296. 0. 0.GRID 33 222. 0. 0.GRID 34 148. 0. 0.GRID 35 74. 0. 0.GRID 36 0. 0. 0.GRID 37 74. -10. 46.GRID 38 74. -10. 184.GRID 39 296. -10. 184.GRID 40 296. -10. 46.SPC1 1 123456 37 38 39 40SPCD,2,37,2,1.0 TABLED1 5 -1. 0. 0. 0. .1 51. .2 0. 100. 0. ENDTTLOAD1, 4, 2, , ACCE, 5 TSTEP 7 50 .01$GRAV 1 0 9810. 0. -1. 0.ENDDATA

Now the explanations for each keyword:

Keyword Meaning

SOL Tells the solver what type of problem you're solving. SOL 109 means “transient using direct-integration”

CEND End of case control. We now move on to executive control

TITLE Description of the problem itself

ECHO Controls the flood of information.

SUBCASE The load-case. Many models have more than one of these. In the file pasted above, I've indented the text for easy reading.

TITLE The title for this load-case.

SPC Refers to the SPC1 that we'll create below in the “bulk” section

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Keyword Meaning

DLOAD Refers to the TLOAD that we'll create below in the “bulk” section

TSTEP Refers to the TSTEP that we'll create below in the “bulk” section

DISPLACEMENTOutput option. I've used all, but you shouldn't. This is strongly related to how you'll post-process the data. Later in this document I'll show the acceleration-history at selected points, but there's a lot more to it than that.

ACCELERATION

SPCFORCES

STRESS

BEGIN BULK This is the “bulk data”. Most of this will be created using your GUI, but not all. The keywords highlighted in yellow are better created here than in your pre-processor. The others should be created in the pre-processor, saved as a text file and either pasted here or “included”.

PARAM POST 0 You may not need this unless you're using Patran for post-processing. It tells Nastran to save an XDB for Patran. If you're using another post-processor, you'll have to modify this. For example, you may prefer an OP2.

PARAM G This specifies “global” damping. More on this later!

PSHELL

These are the element-section, material, element and node data. You can, and should, create these using your pre-processor. (Note that you can also assign a damping factor for each amterial. Should you? We'll come back to this.)

PELAS

MAT1

CELAS1

CQUAD4

GRID

SPC1 This is the specified displacement. In this example, we've fixed all 6 dofs for 4 nodes. I suggest you create this here, rather than in the pre-processor, since it's related to the SPCD card. However, this is moot: there's no harm in creating this in the pre-processor.

Note that the springs are uni-dimensional. Remember that when you review the text-output and interpret warnings!

SPCD This is the enforced displacement. There must be an SPC1 for any node-and-dof that's used here. I recommend you create a separate line for each SPCD node in case you need to excite more than 1 node. All the SPCD cards should have the same id. Note that the last item (1.0 in the example above) is the “amplitude”.

In this example, suppose we also want to excite node 38. Then we'd add the line “SPCD, 2,38,1.0”

TABLED1 This is the x-y- data that represents the time-variation of the excitation. Try plotting for yourself the graphs of the excitation I've used.

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Keyword Meaning

TLOAD1 This is the time-dependent load – cobbles together the SPCD and TABLED1. The 2 refers to the SPCD, and the 5 to the TABLED1. The ACCE tells Nastran we're specifying acceleration-excitation.

TSTEP This is the time-integration control. We're using 50 steps, each of 0.01.

0.01 what? Seconds? Milli-seconds? Hours? Depends on your units. Make sure you use consistent units (I strongly recommend SI – Meters, Kgs, Newtons, Seconds – but obviously it's your call).

$GRAV This card's commented out – that's what the “$” sign indicated. Why have I included it here? As food for thought that we'll come back to shortly.

ENDDATA It's showtime, folks.

Think we Dunit? So we submit the file to Nastran, open the F06 (text output) and check that there are no errors and no warnings (that we can't ignore) and duly view the results in our post-processor. What can we do to check our answer?

You should certainly check reaction forces (hence the SPCFORCES output above), should use some hand calculations (total weight, spring-stiffnesses, etc.) and should also look at the trend of results. Towards the last, I'll present time-history plots of the acceleration.

We'll look at the acceleration vs. time for the nodes highlighted here:

Note that I've exaggerated the springs by drawing thicker yellow lines. Node 37 is where the excitation's been applied, nodes 31 / 1 / 6 / 36 are the 4 corners, and node 21 is close to the

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middle. (I could have meshed it to get a node at the center. Perhaps I should have. You can. Perhaps you should1.)

And here's the acceleration vs. time graph.

What if we reduce the time step size?

To do that, edit the input deck and change the TSTEP in the bulk-section to

TSTEP, 7, 500, .001

That is, we're using 500 steps of size 0.001 each. Note that I've used commas – this means I don't need to worry about right FORTRAN_style “fixed width” formatting. This is great since we're using a text editor and “manually” entering stuff.

1 W i t h a p o l o g i e s to J a y L e n o ' s “C o u l d a , S h o u l d a , W o u l d a ” .

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D a m p in g = 0 .0 2T im e s te p = 0 . 0 15 0 s te p sF in a l tim e = 0 .5



And here's the plot of acceleration vs. time for the same nodes with this smaller time-step size:

Look's reasonable?

I'll look at the “trend”, here, leaving it to you to verify things like the peak value.

NodammitIt's easy to think it does. Node 31 and node 1 are going in opposite directions, which is what we'd expect. The acceleration is dying out after the excitation stops.

Or is it? What will happen if we change the damping to 0.05? That is, we change the “PARAM G” line to

PARAM, G, .05

Here's where the ship springs a leak. The damn acceleration hasn't changed a whit, as shown in these 2 graphs.

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D a m p in g = 0 .0 2T im e s te p = 0 . 0 0 15 0 0 s te p sF in a l tim e = 0 .5



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D a m p in g = 0 .0 5T im e s te p = 0 . 0 0 15 0 0 s te p sF in a l tim e = 0 .5

D a m p in g = 0 .0 5T im e s te p = 0 . 0 15 0 s te p sF in a l tim e = 0 .5



After you've done with gnashing your teeth and cursing whatever you want to curse, pay attention to the storyline once again.

The DenoumentThe problem, my dear Watson, was with the damping that neither barked nor bit. For Nastran, to “use” the damping, we need to convert it to viscous damping. (If we're using modal superposition, instead of the direct integration method used here, we could use modal damping – TABDMP in Nastranese.)

This is nicely explained here, so I won't repeat it.

What we will do, then, is add this line to the file (I've included a few lines before and after so you can see where it's been inserted):

BEGIN BULKPARAM POST 0PARAM G .02param,w3,20.0PSHELL 1 1 13. 1 1

Do pay attention to the article cited above. The value you use for the “frequency” (20.0 in the line above) does affect the results. But now let's look at the results. I've pasted below the images for the acceleration for different damping factors (0.02 and 0.05) and different time step sizes (0.01 and 0.001) – and with different “frequencies” (20 and 200).

That's 8 results – make sure you can figure them out.

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http://www.me.rochester.edu/courses/ME443/NASTRAN/Damping.pdf



Frequency = 20, Damping = 0.02, deltaT = 0.01


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The effect of the time step is easy to catch, and you should try correlating it both with filters (such as the SAE filter) and with stuff you may have studied in a course on Control-Systems (sampling frequency and aliasing).

The effect of the damping factor is harder, but you've probably studied that too, and should brush it up. This is not a bad article to read.

The effect of the frequency on the “W3” keyword is not that easy, unfortunately.

After the Curtain-fallsThis example has, I hope, helped make things clear. I also hope it provides a ready-to-use “deck” for simulations of this type.

But there's a lot more to dynamics, of course, than this example. Quite apart from the modeling aspects, even this little exercise produces a whole lot of information.

And to lay the grounds for the sequel, here's what you should do: read the manual for the MAT keyword (or re-read the article cited above). You can provide material-specific damping too (referred to as GE, and converted to viscous form by the keyword W4).

Also, think about the GRAVITY keyword that was commented out. Should we include gravity? If so, how? To answer the first, you can do worse than plough through at least some sections of Clough and Penzien's classic.

Happy munching.

It's ugly stillAnd incredibly soBut the alternativeis Notepad++

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http://www.iitr.ac.in/outreach/web/CIRCIS/PG/AVN/RC/Revision%20of%20concepts3_Damped.pdf


direct transient analysis using nastran - kfourmetricsdirecttransientanalysisusingnastran.pdf ·...

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