Direct Transient Analysis using Nastran

Transcription

1 February, 0 Direct Transient Analysis using Nastran Casting the Blame There'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 Begins I'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) SPC (Bulk) SPCD (Bulk) TLOAD (Bulk) TABLED (Bulk) Page of 6

2 February, 0 TSTEP (Bulk) PARAM/G PARAM/W3 The Plot Thickens You'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 Wheredunnit Time 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 timeindependent parts of the excitation, and not into spatial variation and time variation. The SPC 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 TABLED (or other TABLEDi keywords). Page of 6

3 February, 0 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? Whydunnit The 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 09 CEND TITLE = Hand edited - CV ECHO = NONE SUBCASE TITLE=Ground excitation SPC = DLOAD = 4 TSTEP = 7 DISPLACEMENT(SORT,REAL)=ALL ACCELERATION(SORT,REAL)=ALL SPCFORCES(SORT,REAL)=ALL STRESS(SORT,REAL,VONMISES,BILIN)=ALL BEGIN BULK Page 3 of 6

4 February, 0 PARAM PARAM PSHELL PELAS CELAS CELAS CELAS CELAS MAT POST G Page 4 of 6

5 February, SPC 3456 SPCD,,37,,.0 TABLED TLOAD, 4,,, ACCE, TSTEP 7 50 $GRAV 0 ENDDATA ENDT Now the explanations for each keyword: Keyword Meaning SOL Tells the solver what type of problem you're solving. SOL 09 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 SPC that we'll create below in the bulk section Page 5 of 6

6 February, 0 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 DISPLACEMENT ACCELERATION SPCFORCES STRESS Output 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. 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 OP. PARAM This specifies global damping. More on this later! G PSHELL PELAS MAT CELAS 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.) SPC 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 preprocessor, 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 SPC 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 node. All the SPCD cards should have the same id. Note that the last item (.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,,38,.0 TABLED 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. Page 6 of 6

7 February, 0 Keyword Meaning TLOAD This is the time-dependent load cobbles together the SPCD and TABLED. The refers to the SPCD, and the 5 to the TABLED. The ACCE tells Nastran we're specifying acceleration-excitation. TSTEP This is the time-integration control. We're using 50 steps, each of 0. 0 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 3 / / 6 / 36 are the 4 corners, and node is close to the Page 7 of 6

8 February, 0 middle. (I could have meshed it to get a node at the center. Perhaps I should have. You can. Perhaps you should.) And here's the acceleration vs. time graph. D a m p in g = 0.0 T im e s te p = s te p s F in a l tim e =0.5 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,.00 That is, we're using 500 steps of size 00 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. W it 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. Page 8 of 6

9 February, 0 And here's the plot of acceleration vs. time for the same nodes with this smaller time-step size: D a m p in g =0.0 T im e s te p = s te p s F in a l tim e = 0.5 Look's reasonable? I'll look at the trend, here, leaving it to you to verify things like the peak value. Nodammit It's easy to think it does. Node 3 and node 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 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 graphs. Page 9 of 6

10 February, 0 D a m p in g =0.0 5 T im e s te p = s te p s F in a l tim e = 0.5 D a m p in g =0.0 5 T im e s te p = s te p s F in a l tim e = 0.5 Page 0 of 6

11 February, 0 After you've done with gnashing your teeth and cursing whatever you want to curse, pay attention to the storyline once again. The Denoument The 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 BULK PARAM POST PARAM G param,w3,0 PSHELL Do pay attention to the article cited above. The value you use for the frequency (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 and 05) and different time step sizes (0 and 00) and with different frequencies (0 and 00). That's 8 results make sure you can figure them out. Page of 6

12 February, 0 Frequency = 0, Damping = 0, deltat = 0 Frequency = 0, Damping = 0, deltat = 00 Page of 6

13 February, 0 Frequency = 0, Damping = 05, deltat = 0 Frequency = 0, Damping = 05, deltat = 00 Page 3 of 6

14 February, 0 Frequency = 00, Damping = 0, deltat = 0 Frequency = 00, Damping = 0, deltat = 00 Page 4 of 6

15 February, 0 Frequency = 00, Damping = 05, deltat = 0 Frequency = 00, Damping = 05, deltat = 00 Page 5 of 6

16 February, 0 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-falls This 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 still And incredibly so But the alternative is Notepad++ Page 6 of 6