Finding a Variable through iterating. This one is killing me!

Question

Finding a Variable through iterating. This one is killing me!

maloneb (Mechanical)

(OP)

26 Aug 11 07:37

Hey guys, I'm relatively new to mathcad and have hit a wall. All the data needed is attached to this message.

The formulae are lifted straight out of DNV-OS-F101 for the Local Buckling - Collapse of off shore Pipelines.

The Problem is that the data provided must be used to find a value of t_nom by setting the value of P_c = P_coll.

In Excel, the program runs with an estimated value of t_nom and iterates until the value of P_c > P_coll, therefore giving a suitable value of t_nom.

Is there any way of doing this in mathcad?

Thanks guys, I'm really stuck here.

jghrist (Electrical) · Answer 1 · 2011-08-26 10:18:51

Generally, this type of problem can be solved using a solve block. Please save the workbook in version 11 or 13 and attach.

maloneb (Mechanical) · Answer 2 · 2011-08-26 10:21:08

Here is the workbook in version 11.

http://files.engineering.com/getfile.aspx?folder=a90f2bd7-845a-4d0b-957c-9e

IRstuff (Aerospace) · Answer 3 · 2011-08-26 10:29:39

In order to get anything to work at all, your units must balance, which they don't. I've added what I think you're trying to do:

http://files.engineering.com/getfile.aspx?folder=d1dfeaeb-63dc-45af-86c6-5b00c4c85e68&file=Collapse2.mcd

TTFN

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maloneb (Mechanical) · Answer 4 · 2011-08-26 10:39:51

To IRstuff: I haven't altered the equation at all though, it's pulled straight out of a DNV document, so you would have thought they'd balance?!?!

In the document you've presented, t_nom is still undefined earlier in the equation, and Find(t_nom) is also undefined, how do I solve this?

I really am a complete newbie with mathcad, I'm talking baby steps...

Occupant (Mechanical) · Answer 5 · 2011-08-27 06:40:56

I have done a simple test and as you can see, it would be difficult for Matcad to find a solution. However, that is assuming I put the correct units in where you neglected to do so.

http://files.engineering.com/getfile.aspx?folder=ec3ae23c-9be0-4f67-b13d-a4

jghrist (Electrical) · Answer 6 · 2011-08-28 10:36:37

Quote:
To IRstuff: I haven't altered the equation at all though, it's pulled straight out of a DNV document, so you would have thought they'd balance?!?!

Often sources show equations, particularly empirically derived ones, with constants that require particular units. You either need to use those particular units and not explicitly show them in MathCAD or adjust the equations for the units used.

IRstuff (Aerospace) · Answer 7 · 2011-08-28 13:30:17

The OP has two variables that he uses that ostensibly should have units, E and sigma.y; assuming both have pascals as units allows the equations to be balanced. However, the RHS expression is extremely flat, while the other side is quite steep, making it difficult for the solver to find a solution.

As a general rule, one should graph the expressions to see whether they behave as expected, and whether a solution is plausibly achievable. The equations, as written have graphical solution ~0.5183226, which seems absurdly small. There also is an anomalous D.0/t.nom expression, where all the other instances are t.nom/D.0. However, changing that one instance makes little difference to the problem as a whole.

http://files.engineering.com/getfile.aspx?folder=0dec261c-5751-42be-8ed0-c874bcf5ac47&file=Collapse2.mcd

TTFN

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jghrist (Electrical) · Answer 8 · 2011-08-28 23:42:56

0.518m doesn't seem absurdly small (it is meters, not mm) if this is pipeline wall thickness. If D.o = 350mm is the pipeline outside diameter, a 518mm wall thickness is impossibly large. If you use Minerr instead of Find, you get a solution 0.5183226*m.

IRstuff (Aerospace) · Answer 9 · 2011-08-29 00:02:26

You're right, I'd forgotten that the quickplot defaulted to meters, and yes, Minerr gets around the issues with Find.

TTFN

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IRstuff (Aerospace) · Answer 10 · 2011-08-29 00:04:22

File with Minerr attached: http://files.engineering.com/getfile.aspx?folder=25bae9ef-13bd-4cab-85e8-32a4b893fc8d&file=Collapse3.mcd

TTFN

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jghrist (Electrical) · Answer 11 · 2011-08-29 09:02:17

The problem might be the units. The modulus of elasticity of steel is about 2·10^11 Pa, not 207000Pa. If you use 2.07·10^11Pa, you get a t.nom = 5.16mm

IRstuff (Aerospace) · Answer 12 · 2011-08-29 10:46:49

The OP seems to have lost interest, but thanks for the new info; it's only just so much math for me, since it's well outside of my purview. Half a millimeter seems a bit thin, to me, but it feels much more plausible than half a meter.

TTFN

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Occupant (Mechanical) · Answer 13 · 2011-08-29 20:39:56

Just for the record, as IRstuff said, the OP has lost interest a long time ago: If you change the Modulus of Elasticity from whatever it was to steel then you probably have to look at Sigma.y too. If you use Pascal as unit, I think, it refers to soft butter.

maloneb (Mechanical) · Answer 14 · 2011-08-30 02:52:33

Hey guys, sorry, I didn't lose interest in this post, but I've been away for the bank holiday weekend. I'm just looking through everything now and will reply properly shortly.

maloneb (Mechanical) · Answer 15 · 2011-08-30 03:17:08

I didn't realise I'd missed the units for E and sigma.y, my bad. The units are MPa.

5.16mm is extremely close to the desired answer, a hell of a lot closer than I had been getting.

Just to clarify, is Minerr a pre-built in function to Mathcad?

Thanks for all the help guys

Occupant (Mechanical) · Answer 16 · 2011-08-30 06:51:56

Yes, Minerr is build in, but I did not use it. With the new units I came to 5.5mm - check it out.

maloneb (Mechanical) · Answer 17 · 2011-08-30 06:54:42

Occupant,

Do you have the file you have used? Could you post it please?

Occupant (Mechanical) · Answer 18 · 2011-08-30 07:20:10

Well, I didn't actually solve it, it is an approximation, based on the fact that the equation has to zero out - but you'll see.

http://files.engineering.com/getfile.aspx?folder=3d6dc67c-f0d2-4c13-a9f5-1e

jghrist (Electrical) · Answer 19 · 2011-08-30 08:35:08

Actually, there are three solutions, -0.579mm, +0.569mm, and 5.51mm. Minerr gives them all, depending on your guess value.

http://files.engineering.com/getfile.aspx?folder=739819b4-8033-4d19-aa38-83

Occupant (Mechanical) · Answer 20 · 2011-08-31 11:46:30

I've blown this thing up including a marker at zero around the region of interest. There really is only one solution of 5.5mm as indicated before.

http://files.engineering.com/getfile.aspx?folder=1f2925f8-aa4e-4628-ae15-4d

jghrist (Electrical) · Answer 21 · 2011-08-31 15:39:41

I think if you'll blow the thing up even more closer to zero, and include a little negative thickness, you'll see the other solutions. The workbook I attached to my post yesterday was your workbook with the new E and sigma values and using Minerr. Your graph showed the two sides of the equation separately and the way I blew it up, they definitely cross in three places.

Spiry (Electrical) · Answer 22 · 2011-09-11 07:45:24

here is the change you have some mistake with the units of there

http://files.engineering.com/getfile.aspx?folder=8d339c81-d95a-4281-aacb-71

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Finding a Variable through iterating. This one is killing me!