3 unknowns but only 2 equations: Iterative approach?

[JBlackhole]

The problem consists of 3 intervals (m) (they are called steps in the data below because the problem represents a physical glued joint with 3 steps (ie 3 different thicknesses) of length Lstep. The numerical problem I need to solve is finding constant A1 and A2 for each step (knowing a number of inputs). I was provided with the “raw” date for the solved problem and it seems that the constant A1 and A2 were found by an iterative process. For each step with length Lstep an initial (random?) value TR, at right hand end of a step together with the value at the left hand end (TL = T given at x=0) and does an Iterative process to calculate A1 and A2.

There are 3 unknowns but only 2 equations, Is there an easy (built-in!) iterative approach that can be used to find the value of TR, A1 and A2?

Thanks

Regards

JXB

[MikeArmstrong]

The problem is, as you stated, you have 3 unknowns and only two equations. I'm positive that there must be another relationship between the inputs which you haven't included.

Looking at it briefly, I don't think it can be solved with the imformation provided.

Mike

[ValeryOchkov]

Mike Armstrong wrote:

The problem has 3 unknowns and only two equations.

See same task:

http://communities.ptc.com/message/158454

[JBlackhole]

A 3rd equation: TR.m = TL.m+1 could do the trick

Physically it represents the fact the the value TR at the right (ie the end ) of step m must be equal to the value at the left (ie the beginning) of step m+1

Regards

JXB

[Fred_Kohlhepp]

A solve block works.

[MikeArmstrong]

Your solve block yields results, but they are not the same as the expected results.

Mike

[Fred_Kohlhepp]

Mike Armstrong wrote:

Your solve block yields results, but they are not the same as the expected results.

Mike

Actually it does if you get the equations in the solve block written correctly!

[MikeArmstrong]

Actually it does if you get the equations in the solve block written correctly!

I think there are still issues with the worksheet, see attached.

I have cleaned the worksheet slightly for clarity.

Mike

[JBlackhole]

Thanks for all the inputs. As pointed by Mike in is last post the solve blocks works because the values for TRs are known. If one puts some randoms values then the values for A1 and A2 are not correct.

There is another equation, see attached doc, available which could be used instead of using the fact that the value TR at the right (ie the end ) of step m must be equal to the value at the left (ie the beginning) of step m+1. The idea is the same. The value of t should be the same at the change of the step. In other words, the value of t should "converge" to the same value if you come from the left side of the step change or the right side. (The loads (T) and shear stresses (t) at the ends common to adjacent steps must be equal.

it looks like I need to spent a bit more time going through the maths

Thanks

Regards

JXB

[MikeArmstrong]

But that new equation is dependant on A1 and A2, which in reality is not know.

I think your missing a step or a bit of Math somewhere along the line.

Mike

[JBlackhole]

Did a bit of digging and I found the following"...The values of the constants A1 and A2 for each step can be obtained by equating the tensions in adherend 1 (T1) and the shear stresses in the adhesive (t) at the ends common to adjacent steps, and by using the following boundary conditions...

Please see the attached doc for all the equations (page 4).

I will most likely closed the discussion as my original query about the solve block has been kindly answered

Thaks

Regards

JXB

[RichardJ]

Your terminology is confusing me. Are the T's (TL, TR) supposed to be the values of tau at the ends of the segments?

You have d/dx of T, but if T is a constant (for example Tin) than d/dx T is zero.

[JBlackhole]

T represent forces in the segment with TL the force at the left end of the segment (ie the beginning) and TR the force at the right end of the segment (ie the end). Tau is the stress distribution along the segment such that in a particular segment the rate of change of the force eqautes to the shear stress (dT/dx=-tau) with the force decreasses with increasing x

[RichardJ]

Your equation does not match your data. Here's how to do it in principle though.

[JBlackhole]

Thanks a lot for that. I will struggle to expand that to deal with n equations as I was planning to expand the problem to cover n (joint) segment. I need to do a bot more work on that.!! I coudln't help but notice that the values for A1 and A2 are differnent? Could it be due to the fact that an integration constant is mmissing in the equation for T?

[RichardJ]

I coudln't help but notice that the values for A1 and A2 are differnent? Could it be due to the fact that an integration constant is mmissing in the equation for T?

The equation you gave for the stress is not consistent with either the Fortran data or the original equations at the top of the sheet (which contain additional constants such as C0, and 1-exp terms).

[RichardJ]

I will struggle to expand that to deal with n equations as I was planning to expand the problem to cover n (joint) segment.

Here.

You still need to figure out what's wrong with the equations though

[RichardJ]

Start with the third segment. TR is known to be zero, so A1 and A2 can be found. For the second segment you have a third equation, because at the boundary tau for the second segment is equal to tau for the third segment. So you can solve for TR, A1, and A2. The same is then true for the first segment.

[JBlackhole]

Thanks for that. Could the same be said for the 1st step (segment) as T1=Tinput at x=0.

How does one write this differential equation problem in MathCAD?

Regards

JXB

[Fred_Kohlhepp]

Thought I recognized this; you have a bonded stepped lap joint.

See attached for some of the basic math and theory:

(I still haven't figured this into Mathcad. Maybe some really smart, enterprising individual with a lot of spare time . . .)

[JBlackhole]

That's correct. There is a more "up-to-date" data sheet which one has to purchase and as it turned out there was a mistake in one of the equations in the data sheet!! With the known A1 and A2 values, the answers for t are the same. see attached

I now need to go-back to square one and figure out to solve for A1 and A2 for the 3 step problem and later one expand the mcad sheet capability to a n step joint

Regards

JXB

[ValeryOchkov]

I must use one unknown but 2 equations by solving this task

http://communities.ptc.com/videos/2045

Why!?

See here http://communities.ptc.com/message/164665 this two equations in the Given-Find block!