Simulating the Bending of Metal Plates? 4

[pratt]

Hello Everybody,

I am trying to find a solution to predicting the curve a metal plate or sheet takes when we apply a compressive load on it to bend it or i should say flex it. IT is very well in is elastic limit and comes back to original shape later. We fix on end and other end is guided. I just want to simulate my assembly and get the final curve the basket takes.Assemblies contain a plate connected to an actuator which pulls the plate to bend it

I am not able to decide will FEA be necessary to give me the defelction. ( I am only interested in the defelection and curvature) Will any FEA software be able to do that. lease advise is FEA is teh way to go, If yes which software will be able to give me these details. Or if not which way will be able to give these details to me.

 

[prex]

There a mistake in my previous post: the quantity in column [tt]A[/tt] is proportional to 1/EJ, not to EJ (or you can change the formula in [tt]B2[/tt] to [tt]=(C3+C1)/(2-(PI()/100)^2/A2)[/tt])

prex

http://www.xcalcs.com

Online tools for structural design

 

[pratt]

Thanks a Ton Prex,

But I have another query. In this calculation you are assuming that the maximum defelction will be at the center (C51) and setting that to 1. Can you explain why you are suggesting that.

This gives me a peak at c51 , but doesnot give me a smooth curve to show the shape of deformation. Remember that there is no point load at the center, but the load is applies by pulling both end of the plate towards each other.

Prex you have given a great path for me to follow, some light will help me find the destination.

Pratt

 

[pratt]

Also Prex,

You say in your previous post that press F9 till values stabalize. They dont, they keep on changing. How will I know when are they stabalised?

Thanks for the help.

Pratt

 

[prex]

Continue with F9 (or set the number of iterations to 100 or 1000 under Excel options). The numbers must stabilize (you don't see changes at recalculating with F9). To check compare the values with a sine curve: must match to the sixth figure or so.
The 1 in the middle is because this equation is homogeneous, so it calculates the values less a constant that must be assigned. However you won't necessarily have a maximum or a peak in the middle: I tried with column A equal to 0.5 over half length and to 1 on the rest: the maximum is 1.26 and it is located (as one would expect) in the 0.5 region.

prex

http://www.xcalcs.com

Online tools for structural design

 

[pratt]

So Prex,

I can change the 1 in the middle after the first calculation.

How to change the equation if the end condition changes.

Can you give the actual equation with all the variable and explanation what becomes constant or zero with end conditions etc.

Thanks for all the help.

Pratt

 

[brad]

john,
You stated:
"And finally whatever theory or method you use, buckling only occurs when the structure can no longer support the applied load and you get catastrophic failure. Up to that point the structure is merely bending or deflecting under load. Thus as Pratt's plates return to their original shapes, then buckling does not occur."

That is not necessarily true. Even one of your cited websites notes snap-through buckling of a dome. The keyboard which I am currently typing on exhibits such bifurcation on every single keystroke. This is buckling, but it is neither catastrophic nor inelastic.

Oil-canning is another classic example--it is not catastrophic, and in fact can be even be entirely linearly elastic. I can cite many other examples in which buckling is part of the designed behavior.

While I acknowledge my earlier error, I strongly stand by my last statement.

Please let me know if you do not agree after this clarificaiton; it may be that I am not making myself sufficiently clear.

Best regards,
Brad

 

[johnhors]

Brad

Fair point, I had always associated buckling with a permanent failure of the component, collapsed beyond elastic limits, and that has always been the case with my experience within the automotive and aerospace industries. A buckled landing gear leg or side stay or car suspension arm will never return to it's original shape.

Out of pure interest, I would like to know of an example where buckling is part of the designed behaivour.

Best regards,
John

 

[brad]

I've already cited keyboard "springs" as an example. Try to slowly depress a single key on your keyboard. You will notice that there is a point at which it is very difficult to keep your finger at the same point. This is because there is a load drop-off. This is a designed buckling of the rubber "spring" underneath. Most keypads exhibit this behavior.

There are also examples of electrical connectors and other "slide connector" components which undergo bifurcation during assembly. Typically the part looks like a cantilever beam which is slid over another component. These sometimes are designed such that they exceed a buckling load (but should not significantly yield).

I agree with your cited examples of landing gear and car suspension. However, a noteworthy characteristic of these is that they are "load-controlled". In a load-controlled situation, buckling typically does result in catastrophic failure. However, some assembly situations are more akin to displacement-controlled. Thus post-buckling behavior is not necessarily catastrophic.

Given the initial description of this problem, my brain started viewing this an an assembly-type operation, which lead me down the path I went. I'm not clear whether or not this is entirely applicable to Pratt's problem (Pratt has not provided enough information on which to judge this). IF this is relevant to Pratt's approach, then the cited formulae are inappropriate.

Brad

 

[pratt]

Hello Brad,

Your vision is very applicable in my problem here. In my scenario it is a displacement controlled system. We know our part will never exceed their elastic strength , because we never flex them so much. Reason is that the flexing is something that these part are deisgned for as the main purpose.

To explain it more. Take a plastic scale and put it verticle on a table (like a slender column), apply compressive load on the top, you will find that after the intial resistance the scale flexs quiet a bit and if you stop applying more load and release it, scale comes back to it original shape.

This is just like what we do in our systems.

As per the geometry is concerned, the cross section is consistant, as the part are made from sheet metal or abs plactic sheets. But the shape it self changes. For example you might have a rectangular plate with cuts on it to give it fin like structure.

I hope this gives you a better idea of the problem.


If you can advise your point of veiw in solving this kind of problem to determine the shape the plates will take. What will be the factors governing the shape they take etc.

Your input will be very helpful

Thanks
Pratt

 

[prex]

pratt,
what you ask is not that simple: the form of the differential equation changes with the end conditions. In fact the equation is M=-EJy'' with M=Py for a pinned end but M=Py-M[sub]o[/sub] for a clamped end, where M[sub]o[/sub] is the unknown end moment.
One issue with finite differences is that every problem requires a different setup: I tried a few minutes to find a setup for the end moment, but failed (no convergence).
Another method found in the literature is by assuming a polynomial with unknown coefficients as the deflection curve, then minimizing the expression of the critical load that leads to a linear system of equations. However this one too requires a quite vast analytical effort.
There is in fact a much simpler method, if you can accept some error in the result. I've checked that, for pinned ends and uniform section, the post buckling deflection curve (sinusoid) and the deflection curve under a uniform lateral load (a polynomial of the fourth order) differ by less than one percent of the maximum deflection (that of course is set equal in the two equations). So I guess that this will remain valid (though a somewhat larger error can be expected) even for a variable section or for other end conditions. So, as the deflection curve of a beam of variable section with uniform lateral load is much simpler to calculate, my suggestion is that you adopt that one.


prex

http://www.xcalcs.com

Online tools for structural design

 

[brad]

This seems like a fairly straightforward nonlinear FEA problem. I have solved many problems very similar to what you are describing. A closed-form solution would be rather difficult.

Do you have FEA software at your company? If not, do you know of any consultants that do FEA? If this is pretty straightforward, you may able to "job-shop" this to an FEA house for a fairly small amount of money (a few thousand US).

Brad

 

[pratt]

Hey Brad,

Can you suggest a few good FEM software which will do this Job. If you can provide price information also , it would be really geat.

Thanks for all the help

Pratt

 

[brad]

This is a classic problem for a nonlinear implicit code. The three dominant nonlinear implicit codes in the US are ABAQUS, ANSYS, and MARC. They are most typically sold on a "subscription" basis, meaning you pay a recurring fee to keep the software. For all three of these, expect to pay over $10K/year (probably closer to $20K). They are generally outside the reach and budget of those who are looking to solve "occasional" problems. Hence my suggestion to consider outsourcing this project to a consultant.

If you are contemplating building an internal analysis capability after hearing this price, let me know and ask more questions. I'm happy to provide answers.
Brad

 

[pratt]

Hey Can any guys help me decide that my problem is flexural or bucking. As I am not able to decide, as I am getting to know more and more about these things. If anybody can give me a website or tell me the basic difference between bending and buckling. That will great. Also Can anybody tell me how to perform flexural analysis.