large deflection calcs/fea 1

[henerythe8th]

Hello All!
I'm currently working on the analysis of a ductwork system that requires the calculation of the stress due to NOPD (normal operating pressure differential).

Some of this ductwork is on the order of 60"x60"x11ga and has fairly high "negative pressure" which is on the order of -0.6psi.

I have attempted to use a simple FEA program to model the stress due to this pressure and continue with a finer and finer mesh with no convergence of stress.

I think that I need a calculation or FEA capable of calcualting stress in a section with large deflection.

Any suggestions?

 

[corus]

You should still get convergence with small deflection theory. Using non-linear geometry, or large deflection will get you a better answer and possibly show if you are getting buckling. You can check your answers by hand by considering a region away from discontinuities and check with Roark. If you're not getting convergence then there's probably some other reason, such as you are modelling a singularity such that when you refine the mesh you continute to get a higher and higher answer. Either that or your FE program is wrong. Ansys/Abaqus/nastran, for example, are programs that will do large deflection if you want them.

 

[pjhype]

Before you choose a code, you need to determine whether the large deflections are elastic or plastic, or whether they are due to bifurcation (e.g. buckling or snap-thru). You should perform a linear stress analysis to determine whether you are close to yielding the material. You should also perform a linear buckling analysis to see how close you are to the critical buckling load. Once you have develop a feel for whether you will need to deal with geometric or material non-linearities, you will be in a much better position to choose a finite element code.

pj

 

[henerythe8th]

Hello!

Corus,
Thank you very much for your interest.
When I state that I am not getting convergence, I mean that I continue to see "change" or as you state "continue to get a higher and higher answer". I have reached the maximum number of nodes allowed by the software and can't mesh any finer to get the "answer" to converge. This answer, by the way, is approaching the value calculated by equations from Roark's. However, the equations from Roarks's are not valid in this circumstance either. Roark's states, "The formulas of this section are based on the following assumptions: (1) The plate is flat, of uniform thickness, and of homogeneous isotropic material; (2) the thickness is not more than about one-quarter of the least transverse dimension, and the maximum deflection is not more than about one-half the thickness; (3) all forces--loads and reactions--are normal to the plane of the plate; and (4) the plate is nowhere stressed beyond the elastic limit."
The second half of number 2, above, is where one of the problems stems from. (14ga material is about 0.0747" and deflections are approximately 0.08" thereby violating the limits of the equations by Roark.

pjhype,
IF the stresses being calculated by either of these methods are in the "ballpark", which I believe they are, then I am definitely in the elastic arena, so to speak.

Any other recommendations...?

P.S. Thank you both very much for your input!

 

[corus]

Henery,
I'm confused when you say that the answer is approaching that of Roark but you say it's not converging?
The thickness criteria will be because of the effects of shear deflection. Either that or the solution depends on extrapolating data outside of the range. Some design codes also give this warning because of this but answers are usaully still fairly close.
I would plot your results against the number of nodes and see if the results are converging to some value. Convergence means that the results will never reach a solution, of course, but the difference between values will be getting smaller and smaller for each iteration. Thus you will always see a change in the results, but the change will get less significant.

 

[henerythe8th]

Corus,
As I stated in my previous post, the stress is converging; but I would, indeed, need to extrapolate to find the value that it is converging toward. Also, after looking deeper in Roarks I found equations for stress in a plate with large deflection. After comparing those results with the "normal" Roarks calculation it was determined that the stress value was nearly identical (something like 7.49ksi with the "normal", or small deflection equations and 7.55ksi using the large deflection equations). However, the large deflection equations showed a slightly lower deflection for the same amount of pressure.

Again,
Thanks for your input!