P-element method Vs. H-code for Pressure vessels

[napoleonm]

P-element method Vs. H-code for Pressure vessels.

Is well known that for thin pressure vessel, most of the FEA studies performed are being done using H-codes as: Nastran, Cosmos and Ansys.

Now for thin vessels a minimum of 5 elements (please consider a simple “Solid” shell model) using Solid elements need to be placed across the wall.

Does anyone know about, how many P- “solid” elements need to be placed for a shell model… does anyone have a paper or reference comparing both methods?.

How well a “p-element” takes the stress gradient across a thin solid section?

Regards.

 

[mloew]

P-Elements (faq828-810)

Best regards,

Matthew Ian Loew


Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.

 

[prost]

Because you are allowed with p-elements to increase the polynomial degree within each element up to p=8 or even higher, depending on the FE code, then p-elements are superior to h-elements for long, thin elements, as long as the analyst uses the full capabilities of the code. An interesting behavior I discovered in grad school is that the so-called 'locking effect' almost completely disappears above p=4 (that is, basis or shape functions are quartics or
higher).

 

[natewebb]

If you are nervous about not having 5 layers, you could always use volume regions to force mechanica to use 5 layers. I think you would find the same results, but it would be an interesting comparison. Perhaps test it on a simple model.

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Cheers mate

 

[prost]

The systematic method of determining whether you need 5 layers is to check numerical convergence of the finite element solution. Because you are using p-elements, this is very easy and should be relatively quick. If you construct the model with 3 elements, then perform an extension of the finite element solution by increasing the polynomial degree from say 6 to 8, check the convergence of the engineering quantity you are most interested in (something that often gets lost on many finite element users is the need to define in advance what the goals of your computation are, and to be as precise as possible. Not "find the max. stress", but "find the max. von Mises stress to within 1% numerical error"); if the convergence allows you to reach your goal of numerical accuracy, then 5 layers is enough. Because you are using p-elements, you should always check the numerical convergence, because, for one thing, it is easy and relatively painless. Obviously when using h-elements, you should check numerical convergence, but most people don't because it takes too much time (which really isn't much of an excuse, in my opinion); my apologies to those who use h-elements and do the proper numerical convergence checks--but you know most h-element users don't check.

 

[prost]

My bad--I meant to say "many people don't because it takes too much time".

 

[natewebb]

yes it's easy but convergence is not the holy grail. It's quite possible to converge on a poor solution due to improper boundary conditions, I see it every day. An engineer might converge on nonsense and assume because he's within 1% convergence he's good to go. I bet statisticly thats more of a problem than anything.

A quick example, find the modal frequency of a square piece of sheetmetal. Pro/mechanica tends to create one or two shell elements only and converge nicely on a total crap answer.

I guess thats off topic, but what I'm saying about volume regions is that it never hurts to add a little h to your p.

 

[prost]

There are many kinds of errors, most of which can be grouped into one of three categories: idealization, numerical, and input errors. Idealization errors are the difference between reality and the model. Numerical errors are errors in the finite element computations. Input errors are mistakes made in load definition, material specification and boundary constraints. The models must be checked for all 3 error types. napoleonm asked whether 5 layers were enough; since that's the goal, to determine whether 5 is enough, the natural assumption is that the rest of the error types has already been checked, and the only question is the number of layers. Hence, I focused on checking numerical errors as opposed to the other types. Of course you could have a billion elements, but the wrong boundary conditions, and still be wrong. I just don't see it as relevant here in the discussion of 'how many layers is enough'?

 

[prost]

I doubt if we are talking about modeling that points such as natewebb made are ever off topic. I personally have asked such questions, about the number of layers (or degrees of freedom), only to discover that my boundary conditions were completely messed up.

As far as 'adding a little h', I agree, of course one should as much as possible take advantage of the advantages of each technique, extension of the number of elements or extension of the polynomial level. For regions of high stress gradients, such as notches or crack tips, it is unquestionably better practice to grade the mesh in the high stress gradient regions by increasing the number of elements. It is difficult with either element type, h or p, to get good results without taking into account what's really going on in the reality you are trying to model.