How 'accurate' is FEM software?

[austim]

Hi, all.

In the Structural engineers forum, some very interesting comments have been posted by Anthae (visitor) regarding the accuracy to be expected from FEM software (eg no better than 35%). I believe that Anthae's comments merit a new thread in their own right, and will be very interested to see what other's experience may have been.

See thread 507-7222, "STAAD vs competitors", posting 42 of 43, 31 August 2001.

 

[GregLocock]

Coming from an automotive background my experience is somewhat different.

In cases where we know the load case well fatigue life predictions would normally be less than a factor of 2 in error. This is roughly 20% in stress.

When we estimate the resonant frequencies of systems I would expect an accuracy of about 5% in the first couple (or so) of flexural modes, for simple systems, up to the complexity of a cylinder block or head. Frequency varies as sqrt(k/m), so if we get m right then that implies a stiffness error of 10%.

So I am reasonably confident that small, well modelled, systems can be substantially more accurate than your correspondent suggests.

Unfortunately we are not really very interested in the behaviour of single components, or small assemblies. Cheers

Greg Locock

 

[ishvaaag]

Even the best thorizations are but models for some practical use. Yesterday Newton's law I read give infinite force of attraction when distance is zero, and we overcome such thoretization with every pace we do.

We are so accustomed to our monre common practices that they seem be "true"...for some elastic analyses on equal things we expect no other thing tha pure equality.

For the building applications in which I work it is clear that codes are but sediment of knowledge attempting to provide some expected or by the code standard safey or serviceability.

Not even the proponents of the code dare to forecast the reduction in building failures upon some code clause change...even staticians would do better if they can gain some oevarall gain in safety factor.

Then the modelizations; to be exact to what significant cypher where nor joints nor lengths and of course attached masonries are dismissed? Where simplifications of the load path are continously being introduced and redistribution of forces upon paulatine yield or crack develops?

Plus the careless modelization by non knowledgeable enough parties.

Plus the unknowns.. a study on moment frame connections left me with the doubt of if any can avoid entering the inelastic range...well such was the case, to the codes I like all refer.

Plus the validity of the predictions; not even without masonries and in the elastic realm the ordinary analyses would duplicate reality; may do at lab tests, but no with most firm designs. Forget ducplication in the nonlinear range, even proponents admit.

So what are we doing?: If we reasonably follow what mandated, obtaining by such methods some unknown but assumed acceptable probability of that the things won't give problems.

I understand that some ppl in the industry (aerospace, nuclear, machines) may need more accuracy and provide it through the whole range of life efforts the thing undergoes. But in the end either it will use the distillated knowledge on whatever in-box or off-the shelf or closed form knowledge is extant, or using the same and statistics and tests some new development will be being produced for the future driving of the process.

Not so different from us in building, we also ensure whole life serviceability of the thing, no?

 

[dozer]

I too read Anthae's comments and must say I was somewhat surprised. To be honest, I took his comment about "no better than ±35%" with a grain of salt.

He mentioned simple 2D trusses. I've actually compared truss analysis between STAAD, COSMOS/M, ROBOT, and ABAQUS and I didn't see wildly different results. As a matter of fact the axial loads were quite close (say withing 1% of each other).

I wouldn't throw your FEA code out just yet. I think a comment like that should be backed up with hard data. Don't get me wrong, I think FEA code has it's share of problems and we would all be better served if these problems were identified and distributed to the users, but this comment struck me as "the sky is falling" sort of thing.

 

[rlnorton]

You're right -- that is quite a thread!

Regarding the comment about "no better than 35%", this needs better definition to support such a sweeping claim.

Firstly, there is a significant difference between exact elements (truss and beam) and elasticity approximations (plates, membranes, solids, etc). Secondly one has to be careful about what the reference is for the comparison, theory or measurements. Finally there is a difference in accuracy for deflection or stress, especially when comparing with measured stress.

Every code I've used gives exact solutions when using exact elements (truss and beam) and comparing with theoretical solutions. When comparing with measurements the errors are largely in boundary conditions, material definitions, joint assumptions, and loading conditions. In typical aerospace structures I'd be very concerned if I didn't get within 5% on deflection.

When using elasticity approximation elements (plates, membranes, solids, etc) and comparing with theoretical results every program I've used will converge to the correct solution within some reasonably small number, usually within 5% for deflection. Accuracy here depends on mesh characteristics (refinement, distortion) and element assumptions. Here it becomes important to understand the limitations in the element formulation. Of course I understand that the vendors don't make it easy to understand these limitations!

Using elasticiy approximation elements to compare with real world results is a little more difficult than with exact elements. In addition to the errors in boundary conditions, material definitions, joint assumptions, and loading conditions you have to include the effects of mesh characteristics, element assumptions, and actual dimensions of the real world structure. When I've had the chance to compare analysis with test and had the time to get careful understanding of the real structure and the time to do the appropriate modeling I've gotten within 5& on deflection.

Trying to compare stress on real world structures is difficult. If the area being examined has a significant stress gradient (often the case) then it is difficult to measure accurately, as well as difficult to compute. If the stress is due to bending of a beam or plate type structure comparision is a little easier, but even then the effects of the support or other interfaces often cause problems.

 

[Qshake]

I agree wholeheartedly with RLNORTON, however, I wish to add that for H-version FE packages mesh characteristics are a source of error but for P-version FE this is not the case. However, the P-version FE is susceptible to the order of the mathematical formulation.

 

[prex]

I also agree with rlnorton.
To add my bit, I would start by recalling that FEM is 'only' an application of the elastic theory, at least in it's commonest uses: so, if the mesh is suitably fine, it will give the same results that may be obtained with theoretical formulae, based on the type of element used.
If you use beam elements, that, as pointed out by rlnorton, are exact, you'll get 'exact' (in the theoretical sense) results irrespective of the mesh refinement. If you use thin shell elements, you'll get the results of the thin plate or thin shell theory, and so on.
So the problem is probably uncorrectly posed: the accuracy of FEM is simply that of the theory the particular element is based on, or, better, may be made as close as desired to it by the choice of a suitable mesh.
How much the theory is accurate, now, is a completely different matter and would be too long to discuss. I would like to point out, however, that, when checking the stability of a structure against a code (then most of the time for a structural engineer) the accuracy of theoretical stresses may be a minor issue, as you must only demonstrate that you are on the safe side: by how much is only a matter of economy, you can always encompass your appreciation of the accuracy with a suitable margin in the model.
prex
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