FEA results and correlation
FEA results and correlation
(OP)
In general what is the accuracy of the results (eg. stress and displacement) produced by FEA softwares when the boundary conditions, material models, loading, mesh size are correct. At this time, I am only interested to know on a static loading case for a structural model in elastic region. I have done several structural analysis and i need to have some good correlation work to show the accuracy to non-FEA people to get convinced. Thanks.





RE: FEA results and correlation
For more complicated geometry (something worth modeling and analyzing), you can be within 5%.
For more complicated analyses (non-linear), 10% is good.
Garland E. Borowski, PE
Borowski Engineering & Analytical Services, Inc.
Lower Alabama SolidWorks Users Group
RE: FEA results and correlation
Most of the FEM codes provide excellent solution accuracy for linear elastic materials as compared to the analytical solution of the same problem.
As the material response gets more non-linear, obtaining an anlytical solution becomes impossible and assessing the accuracy of the FEM solution gets more complicated. The most objective case is to compare the numerical solution to experimental results. However, in many practical situations, it is quite difficult to obtain accurate experimental results. Therefore,in many cases, the validity of any reference solution may remain debatable.
The decent commercial FEM software have manuals including examples and verification problems showing the accuracy of the FE solution.
RE: FEA results and correlation
That was beam elements, although I had previosuly modelled the critical joints as shells to get a good estimate of their stiffness.
The reason I used beam elements is that I then have an optimiser that tries to lighten the structure whilst obeying other constraints. This typically takes several thousand runs altogether, although most are discards. I haven't seen a free optimiser that will handle box like sections in a satisfactory fashion, that is why I used beam elements.
For modal analysis I'd expect to see major modes of a glazed car body within 10%, frequency wise, or better.
Cheers
Greg Locock
Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.
RE: FEA results and correlation
in addition to the interesting example from GregLocock, I can say that, any time we performed experimental measurements on FEAded components, the calculated deformations were always well within 10% error, most of the time the relative error is below 5%.
We are dealing with hydro-power machinery, so the parts never cope with material non-linearities (though we have several other types of non-linearities, such as contacts and non-holonomic restraints).
Regards
RE: FEA results and correlation
In your case (linear static response of an elastic structure), the accuracy of the results obtained by a FE analysis depends mainly
of the data (boundary conditions, loading, material properties).
That means most of it you have listed as 'correct'.
If the data are 'correct', you can refine the mesh to obtain the required accuracy.
So I think your question is badly put.
If you have to convince non-FEA people, perhaps you could compare the accuracy of the FEM to other methods (analytical, numerical and experimental methods).
And there are analytical solutions for some non-linear problems.
Regards,
Torpen
RE: FEA results and correlation
Ed.R.
RE: FEA results and correlation
RE: FEA results and correlation
RE: FEA results and correlation
A material characterized as "elastic" can be
linear elastic, non-linear elastic, described using a small or large strains formulations. Also, the strain and stress measures used in FEA can be different (e.g. Cauchy stress, Kirchhoff stress, 1st or 2nd Piola-Kirchhoff stress).
If you are interested in linear-elastic materials, analyzed using small displacements and small strain formulation (i.e. classical elasticity theory) for materials which are not incompressible, then , with appropriate modeling (meshing, boundary conditions, loading) you can get a very accurate solution.
RE: FEA results and correlation
The point is that there are a lot of variables in any analysis (some of them values we think we know) that can affect the results so it is not a question anyone can give an absolute answer to.....
Ed.R.
RE: FEA results and correlation
You require Young's modulus and Poisson's ratio to convert strain guage readings into stress, but for a linear FEA Young's modulus has no effect on stress levels, only on deflections , and Poisson's ratio has only a marginal effect.
So I'm afraid your statement directly linking the accuracy of the material properties to the accuracy of the analysis is not correct.
RE: FEA results and correlation
If you're using FEA to calculate stresses in a beam then you're right, but then the stiffness is uniform throughout.
corus
RE: FEA results and correlation
RE: FEA results and correlation
A little more detail about what the material is, what the part shape is and what you are trying to get across to common people would help.
A deflection test is the quick and easy way to determine modeling accuracy. If the deflection is correct the stresses show will be correct within a few percent. The only other way to know is to place strain gauges on the surface and load the part. If there is much shape detail that will be difficult or impossible. Otherwise a cycle test is the only other way to actually know the accuracy.
RE: FEA results and correlation
For any determinate structure the stress is independent of the material, however, for an indeterminate structure the stress is dependent on the material....Take any indeterminate structure (say a beam) and you will find that the reactions are a function of Youngs modulus....Then since the strains are the partial derivative of the deflections the strains are also a function of the deflections i.e. the moduli.....Of course the stresses are then a functions of the material properties and the strains so my original point is indeed correct for indeterminate structures....Guess I never thouoght about anyone using FEA to do determinate structures except for check problems (and school problems)
Ed.R.
RE: FEA results and correlation
After thinking for a minute even determinate structures are subject to variations in E.....The deflection for any determinate beam is a function of E....The only reason the stress is independent of E is that the value of E . eps is a constant for a beam (uniaxial stress).....and again the strains are the partial derivative of the deflections...etc....
Ed.R.
RE: FEA results and correlation
RE: FEA results and correlation
General 3-D Hooke's Law is typically written as a function of E & nu....even for linear problems (or the elastic part of non-linear problems)...In some special cases (like beams) it degenerates to the stress being independent of E .....
Ed.R.
RE: FEA results and correlation
"Isn't stress always independent of 'E' in a linear problem? Given a notch or hole in tension, for instance, the stress state can be completely described by the applied far field stress and the geometry. Deflection is a function of the stiffness 'E' of course."
Is 100% correct !!!!
Ed.R.
In a LINEAR ELASTIC analysis, vary the Young's modulus (but keep Poisson's ratio the same), then for the same applied boundary conditions the resulting stresses never change, whilst the displacements are directly propotional to the value of Young's modulus. Whether the problem is determinate or indeterminate is of no consequence !!!
RE: FEA results and correlation
IMHO these general principles may be stated:
1)We deal only with linear elasticity of course
2)As many of you will know, stresses in a structure may be grouped into two big classes:
-load controlled quantities
-deformation controlled quantities
3)A way of defining these is:
-load controlled stresses are those stresses (that may be only part of an actual stress distribution) that are required to satisfy the differential equations of equilibrium (and we know that they'll be in part indeterminate, so additional assumptions are required to fix them)
-deformation controlled stresses are those stresses, additional to the above (but may be the only ones present), that are required to satisfy the compatibility equations
4)Taking the example of beams, any external load will generate load controlled stresses, if the problem is determinate, and both load and deformation controlled stresses if the problem is indetederminate. On the contrary a situation with no external load (thermal expansion, externally generated distortion like settlement of supports) will only have deformation controlled stresses (that by the way will exist only if the problem is indeterminate)
5)A general statement about load controlled stresses is that they do not depend on Young's modulus, just because equilibrium equations do not either!
6)A general statement of the same kind is not possible for deformation controlled stresses. An example of deformation controlled stresses that do not depend on E are the stresses at the boundary between two structures with different behaviours (e.g.a the junction between a head and a shell); if the two Young's moduli are different the stresses will depend on the ratio of them, not on their absolute magnitude. Another example are the stresses due to boundary conditions in an indeterminate beam, that indeed do not depend on E. I can't find at the moment a general rule to describe this situation.
7)It is useful to recall that any Poisson effect (of course this doesn't apply to beams) gives rise to deformation controlled stresses: however this is another example of deformation stresses that do not (generally) depend on E.
prex
http://www.xcalcs.com : Online tools for structural design
http://www.megamag.it : Magnetic brakes for fun rides
http://www.levitans.com : Air bearing pads
RE: FEA results and correlation
corus
RE: FEA results and correlation
Just to make an example (and if I recall correctly), titanium has about half modulus with respect to steel, but as there are alloys with quite high strengths, it has important structural applications (of course where the cost is not a prime issue).
prex
http://www.xcalcs.com : Online tools for structural design
http://www.megamag.it : Magnetic brakes for fun rides
http://www.levitans.com : Air bearing pads
RE: FEA results and correlation
Referring to your original post, if everything in your model:
material properties, loads, boundary conditions and mesh size are correct, the result of FEA should also be 100% correct.
The big question is how did you arrive at the conclusion that everything in your model is correct? The issue is a lot more complicated than posed here. It is impossible to have all of the above 100% correct. It takes too much time, effort and money to do so. Let me ask you a few questions.
1. Did you do any material tests on the material to determine the properties; Modulus of Elasticity, Poison's ratio? In order to use the stress information you will also need to know yield point and the ultimate strength of the material. How many such tests have you done? Do you have a handle on the variability of these properties. What variations are introduced by the manufacturing processes? Is the material truly linear? Or are you using propertis from the literature?
2. Have you estimated the mesh discretization error by doing a convergence study? There is no such thing as a 'correct mesh'. The correct mesh would have to be a continuum. And no supercomputer in the world can handle it. You can use a mesh size and then exactly double it. If this is done you can use Richardson's extraploation to estimate the continuum result. If the mesh is not an exact double you would need three meshes to estimate the continuum result. This assumes that the results are in the asymptotic range.
3. Getting the boundary conditions 100% correct is not possible. There is no such thing as a fixed constraint in real life. Also there is no such thing as a frictionless contact. Correct value of coefficient of friction is hard to estimate. Usually a part works as a part of a bigger assembly. In order to analyze anything we have to isolate a part of the system. This process of isolation involves replacing some parts with boundary conditions. All of the above are called idealizations and introduce error, which is very hard to estimate. Validation experiments are carried out to find out the extent of above error.
4. If you can estimate loads 100% accurately you are lucky or are too optimistic.
The issue of verification and validation (V & V) has been described very well in PTC-60 from ASME on 'Guidelines on verification and validation in computational mechanics'. These guide lines have come out just this year. According to these guidelines there are three steps in determining the accuracy of FEA simulations. They consist of Verification and Validation and are describe below.
1. First part of Verification. This is verification that the code is solving the equations correctly. This is done by checking the code against, analytical solutions, manufactured solutions, or other established benchmarks such as NAFEMS benchmarks.
2. Second part of verificatin is estimation of discretization error as mentioned above.
3. Third step involves validation, which consists of carrying out a validation experiment and comparing the results of the experiment to the results of the simulation.
Step 3 should be carried out after steps 1 and 2 have been completed. An estimation of error in the experimental results needs to be made based on uncertainty quantification. If the difference between the experimental results and the simulation results are not acceptable, then cause of the difference needs to be investigated. This would involve uncertainty/error quantification for the inputs to the simulation (material properties, loads, boundary conditions etc.) and repetetion of the validation experiment.
Absolute value of error is not important. It is first imporant to determine how much error would be acceptable for the simulation to be useful for the intended purpose. Then by above steps the error band can be reduced to the required level.
In order to read further details on this subject I would refer you to SAFESA guidelines of NAFEMS and ASME PTC-60.
Gurmeet
RE: FEA results and correlation
"if everything in your model:
material properties, loads, boundary conditions and mesh size are correct, the result of FEA should also be 100% correct."
I think you have overlooked the fact that FEA is an approximate method and thus will never be able to attain 100% accuracy.
RE: FEA results and correlation
In essence you're looking for a degree of confidence in the results not a degree of accuracy, although the two may be related. If people don't believe your answers then you do have a problem. I think that's what the original question refers to.
corus
RE: FEA results and correlation
The mathematical model is an approximate description of a real (physical) phenomenon (or phenomena if thinking of coupled problems). The mathematical model (PDE,BC,IC) may contain at some point a set of assumptions and simplifications which are more or less accurate with respect to the physical phenomena.
E.g., many times:
-the material is assumed isotropic and homogeneous
-the response of the material is simplified
-the geometry imperfections of the real life body (domain) are ignored
-the boundary coditions are simplified etc.
In addition to these, FEM may introduce other "inaccuracies":
-errors associated with domain discretization
-errors associated with numerical integration schemes
-errors associated with the equations solver
-errors caused by imposing boundary conditions (i.e. penalty method)
-underlying roundoff and truncation errors etc.
Therefore, the FEM solution is an approximate solution to an approximate model.
RE: FEA results and correlation
Corus indicated that Code Verification is carried out by software vendor and not the users. The primary responsibility of Code Verfication rests with the code vendor. However when new versions of code are released Aerospace companies do carry out extensive verification of their own. I would like to know Johnhours (Aerospace) opinion on this.
I think in companies, which do not have a history of doing FEA and which are beginning to venture into FEA,the management places too much emphasis on getting more accuracy. They do not realize that the higher accuracy will come only by spending a significant cost and effort. Also lot of benefits can be gained by trend analysis using FEA. Some testing is necessary to get an idea about cumulative error present due to all the reasons mentioned in the above posts.
It appears that CFD community has done a lot of work already on the subject of Verification and Validation. Another good reference on the subject is:
Roach, P.J., 1998, "Verification and Validation in Computational Science and Engineering", Hermosa Publishers, Albuquerque, NM, USA.
I agree with Corus that important thing is to generate confidence in the mind of customers (internal or external). This should come from successful application on their problems. For new customers this may also involve efforts to educate them.
Gurmeet
RE: FEA results and correlation
In an ideal world the end users would not encounter bugs or problems with software, but unfortunately there have been major issues with new releases of codes in the past, thus the Aerospace companies continue to test them before allowing them out for general usage. There have been instances of bugs generating false results which have then had detrimental consequences. Most experienced users would have come across a buggy release of software at some time.
I'm in the very fortunate position of having access to three major FEA systems at work (Abaqus, Nastran and Lusas) for historical and legacy reasons, plus others like CalculiX and Catia's GPS module. I do compare results from them, using the same mesh and boundary conditions, especially when running non-linear jobs, just to a get a warm feeling, of course the comparison won't tell me if I've made a mistake in applying the BC's, but it does boost your confidence when different solvers agree to within a few percent on a non-linear run. In linear analyses as you would expect, the differences are down to the level of precision round-off errors between Abaqus, Lusas and CalculiX, but strangely MSC/Nastran is very often about a percentage in disagreement with the other three (on large tet mesh models) ! Perhaps someone could shed some light on this ?
You are correct that some managers place too much emphasis on accuracy or have too much confidence in the level of accuracy obtained. I tell them that at a pinch you could have confidence in only the first two significant figures of a result value, with the rest being nothing more than random numbers ! It doesn't usually go down well !
RE: FEA results and correlation
How much of your real world test data is good to 3 sf? How many tests do you run that have a repeatability of better than 1%? How much of your test data do you even know what the accuracy really is?
My real world test data often has repeatability worse than the sort of design improvements I'd like to make, that is, if I could achieve, on average, the performance seen in the outlier runs, I'd have met my objectives.
Cheers
Greg Locock
Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.
RE: FEA results and correlation
I do floor vibrations research and I can usually get the first few natural frequencies of simple structures (joist footbridges, etc.) correct to within 5%. Real buildings are much harder. I can often get the natural frequency within 10%, but the modes will be out of order, etc.
Acceleration, now that's another story. With measured damping, I can get within maybe 20%, but not consistently.