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.
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FEA results and correlation 5
- Thread starter Sripri
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- #21
Well, I'll jump into this E-no E debate with my two cents.
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
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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
: Online tools for structural design
: Magnetic brakes for fun rides
: Air bearing pads
I would have thought that, generally, if stresses didn't depend on E then the steel industry would be out of business. As I've said, secondary effects such as thermal induced stresses, and geometry, give stresses that are related to E. The problem is that most people who do hand calcs don't consider secondary effects and just simplify things to beams. But that's another story..
corus
corus
Well corus, the steel industry relies of course on the high elastic limit and strength of steels, not necessarily on Young's modulus.
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
: Online tools for structural design
: Magnetic brakes for fun rides
: Air bearing pads
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
: Online tools for structural design
: Magnetic brakes for fun rides
: Air bearing pads
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1
- #24
gurmeet2003
Mechanical
Sripri,
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
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
Gurmeet,
"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.
"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.
In gurmeet's 3 steps it's rare to check a proprietary code against theory as it's assumed that the code has been verified. If it's something downloaded off the net then I would do my own checks. What needs to be verified are the boundary conditions and loads imposed as a check against your input. This might be a simple verification of some part of the model where analytical solutions can be compared against the total reaction force in a structural analysis to make sure they equate to your input loads.
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
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
FEM is a numerical method for solving partial differential equations (PDE) with certain boundary and initial conditions (BC, IC) (i.e. a mathematical model=PDE+BC+IC).
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.
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.
gurmeet2003
Mechanical
Johnhours when I made the comment that if the premise (inputs, bcs, material properties and mesh) is correct the FEA results would be 100% correct, I was trying to imply that this is practically not possible due to discretization error that is always present and other reasons mentioned subsequently. Truncation and roundoff errors may also be present (as indicated by xref), but I do not know their magnitude in commercial codes. They will show up during the process of code verification.
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
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
Gurmeet,
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 !
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 !
GregLocock
Automotive
As an aside
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.
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.
For static cases using steel, I've been able to get within a few percent of experimental deflections. When I'm off by more than say 10%, I start looking for model errors.
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.
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.
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