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[WB] Structural Error - Acceptable Values
 
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jonathan.chant
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PostPosted: Fri Jun 12, 2015 4:23 am  Reply with quote

Hi,

I was just wondering if anyone had a rule-of-thumb for acceptable error vales when using structural error plots to evaluate mesh adequacy in a static structural analysis? Obviously the structural error wants to be as small as possible, but is there an acceptable maximum value? Would a maximum allowable error value vary with the size of the model and applied loads?

Thanks,
Jon.
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andrew.kelly
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PostPosted: Fri Jun 12, 2015 12:15 pm  Reply with quote

About 10 years ago I started trying to use Structural Error to assess "goodness" of the model. After a while, I couldn't find value, so I've fallen back to more traditional assessments of quality. Such as tribal knowledge, initial element sizes on curved surfaces, stress gradients, and good old fashioned mesh density studies, or just simply meshing it like you've got nothing better to do.

If I remember correctly, Structural Error is based on the volume of the element. So large low-stress elements would report a high structural error, but small elements with a large stress gradient would report a small structural error. It was very misleading.

I got the impression that it was something required for Mechanical's automatic mesh refinement and didn't have much value outside that.
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christopher.wright
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PostPosted: Fri Jun 12, 2015 2:49 pm  Reply with quote

On Jun 12, 2015, at 6:23 AM, jonathan.chant wrote:

Quote:
I was just wondering if anyone had a rule-of-thumb for acceptable
error vales when using structural error plots to evaluate mesh
adequacy in a static structural analysis? Obviously the structural
error wants to be as small as possible, but is there an acceptable
maximum value? Would a maximum allowable error value vary with the
size of the model and applied loads?

My basic principle is twofold:
1. Never bet the farm on the third significant figure.
2. Never expect to match results from a test you haven't witnessed or
a calculation you haven't reviewed.

The real answer to your question is highly problem dependent and
mostly involves making allowances for things you don't know or
neglect to include. For many years the criterion was 'slide rule
accuracy' meaning arithmetic errors from relatively simple
calculations with design parameters read from charts of 5-10% with
overall design margins of 1.5 or so. In those days the design margins
usually accounted for unknowns from estimated loading, imprecise
analytical procedures or stress concentrations. Acceptable numerical
accuracy for engineering calculations is three significant figures at
the very, very best, with two figures about average.

With FEA there calculations are more precise, but you can rarely
predict the actual service very well nor do you know even basic
material properties with three figure certainty. Fatigue and fracture
data frequently scatter over half an order of magnitude--3 figure
precision in a fatigue analysis is meaningless. Fracture is
microstructure dependent so crack growth rates and Kic data vary over
the same range. Materials strength and stiffness data is more
precisely known but rarely repeatable within 10% from one batch to
the next.

The design itself is always subject to manufacturing variations and
such local defects as weld undercut and built-in stress from forming
operations and thermal processes. My own rule of thumb is never to
expect better than 10% accurate results _provided_ the model passes
sanity checks like static or dynamic equilibrium, boundary condition
and load path verification. If your analysis involves thermal loading
particularly convection 10% accuracy is about the best you'll ever
get, again, considering the scatter of heat transfer measurements.

Test data correlation ranges all over the place, depending very much
on how the test is run. The only way to know for sure is to witness
the test yourself--then you can incorporate any peculiarities into
the finite element model. Simple models and straightforward well-run
and repeatable test results can correlate within a few per cent _if
and only if_ you know material properties and can reproduce the
loading and boundary conditions. Sometimes you can run a simple pre-
test to 'calibrate' estimated model properties, For dynamics testing
the correlation is only as good as your knowledge of damping and how
it might vary with load and frequency.

If you're concerned about accuracy, you need to establish what
accuracy you need. 'I need total accuracy everywhere,' is a cop-out--
you know (or you damn sure better know) why you're doing the work and
what results are expected--review your assumptions and estimate what
effects they have. Or work it backwards--if your results are off 10%
how does that affect the design decision? Once you've looked at the
sources of error you can formalize it into an error analysis and
determine whether you've met the needs of your client. Then formalize
your error estimate and include it in your report.

One last thing: don't mistake a convergence check for an error
analysis. Remember that converged garbage is still garbage.

Christopher Wright P.E. |"They couldn't hit an elephant at
chrisw@skypoint.com | this distance" (last words of Gen.
.......................................| John Sedgwick, Spotsylvania
1864)
http://www.skypoint.com/members/chrisw/



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jonathan.chant
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PostPosted: Mon Jun 15, 2015 12:44 am  Reply with quote

Hi Andrew,

Thanks for the reply. I thought it maybe sounded a bit too easy.
Sounds like I'll just have to rely on common sense and judgement then. Oh dear...

Thanks again,
Jon.
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jonathan.chant
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PostPosted: Mon Jun 15, 2015 1:05 am  Reply with quote

Hi Christopher,

Thanks for taking the time to reply on this. So if, in theory, you were looking to achieve a 10% accuracy, is there a way of relating this to the structural error values given in the error plots (units mJ)?
I've found some information suggesting that the maximum value is an indicator of global mesh quality (lower the better), and the error distribution is an indicator of local mesh quality (more uniform the better). But I can't find anything on how to relate the values to anything useful.

Thanks again,
Jon.
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christopher.wright
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PostPosted: Mon Jun 15, 2015 12:25 pm  Reply with quote

On Jun 15, 2015, at 3:05 AM, jonathan.chant wrote:

Quote:
Thanks for taking the time to reply on this. So if, in theory, you
were looking to achieve a 10% accuracy, is there a way of relating
this to the structural error values given in the error plots (units
mJ)?

I've never found a general way to use error values to judge the
overall usefulness of an analysis. As you've noticed the
explanations of the printed error values are pretty obscure, so I
suspect that if there were a straightforward interpretation of those
error values it'd be plastered all over the user docs and trumpeted
to high heaven in tutorials and seminars. Moreover you'll find, if
you haven't already, that locally poor meshes frequently have only a
local effect and aren't necessarily an indication of overall usefulness.

Moreover I don't think you can judge the engineering validity of an
analysis from an error plot any more than you can judge the severity
of a stress state from colors on a a stress plot. The engineering use
of FEA goes far beyond that kind of simplistic assessment. I've
always felt that judging FEA results against first principles of
mechanics and the engineering practice reflected in the design
assumptions are a far better measure of the usefulness of the
analysis. Engineering is inherently imprecise anyway. ANSYS will give
you six or seven significant figures, even though assumed loads are
attempts to predict the future or material behavior reflects only
idealizations.

Contrary to some cherished beliefs, FEA isn't some sort of virtual
reality exercise. It's a tool which aids in the application of
engineering principles. A user who doesn't understand those
principles might as well pretend to understand the Arthurian legend
from 'Monty Python and the Holy Grail.' Don't pretend that an ANSYS
analysis can tell you everything.


Christopher Wright P.E. |"They couldn't hit an elephant at
chrisw@skypoint.com | this distance" (last words of Gen.
.......................................| John Sedgwick, Spotsylvania
1864)
http://www.skypoint.com/members/chrisw/



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guowei.li
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PostPosted: Mon Jun 15, 2015 3:03 pm  Reply with quote

Error studies are important and necessary but difficult. I don't think it is within the scope of engineering practice but more of an academic topic. In an engineering report, displaying error bar on a plot is not an adequate request for today.

When error is between FEA result and its corresponding "real" value, for example between FEA computed strain and its corresponding measured strain, the error can be split into following two big categories.

#1) error between FEA results and the mathematical solution of its corresponding PDE equations that describes the physical problem
#2) error between the solution of the mathematical PDE equations and its corresponding physical measurement

Most of time, error #1 is discussed and referred. And, I believe that is the error you mentioned in your email. Because this is a pure math issue, it can be and has been addressed for decades. Sometimes you can see o(h), o(h^1.5), and o(h^2) in some literature. It is referring to the error between FEA discrete solution and accurate PDE solution. The error is in the order of magnitude of mesh size (h) or higher. First order is less accurate so smaller mesh size is needed. But displaying this error in plot doesn't help a lot to understand the computation confidence.

For #2 error, it is difficult and expensive to get the error accurately. In strain measurement, the signal can be shifted when the environment temperature shifts because you open/close the lab door. There are more sources of error, e.g. dimension, material properties, machining process, etc.

Without checking against measurement, it is not easy to gain confidence to FEA results. Some measurements are always good to understand the error and to use the modeling results with confidence. In other word, a comparison with measurement is more useful than attempts to display error bar.

Guowei Li
www.westport.com


-----Original Message-----
From: Xansys [mailto:xansys-bounces@xansys.org] On Behalf Of jonathan.chant
Sent: June-12-15 4:23 AM
To: xansys@xansys.org
Subject: [Xansys] [WB] Structural Error - Acceptable Values

Hi,

I was just wondering if anyone had a rule-of-thumb for acceptable error vales when using structural error plots to evaluate mesh adequacy in a static structural analysis? Obviously the structural error wants to be as small as possible, but is there an acceptable maximum value? Would a maximum allowable error value vary with the size of the model and applied loads?

Thanks,
Jon.

------------------------
Jonathan Chant

Stress Engineer
EFC Group
Mechanical Handling Division
Leeds






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jonathan.chant
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PostPosted: Tue Jun 16, 2015 12:10 am  Reply with quote

Hi Christopher,

Thanks again for the response. I was really just interested in the usefulness of the error plots as a way of assessing mesh quality rather than any sort of replacement for validation by hand calculations. I would always validate results by hand calculations as a matter of routine anyway - I've made enough school-boy errors in the past not to. Even so, it sounds like the error plots have fairly limited value.
Nothing wrong with the Monty Python films by the way - although it's a bit of a shock to find out that they're not factually accurate after all these years...

Thanks again,
Jon.
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andrew.sims
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PostPosted: Tue Jun 16, 2015 12:26 am  Reply with quote

Getting off topic...

The Monty Python films may not be factually accurate, but linguistically... there is a fantastic Latin grammar lesson in Life of Brian.

Andrew Sims
ResMed Ltd

-----Original Message-----
From: Xansys [mailto:xansys-bounces@xansys.org] On Behalf Of jonathan.chant
Sent: Tuesday, 16 June 2015 5:10 PM
To: xansys@xansys.org
Subject: Re: [Xansys] [WB] Structural Error - Acceptable Values

Hi Christopher,

Thanks again for the response. I was really just interested in the usefulness of the error plots as a way of assessing mesh quality rather than any sort of replacement for validation by hand calculations. I would always validate results by hand calculations as a matter of routine anyway - I've made enough school-boy errors in the past not to. Even so, it sounds like the error plots have fairly limited value.
Nothing wrong with the Monty Python films by the way - although it's a bit of a shock to find out that they're not factually accurate after all these years...

Thanks again,
Jon.

------------------------
Jonathan Chant

Stress Engineer
EFC Group
Mechanical Handling Division
Leeds






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jonathan.chant
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PostPosted: Tue Jun 16, 2015 12:31 am  Reply with quote

Hi Guowei Li,

Thanks for the response. Yes the structural error that I was referring to is the difference in the strain energy as calculated using the averaged and unaveraged stresses over an element. As I say, I was just interested in it as a tool for assessing local mesh quality rather than any sort of replacement for traditional validation techniques. From the responses on this thread though, it sounds as if it has fairly limited value in this respect.

Thanks again,

Jon.
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jonathan.chant
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PostPosted: Tue Jun 16, 2015 12:38 am  Reply with quote

Quote:
Getting off topic...

The Monty Python films may not be factually accurate, but linguistically... there is a fantastic Latin grammar lesson in Life of Brian.


My personal favourite.
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mitch.voehl
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PostPosted: Tue Jun 16, 2015 12:40 am  Reply with quote

Bf teethv
Quote:
On June 16, 2015 at 2:31 AM "jonathan.chant" <jchant@efcgroup.net> wrote:


Hi Guowei Li,

Thanks for the response. Yes the structural error that I was referring to is
the difference in the strain energy as calculated using the averaged and
unaveraged stresses over an element. As I say, I was just interested in it as
a tool for assessing local mesh quality rather than any sort of replacement
for traditional validation techniques. From the responses on this thread
though, it sounds as if it has fairly limited value in this respect.

Thanks again,

Jon.

------------------------
Jonathan Chant

Stress Engineer
EFC Group
Mechanical Handling Division
Leeds






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jonathan.chant
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PostPosted: Tue Jun 16, 2015 12:49 am  Reply with quote

Quote:
Bf teethv


No idea. Sorry. Do I need that Latin lesson?

Thanks,
Jon.
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christopher.wright
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PostPosted: Tue Jun 16, 2015 12:11 pm  Reply with quote

On Jun 15, 2015, at 5:03 PM, Guowei Li wrote:

Quote:
In other word, a comparison with measurement is more useful than
attempts to display error bar.

So what do you do if you find disagreement? In addition to your
implicit assumption that the test is always error-free, tests have
assumptions, only different assumptions, than FEA. The only thing
that'll save you from an extended shouting match or paralysis by
analysis is the ability to think critically about both sets of
results based on--you guessed it--first principles of mechanics.

Christopher Wright P.E. |"They couldn't hit an elephant at
chrisw@skypoint.com | this distance" (last words of Gen.
.......................................| John Sedgwick, Spotsylvania
1864)
http://www.skypoint.com/members/chrisw/



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andrew.kelly
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PostPosted: Tue Jun 16, 2015 12:23 pm  Reply with quote

Mechanical APDL used to (and still does?) list SMX and SMXB in stress plots. I'd always understood that if the two values were "close", then your discretization error was "negligible". This goes back to Pentium Pro days, so my memory may be a bit fuzzy.

AFAIK, "SMXB" or something similar isn't implemented in Mechanical, so you'd have to write a command object to calculate and extract it. Not difficult, but sort of dumb to have to code it manually. I'm a little disappointed that it isn't implemented in Mechanical, because SMX vs. SMXB would be more useful than "structural error".
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guowei.li
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PostPosted: Tue Jun 16, 2015 9:37 pm  Reply with quote

Disagreement is the starting point of thinking...hopefully it can lead to in-depth understanding or lead to a theoretical breakthrough. FEA or modeling result, by itself and without validation, doesn't have this driven force.

-Guowei
www.westport.com

-----Original Message-----
From: Xansys [mailto:xansys-bounces@xansys.org] On Behalf Of Christopher Wright
Sent: June-16-15 12:11 PM
To: ANSYS User Discussion List
Subject: Re: [Xansys] [WB] Structural Error - Acceptable Values


On Jun 15, 2015, at 5:03 PM, Guowei Li wrote:

Quote:
In other word, a comparison with measurement is more useful than
attempts to display error bar.

So what do you do if you find disagreement? In addition to your implicit assumption that the test is always error-free, tests have assumptions, only different assumptions, than FEA. The only thing that'll save you from an extended shouting match or paralysis by analysis is the ability to think critically about both sets of results based on--you guessed it--first principles of mechanics.

Christopher Wright P.E. |"They couldn't hit an elephant at
chrisw@skypoint.com | this distance" (last words of Gen.
.......................................| John Sedgwick, Spotsylvania
1864)
http://www.skypoint.com/members/chrisw/



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jonathan.chant
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PostPosted: Wed Jun 17, 2015 12:24 am  Reply with quote

Hi Andrew,

Thanks for the tip on the SMX and SMXB values. I'll have to do a bit of digging on how to calculate them using a command object. Strange it's not already implemented - maybe the structural error plots are just prettier.

Anyway. thanks again,
Jon.
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