Discussion:
Straight beam under pure bending
Cheng-Kong Wu
2010-11-11 17:20:05 UTC
Permalink
Dear all,

I have a beam bending problem that I cannot figure out and need some advice.

I tested two composite beams, one made of steel and aluminum and under small deformation. The theoretical stress and strain correlate very well with the ABAQUS results.

I tested another composite beam (Copper + Polyimide) under a small moment. One abaqus model without NLGEOM and one with NLGEOM. The deformed shape was quite different. The one with NLGEOM resulted almost in a circle but the one without have a very large deformation. The deisplacement, stress/strain results of the model without NLGEOM correlate very well with the theoretical values (delta = ML^2/2EI, epsilon = y/rho). However, I think the one with NLGEOM turned on is more reasonable, but the correlation was not good, why?

I searched the internet and my books for large deformation theoretical results, but did not find what I want. Could anyone provide some suggestions?

Thank you for your time!
Cheng-Kong
Dave Lindeman
2010-11-11 19:20:58 UTC
Permalink
(1) When plotting the deformed shape with NLGEOM off, make sure the
displacement scale isn't being exaggerated (i.e., set the deformation
scale to "1.0" in the "Common Options" dialog box.

(2) Theoretical beam solutions are based on small deformation theory.
If the loads your are applying are large enough that NLGEOM=YES is
required, then the theoretical solution will be very inaccurate. Since
you describe your deformed shape as "almost in a circle", then large
deformation effects are definitely important.

Regards,
Dave


-------------------------
Dave Lindeman
Lead Research Specialist
3M Company
3M Center 235-3F-08
St. Paul, MN 55144
651-733-6383
Post by Cheng-Kong Wu
Dear all,
I have a beam bending problem that I cannot figure out and need some advice.
I tested two composite beams, one made of steel and aluminum and under
small deformation. The theoretical stress and strain correlate very well
with the ABAQUS results.
I tested another composite beam (Copper + Polyimide) under a small
moment. One abaqus model without NLGEOM and one with NLGEOM. The
deformed shape was quite different. The one with NLGEOM resulted almost
in a circle but the one without have a very large deformation. The
deisplacement, stress/strain results of the model without NLGEOM
correlate very well with the theoretical values (delta = ML^2/2EI,
epsilon = y/rho). However, I think the one with NLGEOM turned on is more
reasonable, but the correlation was not good, why?
I searched the internet and my books for large deformation theoretical
results, but did not find what I want. Could anyone provide some
suggestions?
Thank you for your time!
Cheng-Kong
------------------------------------
Cheng-Kong Wu
2010-11-11 20:07:41 UTC
Permalink
Dave,

Thank you for the quick respose.

The beam is 80 mm long, 8 mm wide and 0.048 mm thick. The applied moment is 0.1 N-mm.

When NLGEOM is off, the maximun vertical displacement is about 229 mm compared to the theretical value 231 mm. The stress/strain results were almost identical to the theretical value. The auto compute scale factor is only about 0.03.
From some articles, if the beam was going to form a circle, the the radius of curvature can be calculated by L = 2 * pi *rho, where L is the length of the beam and rho is the radius of curvature. The bending moment required can be calculated by M = EI/rho, and is about 0.109 N-mm. From this, I think my applied moment is close to this value, and the deformed shape should looked similar to a circle. I turned NLGEOM on and the maximum vertical displacement was 30.86 mm, and the stress and strains were 5-10% off. Do you know any equation that can describe the displacement field for large deformation?
Thank you!
Cheng-Kong
Subject: Re: [Abaqus] Straight beam under pure bending
Date: Thursday, November 11, 2010, 1:20 PM
(1)  When plotting the deformed
shape with NLGEOM off, make sure the
displacement scale isn't being exaggerated (i.e., set the
deformation
scale to "1.0" in the "Common Options" dialog box.
(2)  Theoretical beam solutions are based on small
deformation theory.
If the loads your are applying are large enough that
NLGEOM=YES is
required, then the theoretical solution will be very
inaccurate.  Since
you describe your deformed shape as "almost in a circle",
then large
deformation effects are definitely important.
Regards,
Dave
-------------------------
Dave Lindeman
Lead Research Specialist
3M Company
3M Center 235-3F-08
St. Paul, MN 55144
651-733-6383
Post by Cheng-Kong Wu
Dear all,
I have a beam bending problem that I cannot figure out
and need some advice.
Post by Cheng-Kong Wu
I tested two composite beams, one made of steel and
aluminum and under
Post by Cheng-Kong Wu
small deformation. The theoretical stress and strain
correlate very well
Post by Cheng-Kong Wu
with the ABAQUS results.
I tested another composite beam (Copper + Polyimide)
under a small
Post by Cheng-Kong Wu
moment. One abaqus model without NLGEOM and one with
NLGEOM. The
Post by Cheng-Kong Wu
deformed shape was quite different. The one with
NLGEOM resulted almost
Post by Cheng-Kong Wu
in a circle but the one without have a very large
deformation. The
Post by Cheng-Kong Wu
deisplacement, stress/strain results of the model
without NLGEOM
Post by Cheng-Kong Wu
correlate very well with the theoretical values (delta
= ML^2/2EI,
Post by Cheng-Kong Wu
epsilon = y/rho). However, I think the one with NLGEOM
turned on is more
Post by Cheng-Kong Wu
reasonable, but the correlation was not good, why?
I searched the internet and my books for large
deformation theoretical
Post by Cheng-Kong Wu
results, but did not find what I want. Could anyone
provide some
Post by Cheng-Kong Wu
suggestions?
Thank you for your time!
Cheng-Kong
------------------------------------
  http://groups.yahoo.com/group/AbaqusYahoo! Groups
Links
Dave Lindeman
2010-11-11 21:28:29 UTC
Permalink
The solution with NLGEOM=NO may agree with the theoretical values, but
with deformations that large, they'll both be wrong.

If you form an 80 mm long beam into a circle, then the radius of
curvature should be 12.73 mm. The maximum vertical displacement in the
beam should then be equal to the diameter of this circle -- 25.48 mm.
Your value (30.86) is approximately 20% larger than this. If you
increased your load from 0.1 N mm to your estimated value of 0.109 N mm,
then your values would start getting pretty close.

Regards,
Dave


-------------------------
Dave Lindeman
Lead Research Specialist
3M Company
3M Center 235-3F-08
St. Paul, MN 55144
651-733-6383
Post by Cheng-Kong Wu
Dave,
Thank you for the quick respose.
The beam is 80 mm long, 8 mm wide and 0.048 mm thick. The applied moment is 0.1 N-mm.
When NLGEOM is off, the maximun vertical displacement is about 229 mm
compared to the theretical value 231 mm. The stress/strain results were
almost identical to the theretical value. The auto compute scale factor
is only about 0.03.
From some articles, if the beam was going to form a circle, the the
radius of curvature can be calculated by L = 2 * pi *rho, where L is the
length of the beam and rho is the radius of curvature. The bending
moment required can be calculated by M = EI/rho, and is about 0.109
N-mm. From this, I think my applied moment is close to this value, and
the deformed shape should looked similar to a circle. I turned NLGEOM on
and the maximum vertical displacement was 30.86 mm, and the stress and
strains were 5-10% off. Do you know any equation that can describe the
displacement field for large deformation?
Thank you!
Cheng-Kong
Subject: Re: [Abaqus] Straight beam under pure bending
Date: Thursday, November 11, 2010, 1:20 PM
(1) When plotting the deformed
shape with NLGEOM off, make sure the
displacement scale isn't being exaggerated (i.e., set the
deformation
scale to "1.0" in the "Common Options" dialog box.
(2) Theoretical beam solutions are based on small
deformation theory.
If the loads your are applying are large enough that
NLGEOM=YES is
required, then the theoretical solution will be very
inaccurate. Since
you describe your deformed shape as "almost in a circle",
then large
deformation effects are definitely important.
Regards,
Dave
-------------------------
Dave Lindeman
Lead Research Specialist
3M Company
3M Center 235-3F-08
St. Paul, MN 55144
651-733-6383
Post by Cheng-Kong Wu
Dear all,
I have a beam bending problem that I cannot figure out
and need some advice.
Post by Cheng-Kong Wu
I tested two composite beams, one made of steel and
aluminum and under
Post by Cheng-Kong Wu
small deformation. The theoretical stress and strain
correlate very well
Post by Cheng-Kong Wu
with the ABAQUS results.
I tested another composite beam (Copper + Polyimide)
under a small
Post by Cheng-Kong Wu
moment. One abaqus model without NLGEOM and one with
NLGEOM. The
Post by Cheng-Kong Wu
deformed shape was quite different. The one with
NLGEOM resulted almost
Post by Cheng-Kong Wu
in a circle but the one without have a very large
deformation. The
Post by Cheng-Kong Wu
deisplacement, stress/strain results of the model
without NLGEOM
Post by Cheng-Kong Wu
correlate very well with the theoretical values (delta
= ML^2/2EI,
Post by Cheng-Kong Wu
epsilon = y/rho). However, I think the one with NLGEOM
turned on is more
Post by Cheng-Kong Wu
reasonable, but the correlation was not good, why?
I searched the internet and my books for large
deformation theoretical
Post by Cheng-Kong Wu
results, but did not find what I want. Could anyone
provide some
Post by Cheng-Kong Wu
suggestions?
Thank you for your time!
Cheng-Kong
------------------------------------
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------------------------------------
Ali Khajehgani
2010-11-11 22:04:18 UTC
Permalink
Have you defined plasticity in the material model for the beam? If you have
plasticity and then turn on the NlGeom on then plasticity will effect your
results as wel.


Br

Ali

-----Original Message-----
From: ***@yahoogroups.com [mailto:***@yahoogroups.com] On Behalf Of
Dave Lindeman
Sent: 11. november 2010 22:28
To: ***@yahoogroups.com
Subject: Re: [Abaqus] Straight beam under pure bending

The solution with NLGEOM=NO may agree with the theoretical values, but
with deformations that large, they'll both be wrong.

If you form an 80 mm long beam into a circle, then the radius of
curvature should be 12.73 mm. The maximum vertical displacement in the
beam should then be equal to the diameter of this circle -- 25.48 mm.
Your value (30.86) is approximately 20% larger than this. If you
increased your load from 0.1 N mm to your estimated value of 0.109 N mm,
then your values would start getting pretty close.

Regards,
Dave


-------------------------
Dave Lindeman
Lead Research Specialist
3M Company
3M Center 235-3F-08
St. Paul, MN 55144
651-733-6383
Post by Cheng-Kong Wu
Dave,
Thank you for the quick respose.
The beam is 80 mm long, 8 mm wide and 0.048 mm thick. The applied moment is 0.1 N-mm.
When NLGEOM is off, the maximun vertical displacement is about 229 mm
compared to the theretical value 231 mm. The stress/strain results were
almost identical to the theretical value. The auto compute scale factor
is only about 0.03.
From some articles, if the beam was going to form a circle, the the
radius of curvature can be calculated by L = 2 * pi *rho, where L is the
length of the beam and rho is the radius of curvature. The bending
moment required can be calculated by M = EI/rho, and is about 0.109
N-mm. From this, I think my applied moment is close to this value, and
the deformed shape should looked similar to a circle. I turned NLGEOM on
and the maximum vertical displacement was 30.86 mm, and the stress and
strains were 5-10% off. Do you know any equation that can describe the
displacement field for large deformation?
Thank you!
Cheng-Kong
Subject: Re: [Abaqus] Straight beam under pure bending
Date: Thursday, November 11, 2010, 1:20 PM
(1) When plotting the deformed
shape with NLGEOM off, make sure the
displacement scale isn't being exaggerated (i.e., set the
deformation
scale to "1.0" in the "Common Options" dialog box.
(2) Theoretical beam solutions are based on small
deformation theory.
If the loads your are applying are large enough that
NLGEOM=YES is
required, then the theoretical solution will be very
inaccurate. Since
you describe your deformed shape as "almost in a circle",
then large
deformation effects are definitely important.
Regards,
Dave
-------------------------
Dave Lindeman
Lead Research Specialist
3M Company
3M Center 235-3F-08
St. Paul, MN 55144
651-733-6383
Post by Cheng-Kong Wu
Dear all,
I have a beam bending problem that I cannot figure out
and need some advice.
Post by Cheng-Kong Wu
I tested two composite beams, one made of steel and
aluminum and under
Post by Cheng-Kong Wu
small deformation. The theoretical stress and strain
correlate very well
Post by Cheng-Kong Wu
with the ABAQUS results.
I tested another composite beam (Copper + Polyimide)
under a small
Post by Cheng-Kong Wu
moment. One abaqus model without NLGEOM and one with
NLGEOM. The
Post by Cheng-Kong Wu
deformed shape was quite different. The one with
NLGEOM resulted almost
Post by Cheng-Kong Wu
in a circle but the one without have a very large
deformation. The
Post by Cheng-Kong Wu
deisplacement, stress/strain results of the model
without NLGEOM
Post by Cheng-Kong Wu
correlate very well with the theoretical values (delta
= ML^2/2EI,
Post by Cheng-Kong Wu
epsilon = y/rho). However, I think the one with NLGEOM
turned on is more
Post by Cheng-Kong Wu
reasonable, but the correlation was not good, why?
I searched the internet and my books for large
deformation theoretical
Post by Cheng-Kong Wu
results, but did not find what I want. Could anyone
provide some
Post by Cheng-Kong Wu
suggestions?
Thank you for your time!
Cheng-Kong
------------------------------------
<mailto:Abaqus%40yahoogroups.com>
Post by Cheng-Kong Wu
<mailto:Abaqus-subscribe%40yahoogroups.com>
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Links
<mailto:Abaqus-fullfeatured%40yahoogroups.com>
------------------------------------

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rstonecmi
2010-11-11 21:53:17 UTC
Permalink
Cheng-Kong,
The displacement field is precisely a circular arc (not necessarily a full 360 circle) since all sections have the same moment and thus the same curvature. The strains for your case are less than 0.2% so large strains are not an issue (just large displacements and rotations). If the material is linear elastic the solution is simply that found in any strength of materials book for pure bending. Even if the material is nonlinear, the strains in the beam section =y/R where y is the distance from the neutral axis and R is the bend radius.
Best regards,
Randy
Post by Cheng-Kong Wu
Dave,
Thank you for the quick respose.
The beam is 80 mm long, 8 mm wide and 0.048 mm thick. The applied moment is 0.1 N-mm.
When NLGEOM is off, the maximun vertical displacement is about 229 mm compared to the theretical value 231 mm. The stress/strain results were almost identical to the theretical value. The auto compute scale factor is only about 0.03.
From some articles, if the beam was going to form a circle, the the radius of curvature can be calculated by L = 2 * pi *rho, where L is the length of the beam and rho is the radius of curvature. The bending moment required can be calculated by M = EI/rho, and is about 0.109 N-mm. From this, I think my applied moment is close to this value, and the deformed shape should looked similar to a circle. I turned NLGEOM on and the maximum vertical displacement was 30.86 mm, and the stress and strains were 5-10% off. Do you know any equation that can describe the displacement field for large deformation?
Thank you!
Cheng-Kong
Subject: Re: [Abaqus] Straight beam under pure bending
Date: Thursday, November 11, 2010, 1:20 PM
(1)  When plotting the deformed
shape with NLGEOM off, make sure the
displacement scale isn't being exaggerated (i.e., set the
deformation
scale to "1.0" in the "Common Options" dialog box.
(2)  Theoretical beam solutions are based on small
deformation theory.
If the loads your are applying are large enough that
NLGEOM=YES is
required, then the theoretical solution will be very
inaccurate.  Since
you describe your deformed shape as "almost in a circle",
then large
deformation effects are definitely important.
Regards,
Dave
-------------------------
Dave Lindeman
Lead Research Specialist
3M Company
3M Center 235-3F-08
St. Paul, MN 55144
651-733-6383
Post by Cheng-Kong Wu
Dear all,
I have a beam bending problem that I cannot figure out
and need some advice.
Post by Cheng-Kong Wu
I tested two composite beams, one made of steel and
aluminum and under
Post by Cheng-Kong Wu
small deformation. The theoretical stress and strain
correlate very well
Post by Cheng-Kong Wu
with the ABAQUS results.
I tested another composite beam (Copper + Polyimide)
under a small
Post by Cheng-Kong Wu
moment. One abaqus model without NLGEOM and one with
NLGEOM. The
Post by Cheng-Kong Wu
deformed shape was quite different. The one with
NLGEOM resulted almost
Post by Cheng-Kong Wu
in a circle but the one without have a very large
deformation. The
Post by Cheng-Kong Wu
deisplacement, stress/strain results of the model
without NLGEOM
Post by Cheng-Kong Wu
correlate very well with the theoretical values (delta
= ML^2/2EI,
Post by Cheng-Kong Wu
epsilon = y/rho). However, I think the one with NLGEOM
turned on is more
Post by Cheng-Kong Wu
reasonable, but the correlation was not good, why?
I searched the internet and my books for large
deformation theoretical
Post by Cheng-Kong Wu
results, but did not find what I want. Could anyone
provide some
Post by Cheng-Kong Wu
suggestions?
Thank you for your time!
Cheng-Kong
------------------------------------
  http://groups.yahoo.com/group/AbaqusYahoo! Groups
Links
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