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## #1 2022-05-23 11:51:32

jlucas
Member
Registered: 2021-12-15
Posts: 12

### Buckling of a cylinder under a twist moment.

Hello,

I am trying to understand how to perform a buckling simulation/analysis using code-aster. My intention is to learn the procedures from a linear Euler analysis to post-buckling. I took note of the reference document [U2.08.04] (Notice de calcul au flambage), along with [U4.51.03] (Opérateur STAT_NON_LINE), but still have some difficulties.

As a simple example (which encloses some of the characteristics I am interested in),  the buckling of a cylindrical tube under a twist moment is considered. An (approximate?) solution can be found for example on Budynas2020 (Roark’s Formulas for Stress and Strain), see enclosed pdf).

Geometry: Cylinder with radius of 30mm, length of 950mm and thickness of 2mm. Material stell (E=207E9 N/m2, nu=0.29)

Buckling is expected for a twist moment of about 19.1 kN.m.

I am performing the following simulations using 3D elements (TETRA10).

1. Linear Euler Buckling (ok) (run01).

The results are as expected. For an applied load of 10kN, the critial factor (lambda) is 1.914.

2. Non-Linear Euler Buckling (Euler extended) under small deformations (ok) (run02).

The results are also as expected. For an applied load of 20kN, the critical factor for the 1st buckling mode approaches 1.0 (=1.0 at an applied load of about 19.189 kN.m at timestep 0.9595).

3. Non-Linear Euler Buckling under large deformations (GROT_GDEP) (not ok) (run03).

Changed in relation to run02 only: on STAT_NON_LINE(COMPORTEMENT=( _F(DEFORMATION='GROT_GDEP'))

The critical factor did not change along the timesteping being the same at first and last step.

In particular:
Le mode de flambement de numéro d'ordre 1 a pour charge critique -1.311160171877e+03.
Le mode de flambement de numéro d'ordre 2 a pour charge critique -1.310881530994e+03.
Le mode de flambement de numéro d'ordre 3 a pour charge critique -8.740587055997e+02.
Le mode de flambement de numéro d'ordre 4 a pour charge critique -1.945797333780e+02.
Le mode de flambement de numéro d'ordre 5 a pour charge critique -1.945624349836e+02.

Also quite far from the boundary (lambda=1.0).

Questions:

a. Is there something particularly wrong with this last simulation (run03)?
(The simulation converged and I could not find any alarm!)

b. Is it possible to perform the Non-Linear Simulation with DEFORMATION='GROT_GDEP' (run03)?

c. How to visualise the buckling modes on a non-linear simulation?

d. Any suggestion / correction/improvement to the command file is welcome.

3. Post-Buckling analysis. Still to perform. Any suggestion for the command file ?

I attach the *comm and *mess files for the 3 simulations. The mesh (cylinder.med) is coarser than the one used in the examples because the file to attach was larger than allowed. By running geometry.py a finer mesh can be generated.

Best regards,
Jorge

Attachments:

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## #2 2022-05-25 07:20:14

jeanpierreaubry
Guru
From: nantes (france)
Registered: 2009-03-12
Posts: 3,823

### Re: Buckling of a cylinder under a twist moment.

hello

the important value is where charge critique changes sign from minus to plus
with  OPTION='PLUS_PETITE',NMAX_CHAR_CRIT=5, you may not catch it, which happens with run03
try OPTION='BANDE',CHAR_CRIT=(-2,2), (or an other range) to try and catch the meanigful values

the range might vary a lot

the above gives good result with run02  but gives me a lot of trouble with run03
with a enormous number of calculated charge critique stopping the calculation

i do not know whether such an analysis is valid with GROT_GEDP

jean pierre aubry

freely available here https://framabook.org/beginning-with-code_aster/

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## #3 2022-05-25 14:02:40

jeanpierreaubry
Guru
From: nantes (france)
Registered: 2009-03-12
Posts: 3,823

### Re: Buckling of a cylinder under a twist moment.

i have added a post with id=26394 related  to this problem

freely available here https://framabook.org/beginning-with-code_aster/

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## #4 2022-05-25 15:36:56

jlucas
Member
Registered: 2021-12-15
Posts: 12

### Re: Buckling of a cylinder under a twist moment.

Hello Jean Pierre Aubry,

Before continuing let me be grateful for your book, which helped me (and I guess many others) to get started with code-aster. I've found it very precious to start the learning curve with some examples which work. Otherwise things can get very frustrating.

As suggested will wait for the reply from support.

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## #5 2022-05-26 08:49:12

jeanpierreaubry
Guru
From: nantes (france)
Registered: 2009-03-12
Posts: 3,823

### Re: Buckling of a cylinder under a twist moment.

hello

may i suggest that you perform the same analysis with shell elements (DKT and DKTG) to see how it goes

jean pierre aubry

freely available here https://framabook.org/beginning-with-code_aster/

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## #6 2022-05-27 11:05:44

jlucas
Member
Registered: 2021-12-15
Posts: 12

### Re: Buckling of a cylinder under a twist moment.

hello,

Meanwhile, let me take a small detour.

How to compute the twist angle?  Following your book: ch19 (Using user filed).

Lets say the twist angle is given by the following formula:

(which is an approximation to the arc length definition: angle=arc_lenght/radius)

DX, DY are supposed to be components of the deformation and
X,Y the coordinates of the nodes

So I tried the following:

'''
TWIST = FORMULE(
NOM_PARA=('X','Y','DX','DY'),
VALE = """sqrt(DX**2+DY**2)/sqrt(X**2+Y**2)""",
);

FLAMB = CALC_CHAMP(
reuse=FLAMB,
RESULTAT=FLAMB,
CHAM_UTIL=_F(
NOM_CHAM='DEPL',
FORMULE=TWIST,
NUME_CHAM_RESU=10,
),
);
'''

Which does not work as it complains on the X,Y variables.

ERREUR LORS DE L'ÉVALUATION DE LA FORMULE 'TWIST' :
>> name 'X' is not defined

How to get the coordinates of the nodes to use them in CALC_CHAMP?

Best wishes,
Jorge

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## #7 2022-05-27 13:30:40

jeanpierreaubry
Guru
From: nantes (france)
Registered: 2009-03-12
Posts: 3,823

### Re: Buckling of a cylinder under a twist moment.

at first i would say it is impossible to retrieve X and Y, node coordinates before deformation
at least i do not know how

but if you make a group with nodes sitting on the outer surface the problem becomes trivial as sqrt(X**2+Y**2)=R

or even simpler (and more accurate ,) TWIST=ATAN(DX/DY)

and this computation could be made directly in Gmsh Post pro appendix B 2.2.1  in my book

Last edited by jeanpierreaubry (2022-05-27 13:33:31)

freely available here https://framabook.org/beginning-with-code_aster/

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## #8 2022-05-27 18:47:29

jlucas
Member
Registered: 2021-12-15
Posts: 12

### Re: Buckling of a cylinder under a twist moment.

Hello,

The use of shell elements (DKT) as suggested by jeanpierreaubry did not change the result. I attach the updated example.

Jorge

Attachments:

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## #9 2022-06-08 17:55:55

jlucas
Member
Registered: 2021-12-15
Posts: 12

### Re: Buckling of a cylinder under a twist moment.

Hi,

By changing DEFORMATION to 'PETIT_REAC', got a slightly lower value for the buckling moment equal to 17.2 kN.m, instead of 19.2 kN.m as computed with the small deformation hypothesis. This makes all sense to me. However, I would expect to get a similar result by using a large displacement formulation like for example 'GROT_GDEP', which is not the case.

I checked the examples listed document U2.08.04 (Notice de calcul au flambage) and none of those listed in "Modes d’Euler et calcul non linéaire" used a deformation other than 'PETIT'. So my suspicion is that the "Non-Linear Euler buckling" computation does not work with other than small deformation hypothesis.

Could someone with more insight confirm or contradict this affirmation?